essays in empirical macroeconomics juan herreno˜
TRANSCRIPT
Essays in Empirical Macroeconomics
Juan Herreno
Submitted in partial fulfillment of therequirements for the degree of
Doctor of Philosophyunder the Executive Committee
of the Graduate School of Arts and Sciences
COLUMBIA UNIVERSITY
2020
© 2020
Juan Herreno
All Rights Reserved
Abstract
Essays in Empirical Macroeconomics
Juan Herreno
This dissertation consists on three essays, inquiring about the usefulness of disaggre-
gated data and cross-sectional causal effects to improve our understanding of traditional
questions in macroeconomics, both for economic fluctuations and long-run outcomes. In
Chapter 1, I explore whether the large body of cross-sectional evidence that established
the adverse effects of cuts in the supply of bank lending on firm outcomes and the allo-
cation of credit is relevant at the aggregate level. I estimate this aggregate effect using a
new general equilibrium model that incorporates multibank firms, relationship banking,
endogenous credit dependence, and bank market power. I use a set of cross-sectional pat-
terns to estimate the key structural parameters of the model. The effect of an aggregate
lending cut on aggregate output is large: a 1 percent decline in aggregate bank lending
supply reduces aggregate output by 0.2 percent. The structure of labor and credit mar-
kets is important in reaching this answer. Under an alternative parametrization of the
model that ignores input market frictions, the response of aggregate output is three times
smaller. Under my preferred parametrization, the cross-sectional effects survive aggre-
gation in general equilibrium. Instead, with frictionless input markets the cross-sectional
patterns over-estimate the aggregate response by a factor of five.
In Chapter 2, written with Sergio Ocampo, we study how the efficacy of develop-
ment policies—such as job-guarantee programs, unemployment insurance, and micro-
finance—depends on the prevalence of low-earning self-employed individuals. To this
end, we develop a new general equilibrium occupational choice model that is consis-
tent with the behavior and composition of self-employment. Our model differs from pre-
vious work by allowing unemployment risk to shape the selection of agents into self-
employment. Models that rely only on financial frictions are at odds with crucial fea-
tures of self-employment in developing economies—in particular, the concentration of
self-employed agents among the lowest earners in the economy, and their willingness to
accept salaried jobs when offered to them. These features support the prevalence of sub-
sistence entrepreneurs in developing economies, who play a critical role in shaping policy
responses. Their willingness to accept jobs at market wages leads to a muted response of
wages to labor demand shocks, such as the implementation of a job-guarantee program.
In addition, offering small unemployment benefits reduces subsistence entrepreneurship,
thereby increasing productivity and output. In contrast, micro-finance exacerbates subsis-
tence entrepreneurship, thereby reducing productivity.
Finally, in chapter 3, with Andres Drenik and Pablo Ottonello, we study the impor-
tance of information frictions in asset markets at the aggregate level. We develop a method-
ology to identify the extent of information frictions based on a broad class of models of
trade in asset markets, which predict that these frictions affect the relationship between
listed prices and selling probabilities. We apply our methodology to physical capital mar-
kets data, using a unique dataset on a panel of nonresidential structures listed for trade.
We show that the patterns of prices and duration are consistent with the presence of asym-
metric information. On the one hand, capital units that are more expensive because of
their observable characteristics tend to have lower duration, as predicted by models of
trading under a full information model. On the other hand, capital units that are expen-
sive beyond their observable characteristics tend to have a longer duration, as predicted
by models of trading under asymmetric information. Combining model and data, we
estimate that asymmetric information can explain 21% of the +30% dispersion in price
differences of units with similar observed characteristics. We quantify the effects of infor-
mation frictions on allocations, prices, and liquidity, and show that the estimated degree
of information frictions can to lead to 15% lower output due to low trading probabilities
of high-quality capital.
Table of Contents
List of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vi
List of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viii
Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xi
Dedication . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiii
Chapter 1: The Aggregate Effects of Bank Lending Cuts . . . . . . . . . . . . . . . . . 1
1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 A Model of Credit Dependence of Multi-Bank Firms . . . . . . . . . . . . . . 7
1.2.1 Firms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
1.2.2 Financing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
1.2.3 Workers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
1.2.4 Other Aspects of the Model . . . . . . . . . . . . . . . . . . . . . . . . 15
1.3 Characterization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
1.3.1 The Aggregate Effects of Loan Term Changes in One Bank . . . . . . 16
1.3.2 The Aggregate Effects of Overall Loan Term Disruptions . . . . . . . 18
1.3.3 The Cross-Sectional Elasticity of Bank-Funding Shocks . . . . . . . . 18
1.3.4 The identification challenge . . . . . . . . . . . . . . . . . . . . . . . . 19
i
1.4 Identification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
1.4.1 The Elasticity of Firm Production . . . . . . . . . . . . . . . . . . . . . 20
1.4.2 The Elasticity of Firm Borrowing . . . . . . . . . . . . . . . . . . . . . 21
1.4.3 Identification Argument . . . . . . . . . . . . . . . . . . . . . . . . . . 22
1.4.4 Firm Fixed Effects Estimator . . . . . . . . . . . . . . . . . . . . . . . . 24
1.5 Full Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
1.5.1 Banks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
1.5.2 Solution Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
1.6 Estimation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
1.6.1 Calibration of Standard Parameters . . . . . . . . . . . . . . . . . . . . 31
1.6.2 Estimation of Key Parameters . . . . . . . . . . . . . . . . . . . . . . . 33
1.6.3 Sensitiviy of Cross-Sectional Elasticities to Structural Parameters . . 34
1.7 Estimated Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
1.8 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
1.8.1 The Aggregate Effects of Bank Supply Shocks . . . . . . . . . . . . . . 43
1.8.2 The aggregate effects of an aggregate bank shock . . . . . . . . . . . . 45
1.8.3 The aggregate effects of an idiosyncratic bank shock . . . . . . . . . . 47
1.8.4 Comparing General to Partial Equilibrium . . . . . . . . . . . . . . . 50
1.9 Counterfactuals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
1.9.1 Bank Disruptions in Small versus Large Banks . . . . . . . . . . . . . 55
1.10 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
1.11 Appendix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58
1.11.1 Full derivation of the model . . . . . . . . . . . . . . . . . . . . . . . . 58
ii
1.11.2 Proofs Section 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
1.11.3 Proofs Identification Section . . . . . . . . . . . . . . . . . . . . . . . . 67
Chapter 2: Self-Employment and Development Policies . . . . . . . . . . . . . . . . . 70
2.1 Self-employment as an outside option . . . . . . . . . . . . . . . . . . . . . . 78
2.2 Empirical evidence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82
2.2.1 Self-employment is concentrated among low earners . . . . . . . . . 85
2.2.2 Constrained agents transition more into self-employment . . . . . . . 87
2.3 Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90
2.3.1 Stochastic Processes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93
2.3.2 Agent’s Problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93
2.3.3 Self-employed production technology . . . . . . . . . . . . . . . . . . 95
2.3.4 Labor market . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96
2.3.5 Equilibrium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97
2.3.6 Discussion of modeling assumptions . . . . . . . . . . . . . . . . . . . 99
2.4 Quantitative analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101
2.5 Policy analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107
2.5.1 Job-guarantee programs . . . . . . . . . . . . . . . . . . . . . . . . . . 107
2.5.2 Unemployment insurance . . . . . . . . . . . . . . . . . . . . . . . . . 109
2.5.3 Micro-finance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113
2.6 Concluding remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114
2.7 Evidence from India . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116
2.8 Model without unemployment risk . . . . . . . . . . . . . . . . . . . . . . . . 119
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2.8.1 Agent’s Problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119
2.8.2 Equilibrium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119
2.9 Computational appendix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121
2.9.1 Solution to HJB equations . . . . . . . . . . . . . . . . . . . . . . . . . 121
2.9.2 Solution to KFE equations . . . . . . . . . . . . . . . . . . . . . . . . . 130
2.10 Additional graphs and tables . . . . . . . . . . . . . . . . . . . . . . . . . . . 133
2.10.1 Mobility across occupations . . . . . . . . . . . . . . . . . . . . . . . . 133
2.10.2 Model: additional graphs and tables . . . . . . . . . . . . . . . . . . . 139
Chapter 3: Information Frictions in K: Micro Measurement and Macro Implications . 141
3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141
3.2 Theoretical Framework . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 147
3.2.1 Environment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 148
3.2.2 Optimization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 150
3.2.3 Equilibrium under Full Information . . . . . . . . . . . . . . . . . . . 154
3.2.4 Equilibrium under Asymmetric Information . . . . . . . . . . . . . . 156
3.2.5 Identification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 160
3.3 Empirical Evidence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 164
3.3.1 The Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 165
3.3.2 Key Data Moments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 169
3.3.3 Alternative explanations . . . . . . . . . . . . . . . . . . . . . . . . . . 174
3.4 The Relevance of Information Frictions in the Capital Market . . . . . . . . . 179
3.4.1 Quantifying Frictions: Model and Data . . . . . . . . . . . . . . . . . 180
iv
3.5 Counterfactual Analyses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 183
3.6 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 186
3.7 Appendix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 189
3.7.1 Empirical Appendix . . . . . . . . . . . . . . . . . . . . . . . . . . . . 189
3.7.2 The online platform . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 189
3.7.3 Representativeness of the dataset . . . . . . . . . . . . . . . . . . . . . 192
3.7.4 Additional Figures and Tables . . . . . . . . . . . . . . . . . . . . . . . 195
3.8 Quantitative Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 200
3.8.1 Goodness of Fit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 200
v
List of Tables
1.1 Fixed Parameters Values . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
1.2 Microeconomic Targets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
1.3 Estimated Elasticities of Substitution . . . . . . . . . . . . . . . . . . . . . . . 38
1.4 Elasticity of Aggregate Output to Aggregate Bank Lending . . . . . . . . . . 45
2.1 Workforce Composition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83
2.2 Quarterly Transition Rates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84
2.3 Second Earner and Transitions from Unemployment . . . . . . . . . . . . . . 89
2.4 Remittances and Transitions from Unemployment . . . . . . . . . . . . . . . 90
2.5 Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103
2.6 Moments for Calibration: Targets and Outcomes . . . . . . . . . . . . . . . . 104
2.7 Change in self-empolyment due to implementation of NREGA . . . . . . . . 117
2.8 Transitions to Self-Employment . . . . . . . . . . . . . . . . . . . . . . . . . . 134
2.9 Transitions to Employment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135
2.10 Transitions to Employment from Unemployment . . . . . . . . . . . . . . . . 136
2.11 Second Earner and Job-Search Activities . . . . . . . . . . . . . . . . . . . . . 137
2.12 Remittances and Job Search Activities . . . . . . . . . . . . . . . . . . . . . . 138
2.13 Model Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139
vi
3.1 Descriptive Statistics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 166
3.2 Price Variation Accounted for by Listed Characteristics . . . . . . . . . . . . 171
3.3 Prices and Duration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 174
3.4 Externally Set Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 180
3.5 Internally Calibrated Parameters . . . . . . . . . . . . . . . . . . . . . . . . . 182
3.6 Regression coefficients . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 183
3.7 The Role of Information: Asymmetric vs Full Information . . . . . . . . . . 187
3.1 Frequency of Price Changes for Capital . . . . . . . . . . . . . . . . . . . . . 196
3.2 Price Variation Accounted for by Listed Characteristics in New Entrants . . 197
3.3 Regression of Prices on Duration - Sale . . . . . . . . . . . . . . . . . . . . . . 197
3.4 Regression of Prices on Duration - Rent . . . . . . . . . . . . . . . . . . . . . 198
3.5 Prices and Clicks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 199
vii
List of Figures
1.1 Share of bank financing as a Function of the cost of funds from the Bankingsector . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
1.2 Shape of the demand curves for different values of θ. . . . . . . . . . . . . . 13
1.3 Shape of the demand curves for different values of T . . . . . . . . . . . . . . 13
1.4 Identification argument for ϕ and θ. . . . . . . . . . . . . . . . . . . . . . . . 24
1.5 HHI Index for C&I Loans . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
1.6 Effect of θ in the cross-sectional elasticity of credit for two levels of α . . . . 35
1.7 Effect of θ in the cross-sectional elasticity of output for two levels of α. . . . 35
1.8 Effect of ϕ in the cross-sectional elasticity of credit for two levels of α . . . . 36
1.9 Effect of ϕ in the cross-sectional elasticity of output for two levels of α . . . . 37
1.10 Targeting of cross-sectional moments - α = 1000 . . . . . . . . . . . . . . . . 38
1.11 Targeting of cross-sectional moments - α = 1 . . . . . . . . . . . . . . . . . . 38
1.12 Sensitivity of the cross-sectional effects on credit of an idiosyncratic bankshock to α . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
1.13 Sensitivity of the cross-sectional effects on output of an idiosyncratic bankshock to α . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
1.14 Sensitivity of the indirect effects on credit of an idiosyncratic bank shock to α 43
1.15 Sensitivity of the aggregate effects of an aggregate bank shock to ϕ . . . . . 46
1.16 Sensitivity of the aggregate effects of an aggregate bank shock to θ . . . . . . 47
viii
1.17 Sensitivity of the aggregate effects of an idiosyncratic bank shock to ϕ . . . . 48
1.18 Sensitivity of the aggregate effects of an idiosyncratic bank shock to θ . . . . 49
1.19 Polar Cases when translating cross-sectional to aggregate elasticities . . . . 51
1.20 Ratio of the aggregate elasticity to back-of-the-envelope aggregations . . . . 53
1.21 Ratio of the aggregate output drop with respect to back-of-the-envelopeaggregations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
1.22 Effect of a shock to a bank as a function of its mean market share . . . . . . . 56
1.23 Effect of a shock to a bank as a function of market structure . . . . . . . . . . 57
2.1 Occupational Choice: Unemployment vs. Self-Employment . . . . . . . . . . 79
2.2 Occupational Choice: Unemployment vs. Self-Employment with Micro-Credit 80
2.3 Self-Employment Rate by Percentile of the earnings Distribution . . . . . . . 86
2.4 Self-Employment Rate by Decile of the Earnings Distribution . . . . . . . . . 105
2.5 Model Performance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106
2.6 Model Performance: Unemployment Insurance . . . . . . . . . . . . . . . . . 111
2.7 Productivity Changes under Unemployment Insurance . . . . . . . . . . . . 112
2.8 Productivity Changes under Micro-Finance . . . . . . . . . . . . . . . . . . . 115
2.9 Productivity Changes under Job Guarantee . . . . . . . . . . . . . . . . . . . 139
2.10 Model Performance - Micro-Finance . . . . . . . . . . . . . . . . . . . . . . . 140
3.1 Competitive Equilibrium under Full Information . . . . . . . . . . . . . . . 156
3.2 Competitive Equilibrium under Asymmetric Information . . . . . . . . . . 159
3.3 Illustration of Identification . . . . . . . . . . . . . . . . . . . . . . . . . . . . 164
3.4 Capital Prices Across Locations . . . . . . . . . . . . . . . . . . . . . . . . . . 168
ix
3.5 Evolution of Prices of Capital Units . . . . . . . . . . . . . . . . . . . . . . . 169
3.6 Distribution of Price Residuals . . . . . . . . . . . . . . . . . . . . . . . . . . 172
3.7 Relationship between Prices and Duration . . . . . . . . . . . . . . . . . . . 173
3.8 Net Present Value of Price-Duration Trade-off . . . . . . . . . . . . . . . . . 176
3.9 Required Holding Costs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 179
3.10 Joint Distribution of (log) Prices and Duration . . . . . . . . . . . . . . . . . . 182
3.11 Prices and Trading Probabilities: Asymmetric Information . . . . . . . . . . 187
3.12 Prices and Trading Probabilities: Full Information . . . . . . . . . . . . . . . 188
3.1 Main Website . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 189
3.2 Options Madrid . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 190
3.3 Available listings in a narrow location in Madrid . . . . . . . . . . . . . . . . 191
3.4 A listing on the website . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 192
3.5 Price Index: Dataset versus Aggregate Data . . . . . . . . . . . . . . . . . . . 193
3.6 Sales Rate: Dataset versus Aggregate Data . . . . . . . . . . . . . . . . . . . . 194
3.7 Distribution of Duration: Confirmed Sales . . . . . . . . . . . . . . . . . . . . 195
3.8 Evolution of Average Duration . . . . . . . . . . . . . . . . . . . . . . . . . . 195
3.9 Capital Prices and Regional Business Cycles . . . . . . . . . . . . . . . . . . 196
3.10 Relationship between Prices and Clicks . . . . . . . . . . . . . . . . . . . . . 199
3.11 Regression Coefficients: Data vs Model . . . . . . . . . . . . . . . . . . . . . . 200
3.12 Histogram of Prices: Data vs Model . . . . . . . . . . . . . . . . . . . . . . . . 201
3.13 Histogram of Predicted Prices: Data vs Model . . . . . . . . . . . . . . . . . . 201
3.14 Histogram of Residual Prices: Data vs Model . . . . . . . . . . . . . . . . . . 202
3.15 Histogram of Duration: Data vs Model . . . . . . . . . . . . . . . . . . . . . . 202
x
Acknowledgements
I would like to thank my advisors, Jennifer La’O, Emi Nakamura, and Jon Steinsson
for all their guidance, encouragement, and patience. They have been the best mentors
and role models one student could hope for. This dissertation, and my doctoral studies,
would have been an impossible challenge without them.
I owe a special debt and gratitude to my coauthors: Andres Drenik, Jonathon Hazell,
Marc Hofstetter, Sergio Ocampo, Pablo Ottonello, Mathieu Pedemonte, and Carlos Ron-
don. They have been outstanding colleagues, friends, and teachers.
I have had the luck to benefit from an amazing environment at Columbia. I am grate-
ful to Miguel Acosta, David Alfaro, Hassan Afrouzi, Claudia Allende, Cynthia Balloch,
Paul Bouscasse, Olivier Darmouni, Nicolas De Roux, Evan Friedman, Matthieu Gomez,
Emilien Gouin-Bonenfant, Harrison Hong, Lorenzo Lagos, Cameron LaPoint, Rui Mas-
carenhas, Xavier Moncasi, Suanna Oh, Stephanie Schmitt-Grohe, Yeji Sung, Martin Uribe,
and Michael Woodford, among many others.
Many people have played a crucial role in my life in these six years. I want to thank
my extended family, and my friends from Bogota, Washington and New York. They have
listened to my half-baked ideas, read my bad drafts, helped me improve my research,
and lifted me up with jokes and support. Thanks in particular to my roommates, Camilo
Hernandez, Julien Grand-Clement Han Huyn and Xavier Moncasi for their patience,
their companionship and their friendship; and to Sofia Correa, Laura Galindo, Isabela
xi
Munevar, Julio Rodriguez, Javiera Selman, and David Zarruk for their friendship and
support during these years in New York.
Finally, my deepest gratitude goes to my parents, Esperanza and Mario; to my brother
and dearest friend, Felipe; and to Mariana. Their love, support, and advice has been a
constant that has filled me with joy. I hope this piece of work brings them a fraction of the
happiness and pride I feel everyday for having them in my life.
xii
Dedication
Le dedico esta disertacion a mi madre y a mi abuela Ana, las dos personas mas
generosas, sabias y carinosas que he tenido el placer de conocer.
xiii
Chapter 1
The Aggregate Effects of Bank Lending
Cuts
1.1 Introduction
This paper addresses the long-standing question of the effect of disruptions in bank
lending on aggregate economic performance. Motivated by this question, a large and ro-
bust body of cross-sectional studies have produced evidence that cuts in the supply of
bank lending affect firm outcomes and the allocation of credit. The gold standard em-
pirical approach in the literature uses microdata to exploit variation in banks’ exposure
to funding shocks, and variation in the exposure of firms and regions to different banks.
Khwaja and Mian (2008), Chodorow-Reich (2014), and Huber (2018), for example, have
used this approach.
Despite a large cross-sectional literature, the debate on the macroeconomic effects of
bank lending cuts persists. The main reason is that cross-sectional studies are often de-
signed to identify relative rather than aggregate effects. It is therefore unclear what their
findings and mechanisms imply for aggregate output or employment. In addition, the
alternative of using aggregate data to answer the question relies on strong identification
1
assumptions, and methodologies using this approach are silent about the extensive find-
ings of the cross-sectional literature, which are the best evidence of causal effects at our
disposal.1
In this paper I study the effects on aggregate output of a cut in the supply of aggregate
bank lending. I develop an explicit model with a tractable setup for banks, firms, and
workers that allows for the main mechanisms behind the cross-sectional patterns of firm
responses after a bank shock. I use those estimated patterns as the primary input to infer
the aggregate response through the lens of the model. This is the first study to provide
an estimate of the macroeconomic impact of cuts in the supply of bank lending informed
by such evidence, characterize its determinants, and account for a wide range of facts. I
find that a cut in the supply of bank lending has a sizeable effect on aggregate output.
This finding is the consequence of frictions in credit and input markets. Ignoring frictions
in input markets would lead us to wrongly conclude that the effects on aggregate output
of a bank lending cut are significantly smaller than what is implied in the cross-sectional
literature.
Relative and aggregate effects would be guaranteed to be equal if the disruption of a
particular bank had zero indirect effects on unexposed banks and on firms that borrowed
from those healthy banks. These conditions may not hold in an environment where both
banks and firms compete in different markets. Banks compete for funding and for cus-
tomers, so a shock to one bank indirectly affects the balance sheet of its competitors.
Firms compete in labor and goods markets, so firms will be indirectly affected even if
their lenders are not directly exposed to a shock. These general equilibrium effects are
transmitted through changes in aggregate prices and quantities and can make a given
pattern of relative effects consistent with different aggregate responses.
1There is an extensive literature on macroeconomics studying the relevance of financial frictions andfinancial intermediaries. These models are usually calibrated or estimated using VARs or Bayesian methodsto fit first and second moments of aggregate time series, as in Gertler and Kiyotaki (2010), Gertler andKiyotaki (2015), Christiano, Eichenbaum, and Trabandt (2015), or Del Negro, Giannoni, and Schorfheide(2015).
2
To measure the aggregate effects, I use a model that speaks to these general equi-
librium effects and to the cross-sectional estimates at the same time. The model has the
three main mechanisms studied in the empirical literature. Two of these mechanisms are
absent from textbook macroeconomic models and are a contribution of this paper. First,
firms borrow from multiple banks, and the strength of bank-firm relationships is a func-
tion of how close these entities are for geographical, historical, or sectoral reasons. Second,
the model allows for flexible patterns of substitution of the sources of finance for the firm.
Firms may substitute funding from one bank in favor of funding from other banks or sub-
stitute away from bank credit altogether. I provide a micro-foundation for these decisions
of the firm based on a discrete choice model with a tractable solution. Two parameters
capture the two margins of substitution. Bank market power emerges naturally in this
framework, as there are only a handful of banks in the economy.
The third main mechanism of the model allows for a labor market in which firms face
an upward-sloping firm-specific (relative) supply curve. This means that in order to hire
additional labor, a firm must pay a higher wage. A market in which an individual firm
can hire any number of workers at the prevailing market wage rate is nested as a special
limiting case. This feature used in other studies is meant to capture the difficulty in mov-
ing labor across firms, which disrupts the ability of the economy to reallocate resources
across firms after an arbitrary shock.
I characterize analytically the elasticity of aggregate output and firm-level output to an
exogenous increase in the cost of loans in the economy. I show that the extent of frictions
that inhibit firms from finding alternative sources of finance, as well as the structure of
labor and goods markets, are informative about the response of aggregate output to a
disruption in the supply of bank credit. The ability of firms to borrow from different
banks and to procure funding from sources other than banks counteracts the negative
shock. When labor markets work without frictions the cross-sectional output effects of a
bank disruption become larger.
3
I extend the simple model to a dynamic model and for banks to set lending rates opti-
mally and raise funds from depositors. I solve the model using state-of-the-art numerical
methods, as in Ahn et al. (2018), that allow for aggregate shocks in macroeconomic mod-
els with heterogeneous agents where the state-space is infinitely dimensional owing to
the relevance of the distribution of firms to forecast prices. In particular, my model has
heterogeneous firms and banks, and since banks are large, even the disruption of one
bank has aggregate consequences.
I then calibrate the model, recovering the parameters that determine the extent of the
two key financial frictions in the model. These parameters are the elasticity with which
a firm substitutes funding from a particular bank with funding from other banks, and
the elasticity with which firms avoid bank credit altogether. I recover these parameters
by combining two elasticities estimated in the microdata: the cross-sectional effect of an
idiosyncratic bank shock on firm credit, and the cross-sectional effect of an idiosyncratic
bank shock on firm employment.
The idea behind the identification of the banking friction parameters is the following.
After a bank disruption, firms that can replace funding from the affected bank with fund-
ing from other banks will experience little change credit exposure or output triggered by
the shock. However, if firms cannot subsitute across banks but can avoid bank credit alto-
gether, they will take on much less debt, but their output losses will be small. Therefore,
with information about the decrease in firm credit and employment after a bank shock,
it is possible to back out the two key parameters in the model. I use these moments as
estimated by Huber (2018), and the methodology can be adapted to target moments in
other countries and time periods.
To discipline the extent of frictions in the labor market I use two sources of evidence.
First, I use direct evidence from Webber (2015), which documents an inelastic firm-specific
labor supply curve. This means that to hire additional labor , a firm must pay a signif-
icantly higher wage. Second, I use the indirect effects of bank lending cuts. In models with
4
flexible input markets, firms without exposure to a bank shock operating in regions where
firms are highly exposed on average, outperform firms without exposure located in low-
exposure regions. This is contrary to the evidence on the indirect effects reported by Hu-
ber (2018), who finds the opposite. This statistic rejects models without rigidities in the
labor market and favors models with costs of reallocation of labor within the region.
I estimate an elasticity of output to lending caused by a shock to the lending supply
of 0.2. This number means that a 1 percent drop in aggregate lending caused by a bank
shock causes a drop of aggregate output of 0.2 percent. This elasticity depends on a num-
ber of different factors. Under an alternative parametrization of the model that ignores
labor market frictions, the elasticity is three times smaller, illustrating the relevance of
the structure of the economy to the result. When labor markets are flexible, the degree of
banking frictions identified by the cross-sectional moments is smaller. The reason is that,
for a given extent of financial frictions, more flexible labor markets imply larger cross-
sectional moments after the same shock. Therefore frictions in the banking sector must be
smaller when labor markets are perfect to target the same microeconomic patterns.
I compare the magnitude of the elasticity I obtain in general equilibrium with the
partial equilibrium aggregations that would be obtained from a back-of-the-envelope ag-
gregation using estimated causal effects in the cross-section. These aggregations are com-
puted by adding up the differences in firm outcomes between each firm in the economy
and comparing them with a control firm with zero direct exposure to the shock. Under my
preferred parametrization of the model, the partial equilibrium aggregation is similar in
size to the general equilibrium aggregation I studied. This means that general equilibrium
forces in the parametrized model do not cause the effects in the cross-section to vanish. I
illustrate that this is not required to be the case for this application. Under the alternative
parametrization of the model with frictionless labor markets, the general equilibrium ag-
gregation is 5 times smaller than the partial equilibrium one. However, the evidence and
the model prefer combinations of the parameter space where general equilibrium effects
5
do not cause the patterns observed in the microdata to vanish.
Literature Review
This paper addresses the long-standing question of the relevance of bank health dis-
ruptions on aggregate economic performance. Bernanke (1983) stated that cuts in the sup-
ply of bank lending make credit more expensive, potentially affecting the aggregate econ-
omy. I analyze the relevance of cuts in the supply of bank lending to firms in determining
drops in aggregate production.2
To measure the effects of an aggregate lending cut on aggregate output, I rely on a
large and robust empirical literature that inquires about the effects of bank health in a
cross- section of firms and banks. This cross-sectional literature exploits variation in bank
exposure to funding shocks and variation in the exposure of firms and regions to differ-
ent banks. This body of evidence concludes that bank disruptions affect the allocation of
firm credit, as in Khwaja and Mian (2008);3 firm outcomes like employment and sales, pre-
sumably because of the existence of sticky firm-bank relationships, as in Chodorow-Reich
(2014);4 and regional outcomes, as in the seminal work by Rosengren and Peek (2000).5
I incorporate this literature by embedding a discrete choice problem in a macroeco-
nomic model with heterogeneous firms. This approach is similar to the Ricardian models
2Bernanke (1983) hypothesized that large firms would be immune to cuts in bank lending. However,Benmelech, Frydman, and Papanikolaou (2019)document that large firms with maturing bonds tried toaccess bank loans after debt markets froze up during the Great Depression. Firms located in regions withmore affected banks suffered larger employment losses during the Depression.
3Other examples of this literature are Gan (2007); Schnabl (2012); Iyer, Peydro, da Rocha Lopes, andSchoar (2013); Benetton and Fantino (2018); Jiminez, Mian, Peydro, and Saurina Salas (2014); Becker andIvashina (2014) ; and Cingano, Manaresi, and Sette (2016).
4The strength of the relationship between firms and banks depends on the closeness of the entities, eithergeographically, like in Degryse and Ongena (2005), Agarwal and Hauswald (2010), Brevoort, Wolken, andHolmes (2010), and Nguyen (2019); historically, as in Huber (2018); or sectorally or culturally, as in Fisman,Paravisini, and Vig (2017). The consequences of bank-firm relationships in the cross-section has been widelystudied. Examples are Darmouni (2017) and Bolton, Freixas, Gambacorta, and Mistrullu (2016). Under thenull hypothesis that funds from a given bank are perfectly substitutable for the firm, an id- iosyncratic bankshock should create zero cross-sectional effects for firms that differ in their pre-existing bank relationships.This null hypothesis is rejected in the data.
5Other examples are Ashcraft (2005); Greenwood, Mas, and Nguyen (2014); and Huber (2018).
6
in the Eaton and Kortum (2002) spirit, used to characterize trade flows between coun-
tries. In particular, I use the extensions made by Dingel, Meng, and Hsiang (2019) and by
Lashkaripour and Lugovskyy (2018). Instead, however, I use it to characterize the flow of
credit from banks to firms and firms’ decisions about how much to borrow. In this set-
ting, banks set lending rates in an imperfect competitive market. Crawford et al. (2018),
Drechsler et al. (2017), Wang et al. (2018) and Xiao (2019) have incorporated bank market
power in macro-finance questions.
This paper contributes to the broad literature that uses cross-sectional estimates to in-
vestigate the macroeconomic effects of aggregate shocks. The approach I follow in this
study uses causal effects measured in cross-sectional settings as inputs to measure an
aggregate elasticity, in this case the elasticity of aggregate output to aggregate lending.
Nakamura and Steinsson (2017) survey the literature and discuss its challenges. The ap-
proach I use here is different than the one followed by an exciting growing literature on
sufficient statistics that derives expressions in generic models to compute aggregate elas-
ticities. Particularly relevant is the work of Sraer and Thesmar (2018). Here I ask what
we can learn from a body of evidence that is already measured in the literature, and dis-
cuss the relevance of the mechanisms in the aggregate, instead of proposing a new set of
elasticities to be measured. The cost of my approach is that it requires more structure.
1.2 A Model of Credit Dependence of Multi-Bank Firms
In this section I present a model that is flexible enough to incorporate the patterns ob-
served in the data and works as a laboratory for analyzing the effect of bank health on
aggregate output. The model features a continuum of firms, a discrete number of banks,
and a representative household. Firms borrow from multiple banks simultaneously. Bank-
ing relationships are imperfectly substitutable in the sense that the relative demand for
funding from a particular bank is downward sloping, not horizontal. Self-finance is also
7
an imperfect substitute for bank credit.
This model is static and makes a number of simplifications that will be relaxed when
the full model is presented. In particular, in this section I will take lending rates as given.
The best interpretation for now is that different banks play the role of different technolo-
gies. Later in the paper, we will incorporate the problem of the banks.
1.2.1 Firms
There is a continuum of monopolistic competitive firms producing differentiated vari-
eties. Each firm is indexed by j in the unit interval. The demand schedule for each variety
is given by:
Yjt = Yt P−ηjt , (1.1)
where Pjt is the relative price of variety j, Yjt is the quantity demanded of each variety
and Yt is aggregate demand. The aggregate price is set to be the numeraire.
Each firm produces by mixing a continuum of intermediates indexed by ω. Think of
these intermediates as projects or tasks the firm has to complete in order to produce its
differentiated product. The firm aggregates the intermediates via a CES function with
elasticity of substitution σ6
Yjt =
(∫ 1
0
(y jt(ω)
) σ−1σ dω
) σσ−1
. (1.2)
Each intermediate good ω is produced with labor in a constant-returns-to-scale pro-
6This elasticity of substitution will end up being irrelevant for the purposes of this paper.
8
duction function, and a firm-wide productivity shifter z
y jt(ω) = z jt l jt(ω). (1.3)
1.2.2 Financing
For a given task, firms decide whether to self-finance or look for funding from a bank.
Firms that choose bank financing must select an individual bank to finance each task.
Different banks offer different terms, based on their comparative advantage in particular
segments, and on the functioning of credit markets that cause similar projects to be priced
differently across banks.
Because firms need to finance a continuum of tasks, the cost of funds for the firm,
which determines its marginal costs, does not depend on the realization of the financing
cost of any particular task, but on structural parameters that capture how substitutable
bank credit is for self-finance, and how substitutable the credit from a particular bank is.
In the two next subsections I introduce these discrete choice problems.
Shopping for a lower rate
The cost of financing task ω is given by TCj(ω), which consists of the wage bill and
the financing costs of financing the wage bill,
TCj(ω) =w j
z jR j(ω)y j(ω). (1.4)
R j(ω) is the interest rate firm j gets to finance ω. As part of its cost minimization
problem, firm j looks for the cheapeast financing option.
In particular
9
R j(ω) = minb, f
Rb f
ε jb f (ω)
. (1.5)
Here f ∈ (B,S) indexes a given financing sector, either banks or self-finance. And b
indexes an option within a given financing option. There are NB banks in the economy
and one self-financing option. The effective cost the firm perceives if it were to choose a
financing option is equal to the cost of funds of that option R, over a shifter, that captures
all the idiosyncratic reasons why one option may be better for some intermediates than
others. For example, some projects of the firm are very difficult to monitor, so the firm
may prefer to self-finance them. Other projects benefit from the know-how of a specific
expert bank, and so on.
I assume the vector ε = ε j,1,B, ..., ε j,NB,B, ε j,NB,B, ...ε j,NS,S is drawn from a nested
Frechet Distribution
Fj(ε) = exp
−
∑s∈(B,S)
ϕs *,
Ns∑b=1
Tjbε−θsb
+-
ϕθ
.
This distribution has been used by Dingel, Meng, and Hsiang (2019), and by Lashkaripour
and Lugovskyy (2018), and it extends the Frechet distribution common in the Ricardian
model of international trade of Eaton and Kortum (2002). An analogy comes to mind
from the literature in international trade. When deciding where to import from, a recepi-
ent country shops around many locations and chooses the one with the lowest effective
price. These locations are cities within countries. The Frechet shifters capture the fact that
some countries have a comparative advantage in the production of some goods, and that
within each country, some cities have comparative advantage. In this application, the
shifters capture the firm’s preference to finance a given task with a given bank. It is akin
to a productivity shock that depends on the financing source and the intermediate. The
nested Frechet distribution captures the variation in the advantage of financing a given
10
task both across banks (some banks are better than others) and across financing options
(some intermediates are perfect for bank financing).
The Tjb parameters capture the strength of the long-term banking relationship between
firm j and bank b, or the absolute advantage of bank b in providing funding for firm j.
Under the assumptions stated before, we can characterize the share of expenditures
financed with each bank ν jb and the cost of bank credit for the firm R jB:
R jB = *,
∑b∈B
TjbR−θb+-
−1/θ
. (1.6)
The share of borrowing needs that firm j gets from bank b is given by:
ν jbt =TjbR−θbt∑k Tj k R−θkt
. (1.7)
The borrowing shares depend on θ, which is the elasticity of substitution of funding
from a specific bank, and on Tib, which is the relative strength of the banking relationship
between firm i and bank b. It is similar to the characterization made by Eaton and Kortum
(2002) for international trade flows. The share of expenditures financed with the banking
sector s j , is given by
s jt =ϕR−ϕjtB
ϕR−ϕjtB + (1 − ϕ)R−ϕjtS
, (1.8)
and the effective cost of funds for the firm is given by the cost of funds index R jt
R jt =(ϕR−ϕjtB + (1 − ϕ)R−ϕjtF
)−1/ϕ. (1.9)
11
s j
R jB
ϕlow
ϕ∞
ϕ0
ϕhigh
Figure 1.1: Share of bank financing as a Function of the cost of funds from the Bankingsector
This discrete choice block is a microfoundation of the desired mix of bank borrowing
that the firm chooses. When bank credit becomes more expensive (R jtB ↑), the firm moves
away from bank lending (s jt ↓). The elasticity at which the substitution occurs is given by
ϕ.
Figure (1.1) plots the share of financing from the banking sector as a function of the
cost of funds for different values of ϕ. The figure shows that as ϕ increases, the relative
demand schedule for bank funds becomes more elastic. In the limit, when ϕ → ∞ the
demand curve becomes horizontal, and firms are perfectly elastic in switching between
bank funding and self-finance. On the other side, when ϕ becomes smaller, the share of
bank financing is less sensitive to the lending rate.
When θ is higher, the demand curves for funding for a particular bank become flat-
ter, which I show in Figure (1.2). In the limit, when θ → ∞ the demand curve becomes
horizontal, and firms are perfectly elastic in switching between banks. On the other side,
when θ tends to zero, the share of bank financing from bank b is less sensitive to bank b’s
lending rate.
The term Tib in the equation has a different purpose than θ. Figure (1.3) illustrates that
the relative demand curve for funds from a particular bank with a higher T is shifted
12
ν jb
R jb
θlow
θ∞
θ0
θhigh
Figure 1.2: Shape of the demand curves for different values of θ.
Note: The x axis shows the market share of a particular bank, and the y axis shows the lending rateof the bank
to the right. That means that for two banks offering the same lending terms, a firm will
borrow proportionally more from banks with higher T .
ν jb
R jb
Tlow
Thigh
Figure 1.3: Shape of the demand curves for different values of T
Note: The x-axis shows the market share of a particular bank, and the y-axis shows the differenceof the interest rate between that bank and the other bank in the economy for an example wherethere are only two symmetric banks.
13
1.2.3 Workers
There is a representative household. It consumes and supplies labor. The household
maximizes the utility function
U(Ct, Lt) = Ct −Lφ+1
t
1 + φ, (1.10)
Where Lt is an aggregator of the labor supply to different firms in the economy:
Lt =
(∫L
1+αα
jt dj) α
1+α
. (1.11)
Workers maximize utility subject to a budget constraint∫w jt L jt + π jt dj = Ct , where
π jt are the profits of firm j. Therefore households supply labor according to the following
relationship:
Lt = w1/φt , (1.12)
L jt = Lt
(w jt
wt
)α, (1.13)
where wt is defined as Lφt .
This specification tells us that the disutility of working more hours for the same firm
is convex. Therefore, the workers need higher pay in order to work more hours for the
same firm.
When α → ∞, the labor market operates under a single wage rate w jt = wt ∀ j. Other-
14
wise, firms that hire more workers than average, pay wages that are higher than average.
1.2.4 Other Aspects of the Model
In this model, it is assumed that lending rates are exogenous. Later in the full model,
I will specify the bank problem that gives rise to the lending rates in equilibrium as a
function of the market structure and the ease of securing funding. I also assumed that
the profits belong to the workers. The problem of the firm owners is included in the full
model as well.
1.3 Characterization
The focus of this section is to characterize the elasticity of aggregate output to an ex-
ogenous lending rate hike of a particular bank, and to the whole banking sector.
There are two main results. First, the aggregate and cross-sectional effects of the lend-
ing rate hike of an individual bank are different, and it is a priori unclear which of them is
larger. The difference in magnitude is dominated by the difference in the Frisch elasticity
of the labor supply and the easiness to reallocate demand and inputs across firms. When
it is easy to reallocate labor and demand across firms, then up to a second order the cross-
sectional effects of output are larger. On the other side, the aggregate effects are large with
an elastic labor supply. Under a perfectly inelastic labor supply curve, an increase in lend-
ing rates that raises firms’ marginal costs will will lead to lower wages without changing
aggregate hours and production.
Second, greater frictions in the banking sector, in the form of low elasticities of sub-
stitution of funds between banks and between funding alternatives, increase the output
losses caused by lending rate hikes. However, it is difficult to back out from a single
cross-sectional elasticity the structural parameters that determine the response of aggre-
gate output.
15
1.3.1 The Aggregate Effects of Loan Term Changes in One Bank
All the results in this section exploit the following assumption.
Assumption 1 There is no sorting in bank relationships. That is, firm-level productivity z j and
the strength of bank lending relationships Tjb are independent. I rule out the possibility that banks
suffering lending rate hikes are linked to firms with lower productivity.
As I show in the appendix, under assumption 1, aggregate output is given by equation
1.14, where the expectation operator is taken across the continuum of firms:
Y =
(η
η − 1
)−1/φ
E
(z
(η−1)(α+1)α+η
j
) (1+φ)(α+η)φ(η−1)(α+1)
E
(R−(η−1)αα+η
j
) (1+φη)φ(η−1)
E
(R−η(α+1)α+η
j
) (1−φα)φ(α+1)
. (1.14)
The first results of this section hold under the following assumption:
Assumption 2 Assume the lending terms of all banks except one are kept constant at an arbitrary
level R, as is the self-financing rate. At these rates, the level of output coming from equation 1.14
is defined as Y . For an arbitrary bank b, the lending terms are disrupted to Reu, for a positive and
sufficiently small u.
Note that after making an assumption about the distribution of T , and setting an arbi-
trary level of lending terms, we can compute numerically the behavior of output accord-
ing to equation 1.14. Assumption (2) is made in order express analytically the aggregate
output effects of lending term disruptions, presented in Proposition (1).
Proposition 1 Under Assumption (2), up to the second order, the log change of output is given
by:
log Y − log Y ≈ −1
φsu
(νb − θ
u2
Υ1 − ϕ(1 − s)u2
Υ2)), (1.15)
16
where νb =∫ 1
0Tjbdj is the average market share of bank b in the symmetric equilibrium,
Υ1 =(νb(1 − νb) − σ2
b
), and Υ2 =
(σ2
b + ν2b
)are constants.
Proof: See Appendix
Proposition (1) shows that for a sufficiently small shock u to the lending terms of one
bank, the response of output depends on three terms. The first term measures the direct
effect of the shock, abstracting from any substitution in funding markets. The drop in
output will be proportional to the relevance of the affected bank sνb, weighted by the
Frisch elasticity of labor supply 1/φ. When the labor supply is inelastic, the increase in
the cost of funds in the aggregate will be compensated for by a fall in the aggregate wage,
limiting the fall in output. The second term captures a counteracting force from the ability
of the economy to subtsitute for the affected bank. Importantly, θ, the cross-bank elasticity
of substitution, helps determine this second term. In a similar way, the third term captures
the ability of the economy to avoid using bank credit altogether, which is determined by
ϕ.
Although only accurate for small enough shocks, Proposition (2), shows that the re-
sponse of output depends on observables, like the average bank-dependence of the real
sector, s, the average market share of the disrupted bank, µb, or the dispersion of the mar-
ket shares, σ2b. It also depends on parameters that have been well studied in macroeco-
nomics and other fields of economics, like the Frisch elasticity of labor supply (see Chetty
et al. (2011)), the elasticity of substitution across goods (see Broda and Weinstein (2006)),
or the firm-specific elasticity of labor supply (see Webber (2015)) . However, the output
response also depends on two less-studied parameters: the elasticity of substitution of
funding from a given bank θ, and the elasticity of substitution of bank-credit ϕ.. In later
sections of the paper I discuss the strategy I use to recover these parameters from the
cross-sectional evidence and use them to estimate the effects of an aggregate bank dis-
ruption.
17
1.3.2 The Aggregate Effects of Overall Loan Term Disruptions
Now I extend the results in Proposition (1) for a generalized disruption in the loan
terms of all the banks. Proposition (2) presents the main result of this section, using As-
sumption (3).
Assumption 3 Assume the lending terms of all banks are disrupted from R to Reu, for a positive
and sufficiently small u. Keep the self-finance rate equal to R.
Proposition 2 Under Assumption (3), up to a second order, the fall of output is given by:
log Y − log Y ≈1
φ
(−su + ϕs(1 − s)
u2
2
). (1.16)
Proof: See Appendix
Proposition (2) shows that the elasticity of substitution between banks is irrelevant
for the aggregate. If every bank offers the same loan terms, the elasticity to reallocating
borrowing between banks is irrelevant up to second order. This does not mean that more
generally, θ is an irrelevant parameter, since a more competitive banking sector where
firms can move will change the behavior of banks in setting lending rates, but when lend-
ing rates are exogenous, then the substitution between banks is irrelevant when all banks
are exposed to a shock.
However, the elasticity of substitution away from bank lending ϕ is still important
through its second-order effect on aggregate output. Up to a first order approximation,
the response of aggregate output is determined by observable and usual parameters.
1.3.3 The Cross-Sectional Elasticity of Bank-Funding Shocks
Under the conditions stated in Assumption (2), Proposition (3) characterizes the de-
terminants of the cross-sectional differences in output with respect to a notional control
18
firm that has zero exposure to the disrupted bank b (Tcb = 0).
Proposition 3 Under Assumption (2), up to a second order approximation, the average cross-
sectional effect on output of a lending rate hike of bank b from R to Reu, with respect to the pro-
duction of a firm with zero direct exposure to bank b Yct , is given by:
E(log Yjt − log Yct) ≈ηα
α + η
(−sνbu +
1
2θ su2
(νb(1 − νb) − σ2
b
)+ ϕs(1 − s)
u2
2
(σ2
b + ν2b
)),
(1.17)
where νb =∫ 1
0Tjbdj is the average market share of bank b in the steady state, σ2
b = var(Tjb) is
the variance of market shares of bank b across firms, s is the credit dependence in the steady state,
and log Y , is the steady state level of output.
Proof: See Appendix
From Proposition (3) we see that the effect is larger when the shocked bank is more
important (νb is large), when firms are credit dependent (s is high), and when the elastic-
ities of substitution between banks (θ) and away from bank-credit (ϕ) are low, and when
it is easy to reallocate demand from one firm to another (η and α) are high. Note that low
real rigidities, in the form of high values of η and α, increase the cross-sectional effects of
bank disruptions.
1.3.4 The identification challenge
Even if we observe the cross-sectional effects on output, we would be missing equa-
tions to back out ϕ, which is the relevant variable for understanding the aggregate effects
of an overall shock. In particular, many combinations of θ and ϕ can produce the same
cross-sectional patterns.
19
1.4 Identification
In this section I use the model to illustrate how the patterns in the data identify θ
and ϕ, the key parameters of the model. I use the insight in this section to estimate the
full model I introduce in the following section. I start by introducing two cross-sectional
estimates used in the literature: first, the elasticity of credit after a bank shock; second, the
elasticity of a firm’s outcome, usually employment or value added.
I will start by introducing two cross-sectional estimates used in the literature. First,
the elasticity of credit after a bank shock. Second, the elasticity of a firm outcome, usually
employment or value added.
1.4.1 The Elasticity of Firm Production
The elasticity of firm production to a disruption in the terms of loans of bank b in
the line of the experiment in the previous section can be estimated through the following
regression:
∆ log Y f = β0 + βoutputTjb + ε f , (1.18)
where ∆ is the difference operator between a pre-period, that I will assume to be equal
to the symmetric equilibrium of the model, and pos-period, when a shock of size u that
increases the interest rate of bank b from R to Reu occurs. The independent variable is the
pre-existing exposure of firm j to bank b, measured by Tjb.
Tjb, the pre-existing borrowing share of firm j with bank b is exogenous and given by
historical reasons as in Huber (2018), or assumed to be endogenous but instrumented as
in Chodorow-Reich (2014). The main empirical concern is that banks that are more prone
to receiving funding shocks are also more likely to pick bad firms, which would induce
a correlation between lending and firm outcomes even in absence of a causal link. The
20
empirical literature has addressed that problem by using an instrumental variables (IV)
approach to deal with selection. The idea is to find variation in the ability of some banks
to give out loans that is not correlated with the quality of the firms they lend to.
The elasticity of production with respect to pre-existing exposure is characterized in
Proposition (4)
Proposition 4 Under assumptions (1) and (2), the regression coefficient of a regression of firm-
level output growth on the pre-existing exposure, accurate up to a second-order, is given by the
following expression
βoutput = −ηα
α + ηsu
(1 − θ
u2M1 − ϕ(1 − s)
u2.M2
). (1.19)
For constantsM1 =
(1 −
cov(T2jb,Tjb)
var(Tjb)
)> 0 andM2 =
(cov(T2
jb,Tjb)
var(Tjb)
)> 0
Proof: See Appendix
Equation (1.19) makes clear that up to a second order, as the elasticity of substitution
across banks (θ) and the elasticity of substitution away from bank credit (ϕ) increase, the
firm-level effects on output of a bank disruption become smaller. On top of the frictions
in the banking sector, the structure of the goods market (η), and the structure of labor
markets α determine the cross-sectional effects of the bank disruption. When α tends to
infinity, the cross-sectional effects tend to η. When both α and η tend to infinity, the cross-
sectional effects diverge, since in this situation all production would take place in the
firms with the lowest marginal costs. The distinction that the elasticities of substitution ϕ
and θ have second order effects on the elasticity of output is important for this paper.
1.4.2 The Elasticity of Firm Borrowing
Instead of analyzing the cross-sectional effects on output, the next regression studies
the effects of the bank disruptions of firm-credit. There is some variation in the specifica-
tion of the regression in the literature, but we will use the following specification:
21
∆ log Loans j = β0 + βcreditTjb + ε j, (1.20)
where ∆ is the difference operator between a pre-period, which I assume to be equal
to the symmetric equilibrium of the model, and pos-period, when a shock of size u that
increases the interest rate of bank b from R to Reu occurs. The independent variable is
the pre-existing exposure of firm j to bank b, measured by Tjb. Gan (2007), Khwaja and
Mian (2008), Schnabl (2012), and Iyer, Peydro, da Rocha Lopes, and Schoar (2013), among
others are examples of this approach.
Proposition 5 Under assumptions (1) and (2), the regression coefficient of a regression of firm-
level output growth on the pre-existing exposure, accurate up to a second order, is given by the
following expression
βcredit = βoutputα + 1
α− ϕ(1 − s)u
(1 + ϕ
u2
sM1 − θu2M2
). (1.21)
For constantsM1 =
(1 −
cov(T2jb,Tjb)
var(Tjb)
)andM2 =
(cov(T2
jb,Tjb)
var(Tjb)
)Proof: See Appendix
Proposition 5 shows that on top of the effect on output times a multiplier (first term),
there is a first order effect of the elasticity of substitution of bank credit ϕ on firm credit.
When firms are more elastic in substituting away from bank credit, credit falls by more.
1.4.3 Identification Argument
The elasticity of credit becomes larger (more negative) when ϕ is larger and when θ is
smaller. The elasticity of output becomes larger when both ϕ and θ are smaller. Therefore
it is possible to back out the values of these two coefficients once we take a stance on the
other coefficients that determine the cross-sectional elasticities.
22
The identification argument is represented in Figure (3.3). The figure presents two
locus of points in the space ϕ - θ, which produce a given estimate for the elasticity of
credit and production, after taking a stance on the other parameters of the economy.
Start by placing yourself on point b1, in the locus of βloan. Now arbitrarily increase the
value of ϕ. Since a larger ϕ causes the elasticity of output to be larger in absolute value,
in order to keep the elasticity constant we must move θ in a direction that compensates
for the change in ϕ. That is, we need to make θ larger, making firms more elastic with
respect to a given bank such that they do not move away from bank credit by much. This
argument implies that the locus of points (ϕ and θ) that keeps the regression coefficient
βloan constant is upward sloping.
Now place yourself on top of point a1 on the locus of βprod . Once again move to a
larger value of ϕ. When firms are more elastic to substitute bank credit, the elasticity of
production becomes smaller in absolute value. In order to keep its value constant, we
need firms to be less able to switch from the affected lender, making θ smaller. Therefore,
the locus of points is downward sloping.
This means that it is possible to find a point such as d1, where the two loci intersect,
satisfying both cross-sectional elasticities.
23
O ϕO
θ
βoutput
βcredit
a1
d1
b1
Figure 1.4: Identification argument for ϕ and θ.
Note:The figure plots the locus of points (ϕ and θ) that achieve a given value for βoutput and βcreditafter taking a stance on the other parameters that influence the values of the statistics. The intersec-tion of the two loci gives the value of θ and ϕ.
1.4.4 Firm Fixed Effects Estimator
Although I will not use a firm fixed-effect regression to calibrate the model7, in this sec-
tion I will discuss what economic mechanisms are identified by fixed-effect regressions,
and which are excluded under the lense of the model.
The result of this section states that firm fixed-effect regressions provide information
about θ, the elasticity of substitution of funds across banks, but it does not provide any
information about the elasticity of substitution of bank credit (ϕ), the substituability of
goods in the goods market (η), or the ability to reallocate labor across firms (α). The result
is intuitive, although it carries significant economic content. Since firm fixed-effects re-
gressions compare reallocations of loans within the firm across banks, they abstract from
any economic mechanism that occurs outside the firm (η and α, and from any mecha-7The reason is that I will use the reported elasticities by Huber (2018), which does not present firm fixed
effect regressions.
24
nism that does not involve bank credit (ϕ). Since in the previous section I showed that
θ is irrelevant up to the second order to determine drops in aggregate output after an
aggregate disruption of the banking sector, then the fixed-effect regression estimation is,
on its own, uninformative about such aggregate experiment. However, these regressions
are still important. By identifying θ, they can be combined with other cross-sectional re-
gressions to recover φ, or study θ, which on its own is interesting to determine aggregate
output fluctuations after an idiosyncratic bank shock.
As I show in the appendix, the log of loan sizes is:
log Loans jb = log Θ +(η − 1)(α + 1)
α + ηlog z j −
(η(α + 1)
α + η− ϕ
)log R j − ϕ log R jB + log ν jb.
(1.22)
By taking the difference of this object with respect to the mean of the same object across
banks, to compute the within firm loan variation across banks, and computing a before-
after difference, yields an expression for ∆ ˜Loans jb = ∆ log ν jb −∆ ¯log ν jb. This shows that
the relevant object in a firm fixed-effect regression of loans is the relative change in the
borrowing share of a given bank with respect to the change in this objects in the average
bank. As I show in the appendix, up to a second-order approximation, the firm fixed-effect
estimator yields the following expression:
βfixed effect = −θub + θ2u2
b
2*,1 −
cov(T2jb,Tjb)
var(Tjb)+-. (1.23)
Equation (1.23) makes clear that up to a second order, the fixed-effect estimator only
identifies θ, the elasticity of subsitution of funds across banks. Compared with Proposi-
tion (5), we see that the economic mechanisms between these two regressions are not the
same, even in the absence of sorting, and the difference depends on the elasticity at which
25
labor may be reallocated across firms (given by α), and the elasticity at which firms can
substitute away from bank credit (given by ϕ).
Just as important, the previous sections of the paper showed that after a shock that
affects all banks symmetrically, θ, the elasticity of substitution of funding across different
banks, is irrelevant in determining aggregate fluctuations up to a second order. Therefore,
a firm fixed-effect regression on its own does not provide any information about such
experiment. It does provide information with regards to the aggregate effects of a one-
bank disruption, although other parameters values, including ϕ, are needed in order to
reach a conclusion on that experiment as well.
1.5 Full Model
In this section I embed the simple model in a consumption/savings model in order
to make the total amount of deposits endogenous, and let banks set lending rates as a
response to balance sheet disruptions. The basics of the model are the same as in the
simple model, and here I only present the new blocks of the model.
Time is continuous. Space is contained in a [0, 1] interval. NB banks are uniformly
spaced in this interval. Firms are distributed uniformly over space. I take as primitive
of the model the closeness of firm j to bank b, and denote it by Tjb as in the simple model.
I take the stance that Ti is a vector of size B × 1, which specifies I take as primitive of
the model the closeness of firm i to bank b, and denote it by Tib as in the simple model.
Tj , a vector of size NB × 1 specifies the closeness of firm j with each bank, and given by
Tj,b = max1 − d × d j,b, 0 where d j,b is the distance between firm j and bank b, and d is
a constant that determines how the distance between a firm-bank pair affects the ease of
creating banking relationships. In the extreme where d = 0, firms are equally likely to
borrow from banks regardless of their distance. When d increases, firms only use banks
that are close to them.
26
Each firm is owned by an entrepreneur, with utility function u(cit) =c1−γit
1−γ . Each en-
trepreneur solves the following problem:
maxcE0
∫ ∞
0e−ρtu(cit)dt.
They maximize utility subject to the budget constraint:
ait = rdit ait + π∗i,t − cit
That is, entrepreneurs earn interest income at rate rdit on their wealth ait , earn profits
π∗i,t , and consume cit .
The effective rate of deposits rdit is a weighted average of the deposit rates at different
banks rdt =∑
k ωktrdkt . And weights given by ωbt =Rχbdt∑
k Rχkdt
. This functional form for
the deposit shares is chosen to be symmetric with the way that firms allocate their loan
demand across banks.
Profits are given by PjtYjt − w jt L jt R jt , prices are given by ηη−1 MCjt , and marginal costs
are given by MCjt =w jt
z jtR jt .
1.5.1 Banks
Banks compete by setting rates.8 Banks understand the structure of demand of each
firm, but do not internalize the aggregate consequences of their actions. That is, banks
take the aggregate wage and aggregate output as given, but they understand that firms
can substitute towards other banks, or substitute away from bank credit, and that firm
8In this model I assume that the loan market is cleared using lending rates. In the data, banks offer multi-dimensional contracts that differ in terms, covenants, size of credit lines, on top of variation on prices. Someof this variation has been has been covered by Payne (2018) and Chodorow-Reich and Falato (2017).
27
optimal scale is decreasing in its cost of funds. I allow for banks to price-discriminate
across firms.
Banks compete by setting rates. They understand the structure of demand of each
firm, but do not internalize the aggregate consequences of their actions. That is, banks
take the aggregate wage, and aggregate output as given, but they understand that firms
substitute to other banks, that firms substitute away from bank credit, and that firm-
level scale is decreasing in the cost of funds that they face. I allow for banks to price
discriminate across firms.
The profits that bank b gets from its relationship with firm j are:
Π jb = w j L j s jν jb(Rb − Rbd).
I am saving on the notation by eliminating the time subscript.
The first order condition
Rbj = Rbdθ jb
θ jb − 1
For θ jb = θ + ν jb(ϕ − θ) +(η 1+αα+η − ϕ
)ν jbs j,
characterizes the optimal pricing of the loans for each bank.
A bank with zero mass (ν jb → 0) faces an elasticity of substitution θ, the elasticity at
which firms switch banks. A monopolist bank (ν → 1)that lends to firms that are fully
dependent on bank credit (s → 1), faces an elasticity of substitution η 1+αα+η , the elasticity
at which higher costs translate into lower firm scale and correspondingly to lower loan
demand. The elasticity is positive since ϕ,η, and θ are positive, and νbj and s j are be-
tween zero and one. Banks charge variable markups. This is an important departure from
models with constant elasticities of substitution.
The balance sheet of the bank is given by:9
9In the model, I interpret Equitybt as another source of funding for the bank that is different than de-posits. It could well be thought of as a generic source of funding.
28
Loansbt = Depositsbt + Equitybt (1.24)
Loans granted by a bank are the integral of the loans given to each firm in the economy,
given by:
Loansbt =
∫ 1
0Loans jbt dj =
∫ 1
0s jtw jt L jtνbjt dj . (1.25)
Similarly, deposits are equal to the integral of the deposits that the bank gets from all
entrepreneurs in the economy
Depositsbt =
∫ 1
0Deposits jbt dj =
∫ 1
0ωbta jt dj . (1.26)
I assume that Equitybt is exogenous, and that banks are owned by agents outside the
economy. It is simple to change that assumption on the ownership of the banking sector.
The supply of deposits at a given bank depends positively on its deposit rate, while
the demand for loans depends negatively on it, through its negative relationship with
the lending rate and the positive relationship between lending and deposit rates. There-
fore, after a decrease in the right-hand side of the balance sheet, the bank will respond
by increasing the deposit and lending rates accordingly, balancing out its balance sheet
again.
The aggregate state vector is S = (Equity, X), where Equity is a K × 1 vector of the
equity of each of the K banks in the economy, and X is the distribution of entrepreneurs
over their individual state-space ς = (z, a,T), where T is a K × 1 vector that represents the
demand shifters for each entrepreneur’s firm with respect to each bank in the economy.
(i) Entrepreneur’s optimization. Taking w(s), Rk(s), Rdk (s) as given, entrepreneurs max-
29
imize utility and their firms maximize profits.
(ii) Household problem. Taking w(s) as given, households maximize utility
(iii) Banks problem. Taking Rdk (s), banks set Rk to maximize profits.
(iv) Market Clearing. w(s), Rdk (s), are such that labor market clears Ls =
∫l(z, a,T)X(dz, da, dT),
and banks’ balance sheet holds Depositsk(s) + Equityk s) = Loansk(s)
1.5.2 Solution Method
Since there are only a handful of banks, a shock to the financial conditions of a bank
will create aggregate disturbances. Therefore, when agents are formulating their policy
functions, they need to forecast the behavior of the input prices in the economy—namely,
the wage rate and the deposit rate at each bank. In order to do so, agents need to fore-
cast the behavior of the cross-sectional distribution of entrepreneurs and banks, which is
an infinite-dimensional object. I take advantage of methods developed byAhn, Kaplan,
Moll, Winberry, and Wolf (2018). In particular, the solution will be globally accurate with
respect to the individual state space, and will be a linear approximation with respect to
the aggregate shocks.
1.6 Estimation
The parametrization of the model takes two steps. The majority of the parameters are
calibrated. Most of these parameters are well studied and I fix them at standard values.
I use microdata to calibrate a subset of parameters that are not widely used in macroe-
conomic models but for which we have good evidence. Then, the key parameters of the
model, θ and ϕ, are estimated to target the patterns observed in cross-sectional studies of
the bank lending channel that were introduced in the previous sections.
30
I offer a preview of the results of this section. In my benchmark calibration, the values
of θ and ϕ I estimate are low, implying low ability to adjust to bank shocks. As an illustra-
tion, Under an alternative specification of the labor market, (high α), the values of θ and
ϕ that are consistent with the cross-sectional elasticities are large.
On top of evidence from labor economics that advocates for an economy with a low α,
I use an additional cross-sectional moment from the banking literature as a sanity check.
I extend the model to have two symmetric regions. In models with flexible labor markets
within the region (α is high), the indirect effects of bank shocks are positive. This means
that a firm without exposure to a shocked bank in a region where the average exposure
to the troubled bank is high will outperform an unexposed firm in a region where the
average exposure to the troubled bank is low. This prediction is at odds with the evidence,
as Huber (2018) has documented. Only when there are substantial rigidities in local labor
markets, the model is consistent with the sign of the indirect effect. Therefore, the model
rejects the limit of high α, consistent with the micro evidence from labor economics.
1.6.1 Calibration of Standard Parameters
Table (1.1) lists the parameters that I fix throughout the estimation. The intertemporal
elasticity of substitution is set to a standard value of 1/2. The Frisch elasticity of labor
supply is 0.75, as suggested by Chetty et al. (2011). This value is significantly lower than
what is used in most macro models. A highly elastic labor supply will increase the ag-
gregate effects of a bank shock, by making it more difficult for wages to go down after a
negative shock, increasing the elasticity of output to bank funding shocks.
I set η, the elasticity of substitution across goods equal to 4, within the range of esti-
mates in Broda and Weinstein (2006). I set the discount rate ρ equal to 0.03 per year as
in Itskhoki and Moll (2019). I set the persistence of the shock ρE at 0.95, consistent with
the persistence used by Gertler and Kiyotaki (2015). I set the parameters of the produc-
tivity Poisson process to target the volatility of 0.056 and a persistence of 0.9 as chosen by
31
0.229 − 0.494
0.177 − 0.229
0.153 − 0.177
0.139 − 0.153
0.120 − 0.139
0.107 − 0.120
0.096 − 0.107
0.084 − 0.096
0.066 − 0.084
0.033 − 0.066
Figure 1.5: HHI Index for C&I Loans
Note: Data: FFIEC. Author’s calculation
Winberry (2018).
I set the number of banks in the economy NB equal to 10 equal-sized banks. This
number replicates the across-MSA10 median Herfindahl-Hirschmann Index (HHI) of 0.11
coming from data from the Community Reinvestment Act (CRA) data that report busi-
ness loans for 2006 in the U.S.. Figure (1.5) presents the dispersion in the HHI index of
business and commercial loans for each MSA during 2006. Specifically, the HHI index
equals∑
i market share2i , the sum of the squares of the market shares of each bank in a
given MSA. I find the number of equal-sized banks that would replicate the median HHI.
This number is 1HHI . As an alternative, using call reports data at the national level, the
HHI of commercial and industrial loans (C&I) for 2006 is 0.05, implying 20 equal-sized
banks. However, this number underestimates the degree of concentration in C&L loans,
since firms prefer banks that are closer to them (see Nguyen (2019)), and banks are con-
centrated in specific geographical regions. The parameter d, controls how many banking
relationships each firm will have. I fix d so that firms have three banking relationships, as
reported by Huber (2018). I set χ, the parameter that governs how much deposits flow out
10Metropolitan Statistical Area
32
Parameter Description Value1/γ Intertemporal Elasticity of Substitution 1/2ρ Discount Rate 0.03η Elasticity of Substitution - Goods Market 41/φ Frisch Elasticity of Labor Supply 0.75z Two-State Markov Process 0.9 - 1.1λ Intensity of Poisson productivity shock 1/3B Number of Banks in the Economy 10ρE Persistence of Equity Shock 0.95d Distance Coefficient 3 bank relationshipsχ Elasticity of deposits to deposit rates 5
Table 1.1: Fixed Parameters Values
Note:The table presents the parameters of the model that I calibrate.
of a bank with lower deposit rates to 5, matching the semi-elasticity reported by Drechsler
et al. (2017).
1.6.2 Estimation of Key Parameters
Using the relative effects in the data as target moments to estimate the full model, I
structurally estimate the parameters values for θ, the elasticity of substitution of firms
across banks, and ϕ, the elasticity at which firms switch away from bank credit. The idea
behind the identification is the same as exposed in the identification section, with the dif-
ference that the full model gives dynamics to simulate a simulated panel dataset, and that
the model is globally accurate with respect to individual policy functions, which are more
accurate than the second-order Taylor expansions we introduced before. Specifically, I
simulate a panel of firms over time after a bank funding shock. With the simulated data, I
run a regression analysis that replicates the cross-sectional analysis, after collapsing a set
of periods before and after the shock into two bins, the pre-period and the post-period.
Table (1.7) specifies the microeconomic targets of the calibration. For a detailed discussion
of the regressions behind these moments, please refer to the identification section.
33
Moment Source ValueBank Credit Elasticity Huber (2018) -0.166Output Elasticity Huber (2018) -0.044
Table 1.2: Microeconomic Targets
Note: Each entry specifies the target for two microeconomic moments.
1.6.3 Sensitiviy of Cross-Sectional Elasticities to Structural Parameters
Before showing the estimation of the model, I illustrate the effect of θ and ϕ in deter-
mining the cross-sectional moments and the effect of different values of α in shifting the
effect of these two parameters.
Figures (1.6) and (1.7) show the effect of changing θ for two values of α, on the cross-
sectional moments of credit and production, respectively, while keeping the rest of the
parameters in the model fixed. As is intuitive from previous sections, a higher value of
θ, by increasing the flexibility of firms on switching across banks, decreases the cross-
sectional elasticities of both output and credit. In the limit, where θ → ∞, the elasticities
tend to zero. Figures 1.6 and 1.7 make an additional point. Because the elasticity is larger
in absolute value when labor markets do not have any frictions, the value of θ that is
consistent with a given elasticity is significantly larger when α → ∞ than when α is low.
Therefore, in order to match the same cross-sectional elasticities, θ will be lower in an
economy with labor market frictions.
34
5 10 15 20 25 30-0.35
-0.3
-0.25
-0.2
-0.15
-0.1
-0.05
0
Cre
dit E
lasticity
= 1
= 1000
Figure 1.6: Effect of θ in the cross-sectional elasticity of credit for two levels of α
Note: This figure shows the cross-sectional elasticity of credit in response to a bank shock for dif-ferent values of θ, the elasticity of substitution of funding across banks. I conduct this exercise fortwo different values of α: first for a market with α → ∞ , and second, for a low level of α whenthere are substantial difficulties in moving labor across firms.
5 10 15 20 25 30-0.3
-0.25
-0.2
-0.15
-0.1
-0.05
0
Outp
ut
Ela
sticity
= 1
= 1000
Figure 1.7: Effect of θ in the cross-sectional elasticity of output for two levels of α.
Note: This figure shows the cross-sectional elasticity of credit in response to a bank shock for dif-ferent values of θ, the elasticity of substitution of funding across banks. I conduct this exercise fortwo different values of α: first for a market with α → ∞ , and second, for a low level of α whenthere are substantial difficulties in moving labor across firms.
Figures (1.8) and (1.9) perform the same exercise for the elasticity at which firms move
35
away from bank credit (ϕ). These figures show that the identification argument holds
beyond the second order approximation we did in the simple model. When ϕ increasesthe
output effects of the shock are smaller, but the credit effects of the same shock are larger.
With respect to α, Figure (1.9) shows that for frictionless labor markets, the value of
ϕ that is consistent with a given elasticity is higher than for markets with frictions. The
intuition for this result is the same as for the results that involved θ. Under a frictionless
labor market, the cross-sectional effects are larger since it is easier to move labor across
firms. In the case of Figure (1.8), when α is larger, which increases the losses of a given
shock, firms move away from credit by more, explaining why the schedule of α = 1000 is
below from the schedule for α = 1.
5 10 15 20 25 30-0.3
-0.25
-0.2
-0.15
-0.1
-0.05
0
Cre
dit E
lasticity
= 1
= 1000
Figure 1.8: Effect of ϕ in the cross-sectional elasticity of credit for two levels of α
Note: This figure shows the cross-sectional elasticity of credit to a bank shock for different valuesof ϕ, the elasticity of substitution from bank credit. I conduct this exercise for two different valuesof α. First for a frictionless labor market, where α → ∞. And second, for a low level of α when thereare substantial frictions in the labor market.
36
5 10 15 20 25 30-0.15
-0.1
-0.05
0
Outp
ut E
lasticity
= 1
= 1000
Figure 1.9: Effect of ϕ in the cross-sectional elasticity of output for two levels of α
Note: This figure shows the cross-sectional elasticity of output to a bank shock for different valuesof ϕ, the elasticity of substitution from bank credit. I conduct this exercise for two different valuesof α. First for a frictionless labor market, where α → ∞. And second, for a low level of α when thereare substantial frictions in the labor market.
1.7 Estimated Parameters
In this section I report the combination of θ and ϕ that match the values of the observed
moments as reported in Table . I report the values that fit the cross-sectional moments
in models where α = 1 and α → ∞, with the purpose of showing that the estimated
structural parameters are vastly different depending on the assumed structure of the labor
market.
37
Parameter Description Value (α = 1) Value (α = 1000)θ Substituability Across Banks 1.5 6.5ϕ Inverse credit Dependence 4.5 20
Table 1.3: Estimated Elasticities of Substitution
-0.3 -0.25 -0.2 -0.15 -0.1 -0.05
Change in Credit
-0.08 -0.06 -0.04 -0.02
Change in Employment
Figure 1.10: Targeting of cross-sectional moments - α = 1000
Note: This table shows the point estimate for each cross-sectional moment provided in Huber(2018), with 95 percent confidence interval bounds. The x mark shows the fit of the model.
-0.3 -0.25 -0.2 -0.15 -0.1 -0.05
Change in Credit
-0.08 -0.06 -0.04 -0.02
Change in Employment
Figure 1.11: Targeting of cross-sectional moments - α = 1
Note: This table shows the point estimate for each cross-sectional moment provided in Huber(2018), with 95 percent confidence interval bounds. The x mark shows the fit of the model.
The estimated parameters in Table (1.3) led me to reject that firms and banks operate
in markets of perfect substituability, which is the limit of θ → ∞ and ϕ→ ∞. The numbers
38
in the table alone do not tell us quantitatively, how important are deviations from perfect
substituability, an answer that I provide in the next section.
Table (1.3) makes clear the importance of the structure of the labor market. Under
frictionless labor markets, the parameters are larger, implying that firms are more flexible
in reacting to a bank shock. Therefore the effects of bank shocks will be lower.
We have shown how α, the parameter that governs the extent of frictions in the labor
market, is important in this model. The reason is that the extent of real rigidities in the
model change the extent to which demand and inputs can be reallocated across firms.
When there are substantial frictions in reallocating labor across firms, the model requires
substantial frictions in banking as well, in order to match the cross-sectional moments.
On the other side, with frictionless labor markets, the banking sector must be relatively
flexible, or the model would predict cross-sectional elasticities that are larger than the
ones observed in the data. The question becomes how to distinguish across values of α.
I use two sources of evidence: direct evidence on the value of α, and indirect evidence
showing that additional cross-sectional patterns in the banking sector reject the case of
labor markets with low frictions.
In particular, I Webber (2015) document an inelastic firm-specific labor supply. This
evidence has already been used in the literature by Chodorow-Reich (2014), and I show
that in a more flexible model with flexible patterns of substitution of firm funding, the
extent of these frictions is still important. I also use an additional cross-sectional moment,
the indirect effects of bank lending cuts, to distinguish across models. The indirect effects
measure how a firm without direct exposure to the shocked bank that operates in a region
where other firms are highly exposed behaves with respect to another firm without direct
exposure to the troubled bank that operates in a region where firms are not highly ex-
posed to the troubled bank. Huber (2018) reports that the indirect effects of bank-lending
cuts are negative. This means that unexposed firms in exposed regions underperform
unexposed firms in unexposed regions.
39
I extend the model to illustrate the behavior of the indirect effects. Specifically, I ex-
tend the model to have 2 symmetric regions. The regions are segmented in the markets
for goods and labor. That is, each firm produces non-tradeable goods, and people cannot
move across regions. However, there is partial financial integration. Lending relation-
ships are determined by distance, regardless of geographical barriers. Therefore, firms
may borrow from banks in their home or a foreign region, but must sell their products
and hire their workers in the local region. As before, the extent to which workers can
move across firms within the same region is given by the parameter α:
∆ log Yjr = β0 + β1ν jr,pre + β2 ¯ν jr,pre + ε jr . (1.27)
Equation (1.27) presents the regression we will run to get the reduced-form indirect
effects. The dependent variable is the log change of an outcome of interest (in this case
output) of firm j located in region r , and the right-hand-side variables are the pre-existing
lending relationship of the same firm and the average exposure of the firms in region r .
β2 is the coefficient of interest; it captures the change in outcomes of a firm with ν jr,pre = 0
in a region where the average exposure is complete ¯ν jr,pre = 1, with respect to a firm with
zero direct exposure ν j−r,pre = 0 in a region −r where the average exposure is also zero
¯ν jr,pre = 0.
To give a clear sense of the effect of α in the model, I show the effect of different
values of this parameter on the three cross-sectional patterns I have documented so far:
the elasticity of credit, the elasticity of output, and the indirect effects. In order to provide
a clean intuition, I fix all the other values of the parameters at arbitrary values, including
θ and ϕ. This approach is in contrast to the previous results where I estimated ϕ and θ for
different values of α.
Figures (1.12) and (1.13) illustrate an argument that is familiar by now. When labor
40
markets exhibit less frictions, the direct cross-sectional effects increase in absolute value.
This happens because the wedge between marginal costs between firms with and without
exposure to the shock increases. As a consequence, the wedge between prices, production,
and credit demand increases as well.
10 20 30 40 50 60 70 80 90 100-0.105
-0.1
-0.095
-0.09
-0.085
-0.08
-0.075
-0.07
-0.065
-0.06E
lasticity o
f C
red
it
Figure 1.12: Sensitivity of the cross-sectional effects on credit of an idiosyncratic bankshock to α
Note: This Figure shows the cross-sectional effect on credit to a bank shock for different values ofα, the extent of frictions in the labor market. All the other parameters are fixed in their calibratedvalues, except θ and ϕ which are fixed in an arbitrary level of 5. The qualitative properties of thefigure do not depend on this choice.
41
10 20 30 40 50 60 70 80 90 100-0.09
-0.08
-0.07
-0.06
-0.05
-0.04
-0.03
-0.02
-0.01
Ela
sticity o
f O
utp
ut
Figure 1.13: Sensitivity of the cross-sectional effects on output of an idiosyncratic bankshock to α
Note: This Figure shows the cross-sectional effect on ouput to a bank shock for different values ofα, the extent of frictions in the labor market. All the other parameters are fixed at their calibratedvalues, except θ and ϕ which are fixed in an arbitrary level of 5. The qualitative properties of thefigure do not depend on this choice.
Figure (1.14) plots the indirect effects of the lending shock for different values of α.
The figure makes clear that as labor markets become more efficient, the indirect effects
of a lending shock become more positive. That is, an unexposed firm in an exposed re-
gion experiences a outperforms an unexposed firm in an exposed region. On the contrary,
Huber (2018) reports that firms in exposed regions underperform unexposed firms in ex-
posed regions. Although the confidence intervals on the indirect effects reported by Hu-
ber (2018) are wide, they reject positive values of the indirect effects, which means that
the model rejects values of α greater than 1.
42
0 1 2 3 4
log( )
-0.01
0
0.01
0.02
0.03
0.04
0.05
0.06
0.07
Ind
irect
Effe
cts
Figure 1.14: Sensitivity of the indirect effects on credit of an idiosyncratic bank shock to α
Note: This figure shows the indirect effects of a bank shock for different values of α, the extent offrictions in the labor market. All the other parameters are fixed at their calibrated values, exceptθ and ϕ , which are fixed at an arbitrary level of 5. The qualitative properties of the figure do notdepend on this choice.
The insight that the model rejects perfectly competitive labor markets by using the
indirect effects is key in the estimation of the aggregate effects of bank shocks. As Figure
(1.14) shows, only values of α < 1 can rationalize negative indirect effects. Therefore, we
can reject the limit of frictionless labor markets, and with it, the small elasticities of output
to lending they entail.
1.8 Discussion
1.8.1 The Aggregate Effects of Bank Supply Shocks
In this section I analyze the aggregate effects of a cut in the supply of bank lending. In
particular I compute the ratio between the integral of the discounted value of aggregate
output drops over the integral of the discounted value of the funding shock. Formally, I
compute an elasticity εM as follows:
43
εM =
∫ T0
e−ρt (log(Yt) − log(Y )
)dt∫ T
0e−ρt log(Lendingt) − log( ¯Lending)dt
). (1.28)
The reason to compute the elasticity of output to lending in this way is that output
may exhibit different persistence than total lending, and that the shock that is feeding the
economy is persistent, inducing additional responses in output and lending beyond the
response on impact. Note as well that the elasticity is computed with respect to lending,
not with respect to the shock. There are two reasons for this. First, the policy-relevant
variable is the reduced ability of banks to make loans—or to put it another way, the drop
in the right-hand-side of the balance sheet of the banking sector. Second, this definition
admits comparisons with back-of-the-envelope aggregations that cross-sectional studies
make by abstracting from general equilibrium effects.
εM should be interpreted as the elasticity of output to lending caused by a shock in the
supply of bank lending. It is the macroeconomic equivalent of an instrumental variables
(IV) specification. In an IV, we compute regressions between two endogenous variables,
and find an instrument that affects the right-hand-side variable (lending in this case), and
that only affects the dependent variable (aggregate output), through its effect on lend-
ing.11
The result of this section is an estimation of this elasticity, and I will show the sensitiv-
ity of the elasticity for both experiments with respect to the key parameters of the model.
As before, we will consider results for two extreme values of α, the extent of rigidities in
the labor market.11Computing an elasticity between two endogenous variables in macroeconomics is commonplace. The
Phillips Curve slope for instance is the elasticity of inflation to unemployment caused by a demand shock.Interest rate parities relates exchange rates to interest rate differentials.
44
Calibration α = 1 α = 1000Benchmark (%) 19.63 6.73
Table 1.4: Elasticity of Aggregate Output to Aggregate Bank Lending
Note: This table shows the elasticity of output to lending to bank lending. Each column shows theelasticity of output to bank lending for two assumptions of the labor market. One where there aremeaningful frictions in the labor market (α = 1), and for a case where labor markets are frictionless.
1.8.2 The aggregate effects of an aggregate bank shock
We start by performing an experiment in which every bank in the economy is shocked
at the same time. This experiment is interesting for several reasons. One, this type of shock
captures the attention of macroeconomists and policy experts. Second, it speaks to situ-
ations without meaningful heterogeneous exposure to the shock, where using the cross-
section to estimate effects is implausible. However, we will inquire how the knowledge
of the structural parameters we gained from the cross-sectional estimates extrapolates to
an aggregate shock.
Figures (1.15) and (1.16) show the effects of the key parameters, ϕ and θ, in determin-
ing the output effects of an idiosyncratic shock. The x-axis of these figures is the value of
one parameter, and the y-axis is the elasticity of aggregate output to aggregate lending
after an aggregate bank shock. The solid line shows the preferred case when α = 1, and
the dashed line shows the case of frictionless labor markets, when α → ∞. The marker in
each line shows the estimated value of the parameter for each case.
Figure (1.15) shows that higher values of ϕ, which decrease the extent of financial fric-
tions, diminishes the elasticity of output to lending. Under frictionless labor markets, the
estimated parameter of 20, implies that the elasticity of output to lending is one third the
elasticity estimated when there are meaningful frictions in the labor market. The solid
and dashed line are over the other for two indicating that other than ϕ, no other parame-
ters that differ across the two parametrizations of the model α or θ change the size of the
elasticity.
On the other side, Figure (1.16) shows that θ is not quantitatively relevant for deter-
45
mining the aggregate elasticity since the lines are flat around the estimated values. This
is true even when θ is relevant at determining the cross-sectional responses, as shown in
previous sections. This result indicates that irrespective of the value of θ, the response of
output to lending is the same. It does not mean that θ is irrelevant in the aggregate. To
think about this issue it is useful to remember that the elasticity of output to lending is
equal to the elasticity of output to the shock, divided by the elasticity of lending to the
shock. The flatness of the elasticity of output to lending indicates that the behavior of
lending follows the same pattern.
5 10 15 20 25 300
0.05
0.1
0.15
0.2
0.25
0.3
0.35
Ela
sticity o
f O
utp
ut to
Lendin
g
= 1
= 1000
Figure 1.15: Sensitivity of the aggregate effects of an aggregate bank shock to ϕ
Note: This Figure shows the aggregate output drop after an idiosyncratic bank shock for differentvalues of ϕ, the elasticity of credit dependence. We perform this exercise for two different valuesof α. First for a frictionless labor market, where α → ∞. And second, for a low level of α whenthere are substantial frictions in the labor market. All the parameters are fixed in their calibratedor estimated values except for ϕ. The dot on each line represents the estimated value for ϕ and thecorrespondent output drop.
46
5 10 15 20 25 300
0.05
0.1
0.15
0.2
0.25
0.3
0.35
Ela
sticity o
f O
utp
ut to
Len
din
g
= 1
= 1000
Figure 1.16: Sensitivity of the aggregate effects of an aggregate bank shock to θ
Note: : This Figure shows the aggregate output drop to a bank shock for different values of θ,the substituability of funds across banks. We perform this exercise for two different values of α.First for a frictionless labor market, where α → ∞. And second, for a low level of α when there aresubstantial frictions in the labor market. All the parameters are fixed in their calibrated or estimatedvalues except for θ. The dot on each line represents the estimated value for ϕ and the correspondentoutput drop.
1.8.3 The aggregate effects of an idiosyncratic bank shock
So far, I presented results about the effects on aggregate output of a cut in the supply
of bank lending of the whole banking sector, a truly aggregate shocks. However, idiosyn-
cratic bank lending cuts have aggregate consequences in the model. The reason is that
banks in the model are large entities. In this section I illustrate the macroeconomic effects
of an idiosyncratic bank shock. I measure the elasticity of aggregate output to the cut in
the supply of bank lending of one entity with the following elasticity:
εM,b =
∫ T0
e−ρt (log(Yt) − log(Y )
)dt∫ T
0e−ρt log(Lendingbt) − log( ¯Lendingb)dt
). (1.29)
Where εM,b is the macro elasticity of output after a cut in lending of bank b. The inter-
47
pretation of the elasticity is the same as before. It is the macroeconomic equivalent of an
instrumental variable regression, where after taking a stance in a source of variation, we
compare the effect of that shock on two exogenous variables.
The main result of this section is that opposed to the case of a truly aggregate shock,
in this case, θ the elasticity of substitution of funds across different banks is important
in determining aggregate outcomes. The economic intuition behind this result is clear.
When one bank suffers a given shock that induces the bank to offer less attractive loan
terms to its customers, the elasticity at which firms switch away from the affected bank
dictates their change in marginal costs and their output as a consequence. This result is
the numerical equivalent of the qualitative argument presented in the theoretical sections
of the paper, that shows that when one bank is disrupted, both θ and ϕ are important in
determining the aggregate response of output.
5 10 15 20 25 300.005
0.01
0.015
0.02
0.025
0.03
0.035
0.04
0.045
Ela
sticity o
f O
utp
ut to
Len
din
g
= 1
= 1000Estimation = 1
Estimation = 1000
Figure 1.17: Sensitivity of the aggregate effects of an idiosyncratic bank shock to ϕ
Note: This Figure shows the aggregate output drop after an idiosyncratic bank shock for differentvalues of ϕ, the elasticity of credit dependence. We perform this exercise for two different valuesof α. First for a frictionless labor market, where α → ∞. And second, for a low level of α whenthere are substantial frictions in the labor market. All the parameters are fixed in their calibratedor estimated values except for ϕ. The dot on each line represents the estimated value for ϕ and thecorrespondent output drop.
48
5 10 15 20 25 300.005
0.01
0.015
0.02
0.025
0.03
Ela
sticity o
f O
utp
ut to
Len
din
g
= 1
= 1000Estimation = 1
Estimation = 1000
Figure 1.18: Sensitivity of the aggregate effects of an idiosyncratic bank shock to θ
Note: This Figure shows the aggregate output drop to a bank shock for different values of θ, thesubstituability of funds across banks. We perform this exercise for two different values of α. Firstfor a frictionless labor market, where α → ∞. And second, for a low level of α when there aresubstantial frictions in the labor market. All the parameters are fixed in their calibrated or estimatedvalues except for θ. The dot on each line represents the estimated value for ϕ and the correspondentoutput drop.
Figure (1.17) shows on the x axis the elasticity of substitution away from bank credit,
and on the y axis, the elasticity of aggregate output to idiosyncratic bank lending. Here,
I estimate an elasticity of 0.025, which means that if the shocked bank (that had a bank
share of 10 percent) cuts its lending by 1 percent, then aggregate output will fall by 0.025
percent. The figure also shows that when α → ∞, the case of perfect labor mobility, this
elasticity would be roughly 0.007.
Figure (1.18) shows on the x axis the elasticity of substitution across banks, and on the
y axis, the elasticity of aggregate output to idiosyncratic bank lending. This figure makes
clear that θ, the elasticity of substitution across banks, is important in determining the
aggregate response of aggregate output to an idiosyncratic bank shock.
The fact that the elasticity is lower is no surprise, as illustrated in the theoretical section
of the paper, the effect of a disruption of one bank is weighted by its market share in the
pre-period. What is worth emphasizing is that the elasticity of substitutition of funding
49
across banks is now relevant to determine aggregate fluctuations. The estimation of the
model suggests that a 10 percent drop in lending of a bank with 10 percent market share
would generate a drop in aggregate activity of 0.25 percent.
1.8.4 Comparing General to Partial Equilibrium
An important use of the parametrized model is to compare the estimated aggregate
bank-lending channel to the alternative measure when general equilibrium effects are
ignored. These aggregations are important because after estimating a result in the cross-
section using micro data and regression analysis, empirical researchers want to assess the
potential of their findings to have aggregate implications. Empirical researchers recognize
that the existence of general equilibrium effects may or may not change their findings.
To clarify concepts, Figure (1.19) shows three alternative escenarios illustrating how
the same finding in the cross-section are consistent with different aggregate elasticities.
In this illustrative example we assume there are only two groups of firms, those who are
exposed directly to a shock (via their banks in our application), and those who are not. In
each panel, the solid red line represents the log change in firm-output of a firm exposed
to a shocked bank, while the dashed blue line represents the behavior of a firm with zero
direct exposure to the affected bank.
In both cases the cross-sectional response is the same, since the difference between
the red and blue lines are the same. Therefore, a back-of-the-envelope aggregation that
computes the aggregate effect as the difference between exposed and unexposed firms
times the average exposure to a shock in the distribution of firms, is the same for the
three panels. However, the true aggregate response, which is measured by the average
between the blue and the red line is not equal across the three panels. In the first panel
the aggregate response is larger than the implied by the partial equilibrium aggregation.
In the second panel, the aggregate response is equal to zero. In the third case, because the
aggregate response is the same as the partial equilibrium aggregation. The reason is that
50
t
∆ log Yj
t
∆ log Yj
t
∆ log Yj
Figure 1.19: Polar Cases when translating cross-sectional to aggregate elasticities
firms with zero direct exposure (control group) are not indirectly affected by the shock.
Under those conditions, the partial equilibrium responses aggregate up.
The partial equlibrium aggregation measures the difference in any given firm outcome
between each firm in the economy with respect to least exposed firm to the shock, the con-
trol firm which we denote with c. In the model we can present an intertemporal version
of the partial equilibrium aggregation in present value given by the following expression
εcs =
∫ T0
e−ρt∫ 1
0
(log(Yjt) − log(Yct)
)djdt∫ T
0e−ρt
∫ 1
0log(Borrowing jt) − log(Borrowingct)djdt
, (1.30)
computing the equivalent of the area between the red and blue lines in Figure (1.19)
in present value.
To compare the general and partial equilibrium aggregations, I simulate an experi-
ment in which I shock only one bank. The parametrization of the model indicates that
the partial equilibrium aggregation (εcs) is 10 percent higher than the general equilib-
rium response (εM). This message is important. The preferred estimation of the model,
that is consistent with many patterns documented over the years in the corporate finance
literature, indicates that general equilibrium forces of the model do not cause the micro
patterns to vanish in the aggregate.
However this result does not need to hold, and it depends on the parameters we have
51
estimated. For instance, under an alternative model with frictionless labor market fric-
tions, the partial equilibrium aggregation is only one fifth of the general equilibrium ef-
fect. Meaning that extrapolating from cross-sectional estimates in such a world would
lead researchers to overestimate the relevance of the firm credit channel by a factor of
five. However, such a world with frictionless labor markets is at odds with the evidence.
Figure (1.20) shows how the extent of financial frictions in the model, the substitution
from bank credit (ϕ), and the θ, change the ratio between the general equilibrium and the
partial equilibrium elasticities for two parametrizations of the labor market. In particu-
lar, it shows that the General Equilibrium aggregation can be higher or lower than the
partial equilibrium one as θ and ϕ change. It also shows that general equilibrium effects
are stronger when labor markets work better, as illustrated in the theoretical sections of
the paper. It shows that the ratio between general equilibrium and partial equilibrium
elasticities is more or less stable, and higher for a model with input market frictions.
However, although Figure (1.20) presents important information with respect to the
output effects of a given lending drop, it does not answer the question of whether back-
of-the-envelope aggregations over or underestimate drops in output. The reason is that
for the same shock, the aggregate and the cross-sectional drop in lending are different.
Specifically, Figure (1.20) shows that for each 1 percent of a lending drop caused by the
shock, output reacts by with a given elasticity. However the two aggregations differ in
the percent change in lending they exploit. The general equilibrium aggregation exploits
the drop in aggregate lending, while the partial equilibrium one exploits the differential
change in lending across banks.
To provide a more clear view, Figure (1.21) shows the ratio of the output aggregations,
which means the ratio of the numerators of εM and εcs. The figure makes several points.
First, it shows that across the parameter space, in principle the general equilibrium ef-
fects on output can be larger, similar, or smaller than is implied by partial equilibrium
estimates. However, the estimation of the model imposes restrictions on the size of the
52
0 10 20 300.87
0.88
0.89
0.9
0.91
0.92
0.93
GE
/ P
E
0 10 20 300.2
0.25
0.3
0.35
GE
/ P
E
0 10 20 300.896
0.8965
0.897
0.8975
0.898
0.8985
GE
/ P
E
0 10 20 30
0.2275
0.228
0.2285
0.229
GE
/ P
E
Figure 1.20: Ratio of the aggregate elasticity to back-of-the-envelope aggregations
Note: This figure shows four panels. The left column shows figures when there are significantfrictions in the labor market α = 1. The right column shows the case when α → ∞. The top rowshows results for the elasticity of substitution away from bank credit ϕ, while the bottom rowshows results for the elasticity at which firms substitute funding from a particular bank, θ. Eachpanel shows the ratio between the elasticity of aggregate output to aggregate bank lending (εM ),to the back-of-the-envelope aggregation εcs . The x axis shows the value of a parameter keepingconstant all the other parameters in the parametrization.
difference. By preferring a model with input market frictions rather than a model with
frictionless input markets, the ratio of the output responses is around 2/3 rather than
around 1/6, or put differently, the extent of labor market frictions elevates the ratio of
the output effects in GE to PE aggregations by a factor of 4. Second, within worlds with
frictions in input markets, the estimated parameters of financial frictions ϕ and θ indicate
that the output drops in GE are around 70 percent those implied in PE.
So far we have considered two extreme cases. Situations where one bank is shocked
which we used to gather information about the cross-sectional effects of lending cuts, and
aggregate shocks, where aggregate meant that all the banks where affected by the same
shock. However, in the data, bank disruptions are characterized by events that look like
53
0 10 20 300.6
0.65
0.7
0.75
0.8
GE
/ P
E
0 10 20 300.1
0.15
0.2
0.25
GE
/ P
E
0 10 20 300.6
0.7
0.8
0.9
1
1.1
1.2
1.3
GE
/ P
E
0 10 20 300.14
0.15
0.16
0.17
0.18
0.19
0.2
GE
/ P
E
Figure 1.21: Ratio of the aggregate output drop with respect to back-of-the-envelope ag-gregations
Note: This figure shows four panels. The left column shows figures when there are significantfrictions in the labor market α = 1. The right column shows the case when α → ∞. The top rowshows results for the elasticity of substitution away from bank credit ϕ, while the bottom row showsresults for the elasticity at which firms substitute funding from a particular bank, θ. Each panelshows the drop of aggregate output to the drop in output inferred from a back-of-the-envelope-aggregation. The x axis shows the value of a parameter keeping constant all the other parametersin the parametrization.
the combination of these two extreme cases. All the banks are to some extent affected by a
funding shock, but then there is heterogeneity across banks in the exposure to the shock.
This pattern suggests an interesting question. Is the response of the economy different
when the profile of shocks exhibits the “across-the-board” plus heterogeneous exposure
compared to a situation with only each element separately. This question becomes in-
teresting because the cross-sectional studies we have studied so far explot precisely the
heterogeneous exposure that is on top of an aggregate shock.
To check these level effects I compare three different exercises. One in which I shock
all the banks, another in which I shock only one bank, and another in which I shock all
54
the banks at the same time, but one particular bank has a higher exposure to the shock.
In this experiment, the sum of the exogenous shock of the first and second experiment
are equal to the exogenous shock of the third experiment. I check that their aggregate
responses are similar in magnitude. The idiosyncratic shock experiment exhibits an ag-
gregate fall of output of 10.27% of the one where all the banks are shocked in the same
way. The aggregate shock plus heterogeneity, has an output fall that is 1.1020 times as
large as the experiment where all the banks suffer in an homogeneous fashion. Since
1.1020 is roughly equal to 1 plus 0.1027, I conclude that under the lenses of the model,
and the solution method I employ, the aggregate response that I get from an experiment
with one bank being shock is consistent with one where all the banks are shocked, and
one particular bank suffers additional exposure.
1.9 Counterfactuals
This section performs different experiments in the model, illustrating the effects of
heterogeneity, different types of shocks, and alternative policy scenarios
1.9.1 Bank Disruptions in Small versus Large Banks
One policy relevant question is the difference in effect of a shock that affects banks that
are more or less important in the aggregate economy. The counterfactual we are analyzing
is one in which we make the affected bank smaller. The source of variation I consider is to
increase the importance of distance in determining firm-bank relationships. This source
of variation makes the shocked bank more distant from the average firm, and therefore
decreases its market share before the onset of the shock.
The y axis of Figure (1.22) shows the normalized drop in aggregate output relative to
a situation where the affected bank has a market share of 10 percent. the x-axis shows the
market share the affected bank had previous to the shock. The Figure makes a couple of
55
8.8 9 9.2 9.4 9.6 9.8
Market Share in Steady State (%)
85
90
95
100
Agg
reg
ate
Ou
tpu
t D
rop (
%)
Relative Output Drop
Reference Line
Figure 1.22: Effect of a shock to a bank as a function of its mean market share
Note: The Figure plots the relative drop in aggregate output as a function of the pre-existing marketshare of the shocked bank. The dotted line shows a reference line, where the relative drop in outputdecays at the same rate that the market share in the pre-period.
points. The first one is that when the affected bank has lower market shares in the pre-
period, a shock to it creates smaller aggregate effects. The second point the Figure makes
is that this relationship is non-linear. In particular, the relative drop in output in the figure
falls faster than the market share of the bank. The dotted line shows a reference line where
the relative aggregate output drop falls as fast as the market share, highlighting that the
effects of distance, or centrality of a bank in determining aggregate output drops.
Instead of using distance as a source of variation, I also explore changing the market
structure of the economy. In particular I show how the aggregate effects of a shock to an
individual bank change when the banking sector becomes more competitive.
Figure (1.23) shows the effect of having more banks in the economy. The x-axis shows
the pre-existing market share of the shocked bank. In the pre-period banks are roughly
the same size, so a market share of 20% translates into an economy with 5 banks for exam-
ple. The economies depicted in the figure change from having 100 banks to having only
56
5 10 15 20
Market Share in Steady State (%)
10
20
30
40
50
60
70
80
90
100
Agg
reg
ate
Ou
tpu
t D
rop (
%)
Relative Output Drop
Reference Line
Figure 1.23: Effect of a shock to a bank as a function of market structure
Note: The Figure plots the relative drop in aggregate output as a function of the pre-existing marketshare of the shocked bank. The underlying experiment is an increase in the number of banks in theeconomy. The dotted line shows a reference line, where the relative drop in output decays at thesame rate that the market share in the pre-period.
five. The main message of the figure is that when the banking sector becomes more com-
petitive, the relevance of a single bank in aggregate fluctuations diminishes more slowly
than the market structure itself. The reason is that in the experiment I am considering,
banks are located uniformly throughout space.12 Therefore, many banks enter but they
do not lend to the firms that had relationships with the affected bank.
1.10 Conclusion
The aggregate effects of cuts in the supply of bank lending are difficult to measure
using aggregate time-series because bank funding disruptions coincide with other shocks
that affect loan demand and output at the same time, and because banks are sensitive to
12remember that space is not to be taken literally. It just means that some banks are closer to some firmsthan others, for whatever reason, not limited to geography.
57
drops in economic conditions creating reverse causality concerns.
Using direct and indirect evidence on the cost of reallocating inputs across firms, and
on the relative effects of bank shocks on firm outcomes and credit, I conclude that the
aggregate consequences of bank lending cuts are large. When lending drops by 1 percent
due to a disruption in bank funding, aggregate output is reduced by 0.2 percent.
This elasticity depends on the extent of bank dependence, and this paper uses cross-
sectional evidence to recover this elasticity. Although the ease with which firms can bor-
row from different banks is relevant in the cross-section, it is not quantitatively relevant
in determining the aggregate effect of an aggregate bank shock. Taking a stance on the
frictions needed to reallocate inputs and demand across firms is important, even under
the experiment of an aggregate shock where all firms are shocked symmetrically. This
happens because, in order to target the same cross-sectional moments, frictionless input
and demand markets require banking frictions to be milder than in an economy with
substantive frictions in reallocating inputs and demand.
1.11 Appendix
1.11.1 Full derivation of the model
Firms
There are a continuum of firms and a discrete number of banks. Each firm is denoted
by j and banks by b. I will save in the time subscript for brevity, unless necessary. Firms
face a downward-sloping demand curve
Yj = Y P−ηj
.
On the production side, firms produce by mixing a continuum of intermediates with
58
a CES technology with elasticity of substitution σ. For reasons clear below, σ will be
irrelevant in the model conditional on a restriction on the parameter space
Yj =
(∫ 1
0
(y j(ω)
) σ−1σ dω
) σσ−1
, (1.31)
and each intermediate good ω is produced with labor in a constant returns to scale
production function, and a firm-wide productivity shifter z
y j(ω) = z j l j(ω). (1.32)
Firms face a two-stage financing problem. In the first stage firms must decide whether
to self-finance the task, or to look for funding in the banking sector. For tractability, I
assume that firms do not observe the exact lending rates of each bank for a given task,
but they can form expectations about it. This assumptions lets me to break the problem
in two distinct stages and gives analytical tractability to the problem.
The Total Cost to finance intermediate ω with option F ∈ S, B is given by:
TCjF(ω) = w j l j(ω)R jF(ω)
,
and R jF is described by
R jF(ω) =
RjS
ε jS(ω)if F = S
RjB(ω)
ε jB(ω)if F ∈ B.
(1.33)
As it is clear from equation 1.33, each lending cost is scaled by a shifter. These shifters
are meant to capture reasons why firms use bank credit for some production tasks and
not for others, and they take a form that is isomorphic to a productivity shock at the firm-
59
finance option-intermediate level. They can also be interpreted as a taste from the owner
of the firm, or a source of idiosyncratic variation across intermediates. The equation also
clarifies that the cost of funds from the banking sector for a particular bank depends on
the task. After the firm decides to use the banking sector, it has to go to a set of the banks
and ask for quotes to finance the intermediate.
As mentioned before, the firm makes the first-stage decision before getting quotes
from the banks, therefore it choosess the financing option that minimize the expected
value of the marginal cost of a particular task, which is made explicit by
MCjF(ω) =w j
z jR jF(ω)
.
Because the marginal cost is linear on the lending cost, the firm will use one and only
one financing source for task ω. Therefore the firm picks the option
argminS,BE(MCjF(ω)) =w j
z j
R jF
ε jF(ω),
where R jB = ER jB(ω) and will be defined later. Because w j and z j are firm-level vari-
ables and do not depend on the financing choice for any intermediate, then the decision
of the firm in this stage collapses to compute the minRjS
ε jS(ω),
RjB
ε jB(ω).
The terms ε jF(ω) is sampled from a Frechet distribution with CDF F(ε) = e−ϕFε−ϕ
. I
impose without loss that ϕS + ϕB = 1, and rename ϕB = ϕ.
The derivation below is standard in discrete choice models with Frechet shifters. For
a reference, see Eaton and Kortum (2002).
We start the derivation by computing the probability that RjF
ε jF (ω)is lower than an arbi-
trary level x.
P(
R jF
ε jF(ω)< x
)= P
(R jF
x< ε jF(ω)
)= 1 − e−ϕF R−ϕjF xϕ
60
Now, we compute the probability that the minRjS
ε jS(ω),
RjB
ε jB(ω) is lower than an arbitrary
level x
P(min
R jS
ε jS(ω),
R jB
ε jB(ω)
)= 1 − ΠS,B
(1 − P
(R jF
ε jF(ω)< x
))(1.34)
= 1 − ΠF∈S,Be−ϕF R−ϕjF xϕ (1.35)
= 1 − e−∑
F ∈S,B ϕF R−ϕjF xϕ (1.36)
Importantly, the term∑
F∈S,B ϕF R−ϕjF is the key parameter term that determines the dis-
tribution of borrowing costs for firm j. In a similar spirit to the work of Eaton and Kortum
(2002), there are three important properties. First, the share of borrowing from the bank-
ing sector is given by
s j =ϕR−ϕB j
ϕR−ϕB j + (1 − ϕ)R−ϕS j
. (1.37)
Second, conditioning on the financing source does not an effect on effect on the distri-
bution of prices. When one source is more efficient than the other, this will materialize in
a higher financing share from that source, but not on a different price distribution of the
terms contracted from that source. Finally, The exact cost of finance for the firm, R j takes
closed form,
R j =(ϕR−ϕB j + (1 − ϕ)R−ϕS j
)−ϕ. (1.38)
With this knowledge we can move to the second stage of the problem. Where for an
intermediate that was decided to be financed with the banking sector, the firm decides
the bank with which to borrow from.
61
In a similar spirit than before, the marginal cost of choosing bank b to finance task ω
is given by
MCjb(ω) =w j
z jε jB(ω)R jb(ω)
.
Where R jb =Rjb
ε jb(ω). All the banks inherit the shifter ε jB(ω). However, the draw of
this shifter is irrelevant for the decision of which bank to use, since it is common to all
the banks in the economy. The same happens for the firm-shifter z and the wage rate w j .
Since the marginal cost is linear in the lending rate R jb(ω), then the firm chooses one and
only one bank to finance intermediate ω.
The terms ε jb(ω) is sampled from a Frechet distribution with CDF F(ε) = e−Tjbε−θ
. I
impose without loss that sum∀bTjb = 1
In a similar spirit than before, we start the derivation by computing the probability
that Rb
ε jb(ω)is lower than an arbitrary level x.
P(
Rb
ε jb(ω)< x
)= P
(Rb
x< ε jb(ω)
)= 1 − e−θF R−θ
bxθ
Now, we compute the probability that the minRjb
ε jb(ω) is lower than an arbitrary level
x
P(min
Rb
ε jb(ω)
)= 1 − Π∀b
(1 − P
(Rb
ε jb(ω)< x
))(1.39)
= 1 − Π∀be−TjbR−θb
xθ (1.40)
= 1 − e−∑∀b TjbR−θ
bxθ (1.41)
Importantly, the term∑∀b TjbR−θb is the key term that determines the distribution of
bank borrowing costs for firm j. In a similar spirit to the work of Eaton and Kortum (2002),
62
there are three important properties. First, the share of borrowing from the banking sector
is given by
ν jb =TjbR−θb∑∀b TjbR−θb
. (1.42)
And the bank borrowing cost is given by:
R jB = *,
∑∀b
TjbR−θb+-
−1/θ
1.11.2 Proofs Section 2
Derivation of Aggregate Output in the simple model
We start with the expression of firm-level labor demand. I save on the time subscript
for brevity.
L j =
(η
η − 1
)−ηY zη−1
j w−ηj R−ηj
The firm takes as given the labor supply curve w j = w( L j
L
) 1α . Plugging this relation-
ship into the labor demand equation, we get the following:
L j =
(η
η − 1
)− ηαα+η
Yα
α+η z(η−1) α
α+η
j w−η α
α+η R−η α
α+η
j
By elevating to the power α+1α , integrating over firms, and elevating to the power α
α+1 ,
we get an expression for aggregate labor:
L =
(η
η − 1
)−ηYw−ηE
(z
(η−1) αα+η
j
) α+ηα+1
E
(R−η α+1
α+η
j
) α+ηα+1
This expression is useful because it let us to plug in the aggregate labor supply equa-
63
tion, replacing away L
w =
(η
η − 1
)− ηφ1+ηφ
Yφ
1+ηφE(z
(η−1) αα+η
j
) α+ηα+1
φ1+ηφ
E
(R−η α+1
α+η
j
) α+ηα+1
φ1+ηφ
Since Yj = z j L j , then
Yj =
(η
η − 1
)− ηαα+η
Yα
α+η zη αα+η
j w−η α
α+η R−η α
α+η
j
Taking the η−1η power, integrating over all the firms, and taking the power η
η−1 , we get
an expression for Y . By replacing the expressions we derived for L and w, we get the result
Y =
(η
η − 1
)−1/φ
E
(z
(η−1)(α+1)α+η
j
) (1+φ)(α+η)φ(η−1)(α+1)
E
(R−(η−1)αα+η
j
) (1+φη)φ(η−1)
E
(R−η(α+1)α+η
j
) (1−φα)φ(α+1)
Proof of Proposition 1
Start from equation (1.14). Take logs and omit the constant term and the productivity
term by the assumption of no sorting.
log Y ∝1 + ηφ
φ(η − 1)log
∫ 1
0R−(η−1) α
α+η
j dj +1 − αφ
φ(α + 1)log
∫ 1
0R−η α+1
α+η
j dj
Then we will do a second-order Taylor expansion around a point where all the lending
rates take value of R. According to assumption 2, all the lending rates will stay at that
level, except for the lending rate of an arbitrary bank b that will suffer a disruption of its
lending terms to Reu for a positive and sufficiently small u.
log Y ≈ log Y +d log Yd log Rb
u +1
2
d2 log Yd log R2
b
u2
Define X as the value of variable X at the point where the lending rates are equal to R.
Up to the second order:
64
(1.43)R−(η−1) α
α+η
j ≈ R−(η−1) α
α+η
j − (η − 1)α
α + ηR−(η−1) α
α+η
j s j ν jbu
− R−(η−1) α
α+η
j
(−θ s j ν jb(1 − ν jb) − ϕν2
jb s j(1 − s j) −α
α + ηs2
j ν2jb
)u2
2
Which includes the fact that dνjbd log Rb
= −θν jb(1−ν jb) and that ds jd log Rb
= −ϕν jbs j(1−s j). In
the point around we are taking the second-order Taylor expansion, nu jb = Tjb and s j = s,
where s is the share of bank credit when all the lending rates are set at R.
(1.44)ER−(η−1) α
α+η
j ≈ R−(η−1) α
α+η
j
(1 − (η − 1)
α
α + ηsE(Tjb)u + θ sE(Tjb(1 − Tjb))
u2
2
+ ϕE(T2jb)s(1 − s)
u2
2+
α
α + ηs2E(T2
jb)
)u2
2
Applying logs and using the fact that u is sufficiently small such that the two
(1.45)logER
−(η−1) αα+η
j ≈ log R−(η−1) α
α+η
j − (η − 1)α
α + ηsE(Tjb)u + θ sE(Tjb(1 − Tjb))
u2
2
+ ϕE(T2jb)s(1 − s)
u2
2+
α
α + ηs2E(T2
jb)u2
2
By applying the same procedure to the third term in the first equation of this subsec-
tion, and renaming E(Tjb) ≡ µb, and var(Tjb) = σ2jb, yields the following expression for
output:
(1.46)log Y = log Y −1
φsµbu
(1 − µb
u2
)+
u2
2θ sΩ
(µb − σ
2b − µ
2b
)+ ϕ
u2
2s(1 − s)Ω
(σ2
b + µ2b
)By substracting log Y , we get the result.
Proof of Proposition 2
Will be here soon
65
Proof of Proposition 3
Firm-level output can be expressed as a function of aggregate variables and firm-level
shifters as in:
Yj =
(η
η − 1
)−η αα+η
Yα
α+η zη(α+1)α+η
j Lη
η+αw−η α
α+η R−η α
α+η
j
Define as Y cj the level of output of firms that do not have any relationship with shocked
bank b. The difference between any particular firm with a relationship with bank b and a
control firm is given by:
log Yj − log Y cj = −η
α
α + η
(log R j − log Rc
j
)+ η
α + 1
α + η
(z j − zc
j
)Now we take expectations across firms, and using the assumption of no sorting, we
cancel out the productivity term. That is, firm-level productivity is independent of the
existence of bank relationships.
E(log Yj − log Y cj ) = −η
α
α + ηE(
(log R j − log Rc
j
))
A second-order Taylor expansion of R j with respect to a disrpuption of the lending
terms of bank b as stated in Assumption 2, around a symmetric point where all the lend-
ing rates are equal to R yields:
R j ≈ R j
(1 + sν jbu + s2 ν2
jbu2
2− θ sν jb(1 − ν jb)
u2
2− ϕs(1 − s)ν2
jbu2
2
)And Rc
j = R j . By plugging combining these expressions we get the result:
E(log Yj − log Y cj ) = −
ηα
α + η
(sµbu(1 + µb
u2
) − θ sETjb(1 − Tjb)u2
2− ϕs(1 − s)E(T2
jb)u2
2
)
66
1.11.3 Proofs Identification Section
As shown in the previous section, firm-level output can be written as:
Yj =
(η
η − 1
)− ηαα+η
Yα
α+η zη αα+η
j w−η α
α+η R−η α
α+η
j (1.47)
Taking logs we get:
log Yj = −ηα
α + ηlog
(η
η − 1
)+
α
α + ηlog Y + η
α
α + ηlog z j − η
α
α + ηlog w − η
α
α + ηlog R j
(1.48)
I will collapse the first, second, and fourth term into a single term called log Θt , which
is common to all the firms, and will therefore become irrelevant in computing the result.
log Yj = log Θt + ηα
α + ηlog z j − η
α
α + ηlog R j (1.49)
Taking temporal differences we get:
∆ log Yj = ∆ log Θt + ηα
α + η∆ log z j − η
α
α + η∆ log R j (1.50)
A second-order Taylor expansion of log R j that coincides with assumption 2 yields:
log R j ≈ log R j + sν jbu − θ sν jb(1 − ν jb)u2
2− ϕs(1 − s)ν2
jbu2
2(1.51)
67
Taking temporal differences with respect to a pre-period where log R j = log R j , yields:
∆ log R j ≈ sTjbu − θ sTjb(1 − Tjb)u2
2− ϕs(1 − s)T2
jbu2
2(1.52)
Plugging this expression into equation 1.50 yields a second order approximation of
firm-level output after one shock suffers an increase in its lending terms.
∆ log Yj = ∆ log Θt + ηα
α + η∆ log z j − η
α
α + η
(sTjbu − θ sTjb(1 − Tjb)
u2
2− ϕs(1 − s)T2
jbu2
2
)(1.53)
The cross-sectional regression of log output changes on pre-existing exposure is the
equivalent of running the following regression by OLS:
∆ log Y f = β0 + βrealTjb + ε f (1.54)
In this setting the exposure in the preperiod to the affected bank is just Tjb.
The regression coefficient is given by the covariance between ∆ log Yj and Tjb. Since
all the firms have the same ∆ log Θt regardless of their specific Tjb, and because we are
imposing a no-sorting condition that implies cov(∆ log z j,Tjb) = 0, then:
68
βreal =cov
(∆ log Yj,Tjb
)var(Tjb)
(1.55)
=1
var(Tjb)cov
(−η
α
α + η
(sTjbu − θ sTjb(1 − Tjb)
u2
2− ϕs(1 − s)T2
jbu2
2
),Tjb
)(1.56)
= −ηα
α + ηsu + θη
α
α + ηs
u2
2
cov(Tjb(1 − Tjb),Tjb)
var(Tjb)+ ϕη
α
α + ηs(1 − s)
u2
2
cov(T2jb,Tjb)
var(Tjb)
(1.57)
= −ηα
α + ηsu + θ
ηα
α + ηs
u2
2*,1 −
cov(T2jb,Tjb)
var(Tjb)+-
+ ϕηα
α + ηs(1 − s)
u2
2*,
cov(T2jb,Tjb)
var(Tjb)+-(1.58)
This is the main result. The regression coefficient in the population is larger when
consumers are more elastic in reallocating demand across varieties (η higher), when labor
markets work without frictions αα+η . Both substitution across banks and substitution away
from bank credit make the elasticity less negative. Note the term(1 −
cov(T2jb,Tjb)
var(Tjb)
)in the
second term that accompanies the θ. Since the shifter T are between 0 and 1, the covariance
can be equal to the variance if the T terms only take either 0 or 1. When that is the case,
firms are completely dependent of one bank. Therefore θ becomes irrelevant.
69
Chapter 2
Self-Employment and Development
PoliciesWith Sergio Ocampo
Business ownership is regarded as a booster of innovation, economic dynamism, and
growth. However, a cross-country comparison of self-employment rates offers a puz-
zling picture. Self-employment rates are higher in developing countries than in developed
ones.1 This apparent contradiction is due to the large fraction of self-employed individ-
uals in the developing world who are engaged in small and unproductive enterprises
that provide only subsistence income (Schoar, 2010; Poschke, 2013a,b). The reality of self-
employment in developing countries is one of street vendors, not one of growing startups.
Aiming to spur economic growth, policymakers advocate development policies that
alleviate barriers to the entry and growth of firms. These policies are intended to pro-
mote business ownership and improve allocative efficiency, thus reducing the productiv-
ity gaps behind differences in standards of living across countries (see Hsieh and Klenow,
2009, 2014; Banerjee and Moll, 2010; Restuccia and Rogerson, 2013; Midrigan and Xu,
2014). However, as we expand on below, the specifics of the mechanisms that lead indi-
1According to the World Development Indicators, 70 percent of the workforce is self-employed in India,50 percent in Colombia and 30 percent in Mexico. This contrasts with the share of self-employed individualsin developed countries, which tends to be much lower (about 10 percent for Japan, Germany and the U.S.).
70
viduals to opt into self-employment play a crucial role in shaping the aggregate response
to policy.
In this paper we evaluate the effect of development policies in environments where
subsistence entrepreneurship is prevalent. We study the aggregate effects of three major
policies: job-guarantee programs, unemployment insurance, and micro-finance. To find
the macroeconomic effects of these policies, we use a general equilibrium occupational
choice model that is consistent with salient features of self-employment in developing
economies. Our model differs from previous work by introducing unemployment risk,
which directly affects the selection of agents into self-employment. Unemployment risk
allows the model to explain the mass of subsistence entrepreneurs that characterizes devel-
oping economies and shapes the efficacy of economic policy.
The policies we consider have the following effects. Job-guarantee programs generate
small increases in real wages and limited crowding out of private employment, as subsis-
tence entrepreneurs opt out of self-employment and into the new salaried jobs. Unemploy-
ment insurance deters subsistence entrepreneurship and increases output, as it increases the
size of the most productive enterprises and reallocates labor away from low-productivity
self-employment. Micro-finance, on the other side, makes self-employment more attrac-
tive for individuals with low wealth and productivity, decreasing aggregate productivity
as a result.
To illustrate the major features of self-employment in developing countries, we study
micro-data from Mexico and India. We highlight three main takeaways. First, there is a U-
shaped relationship between self-employment and earnings, with high self-employment
rates among the lowest and highest earners of the economy, and most of the self-employed
are concentrated at the lower end of the earnings distribution.2 Second, individuals who
are more likely to be (income-)constrained are also more likely to opt into self-employment.3
2Both developing and developed countries exhibit the U-shaped pattern of self-employment and earn-ings. However, in developed countries the self-employed are more concentrated among high earners.
3These are unemployed individuals who live in households with no other earners or who do not receiveincome from other sources (such as remittances).
71
This is consistent with the presence of subsistence entrepreneurs. Third, the self-employed
are willing to accept salaried jobs at market wages when such jobs are offered to them.
This evidence comes from the implementation of job-guarantee programs4 and from ran-
domized labor demand shocks to local markets in India documented by Breza, Kaur, and
Shamdasani (2017). Importantly, the experimental evidence shows that an increase in la-
bor demand has no effect on wages, indicating that self-employment provides slack in
the market as low-earning self-employed agents meet the additional demand.
These characteristics are powerful in identifying the relevant mechanisms of the model
and distinguishing between model specifications in the spirit of Nakamura and Steinsson
(2018). In particular, the data reject the workhorse model frequently used to study en-
trepreneurship and development (Moll, 2014; Midrigan and Xu, 2014; Buera, Kaboski,
and Shin, 2015). This class of models focuses on financial frictions that prevent productive
entrepreneurs from operating at their optimal size. In these models, self-employment is
only taken up by agents who are productive or wealthy enough to earn a higher income
in self-employment than they can as employed workers. Therefore, these models can-
not explain the large mass of low-earning self-employed that characterizes developing
economies.
We show that a tractable extension of the occupational choice model of Buera, Ka-
boski, and Shin (2015) that incorporates unemployment risk can account for the pat-
terns in the data. Because unemployed agents with low assets cannot tolerate unem-
ployment, they turn to self-employment as a source of income regardless of their en-
trepreneurial ability. This mechanism allows the model to replicate the U-shaped rela-
tionship between self-employment and earnings as low-productivity/low-wealth agents
opt into self-employment. Crucially, the introduction of unemployment risk also allows
the model to match the limited response of wages to labor demand shocks. As in the
data, low-earning self-employed agents meet additional labor demand without affecting
4We study the implementation of the National Rural Employment Guarantee Act (NREGA) in India, aprogram that provides short-term jobs at market wages in rural districts.
72
wages. Absent unemployment risk, the reaction of wages is an order of magnitude higher
(since the self-employed have to be compensated to switch occupations) and is strongly
at odds with the experimental evidence.
The model explicitly incorporates relevant dimensions of heterogeneity across agents’
occupations (employed, unemployed and self-employed), as well as in their wealth, en-
trepreneurial ability (productivity), and labor income (if employed). Agents are free to
engage in self-employment at any point, but can only become employed following the ar-
rival of a job offer, which introduces unemployment risk in a parsimonious way. We lever
on recent advances in continuous time methods that give us a computational advantage
in the solution of the model (e.g., Moll, 2014; Achdou, Han, Lasry, Lions, and Moll, 2017).
We use a calibrated version of the model to study how self-employment affects the
response of the economy to three policies: job-guarantee programs, unemployment in-
surance, and micro-finance.
Job-guarantee programs These programs increase labor demand by introducing government-
provided jobs that involve low-skill (typically clerical) tasks and pay (minimum) market
wages. The scope of these programs can be massive. For instance, the NREGA program in
India reached 53 million beneficiaries in 2010-2011 alone. Because these programs are usu-
ally implemented in areas with low (official) unemployment (Feng, Lagakos, and Rauch,
2018), the additional labor demand created by the government is met by crowding out
employment in the private sector or by self-employed agents who accept the new salaried
job offers.
We show that when subsistence entrepreneurs are prevalent among the self-employed,
as the data suggest, the crowding out of private employment is limited, and the response
of wages is low, in line with the effects of job-guarantee programs in the data. On the
contrary, if self-employment is dominated by productive entrepreneurs (as in models with-
out unemployment risk), the response of wages is an order of magnitude higher, as the
self-employed must be convinced to leave their entrepreneurial activities to meet the ad-
73
ditional labor demand. In equilibrium, the program increases wages and reduces private
demand for labor.
Unemployment insurance We show that unemployment insurance can be used as an
instrument to improve productivity by changing the type of individual who selects into
self-employment and increasing the labor supply. The effects on productivity come in
addition to the usual benefits from insurance to labor income fluctuations. Even though
self-employment already provides a way for individuals to self-insure against job loss,
engaging in self-employment can have negative (long-run) effects on the ability of an
individual to regain employment. For instance, recent evidence for the U.S. shows that
take-up of “gig-economy” jobs (such as Uber or TaskRabbit) reduces individuals’ earn-
ings and employment for at least four years (Jackson, 2020). In our calibrated model,
engaging in self-employment reduces one’s chances of receiving a job offer, causing sub-
sistence entrepreneurs to become stuck in self-employment, which in turn lowers aggregate
productivity.5
Unemployment insurance improves productivity by deterring unproductive individ-
uals from engaging in entrepreneurial activities, thereby reducing the share of low-earning
self-employed. The implementation of the program leads to an increase in output, which
is explained by an increase in the number of high-productivity enterprises and a reduc-
tion in the share of subsistence entrepreneurs. These effects follow even if the insurance is
relatively small. In the simulated exercise we provide insurance equal to 5 percent of the
minimum market wage.
Micro-finance Micro-finance programs are widespread in developing countries, where
they frequently target poor individuals who lack access to funding for their entrepreneurial
activities. These programs can alleviate the financial constraints that curtail the growth of
productive entrepreneurs. However, it is well understood that micro-finance programs
5This need not be the case a priori. The quantitative difference in the arrival rate of job offers betweenunemployed and self-employed agents is implied by the calibration of the model and informed by lowerjob-finding rates from self-employment relative to unemployment.
74
also lower aggregate productivity by inducing low-productivity individuals to engage in
entrepreneurship (Buera, Kaboski, and Shin, 2017). The effect of the program on the pro-
ductivity distribution depends crucially on the initial composition of the self-employed.
In models without unemployment risk, the change in selection comes from a lower pro-
ductivity threshold for agents who enter into self-employment. This lower threshold re-
duces the productivity of the marginal entrant, but still keeps the lowest-productivity
agents out of self-employment. We show that this mechanism is modified by the intro-
duction of unemployment risk, as poor agents of all productivity levels engage in en-
trepreneurship out of necessity (Poschke, 2013a). Therefore the change in the productivity
distribution is driven by the intensity with which the lowest-productivity agents opt into
self-employment.6
Our results suggest that labor market frictions are central to matching the characteris-
tics of self-employment in developing economies. We show that models that rely only on
financial frictions are at odds with the prevalence of low-earning self-employed persons
in developing countries, as well as the response of wages to labor demand shocks. Fur-
thermore, labor market frictions shape the response of the economy to various policies by
affecting the occupational choice of agents. Unemployment risk drives low-productivity
individuals into self-employment, which accounts for the bulk of low-earning self-employed
in the data. Because these subsistence entrepreneurs are willing to take on jobs at current
market wages, the response of wages to labor demand shocks (such as job-guarantee
programs) is muted, in line with experimental and quasi-experimental evidence. Subsis-
tence entrepreneurs are also sensitive to the provision of unemployment insurance. Offer-
ing even low payments to the unemployed drives unproductive individuals out of self-
employment, increasing productivity and output in the economy. Finally, the presence
6Our results are also consistent with recent experimental evidence on the heterogeneous effects of micro-finance. Banerjee, Breza, Duflo, and Kinnan (2019) show that loans only have a positive lasting effect onindividuals who were already engaged in entrepreneurial activities, suggesting that individuals who optinto self-employment because of the introduction of a micro.finance program have lower productivity, andthat productive low-wealth individuals are the ones that benefit from increased access to credit.
75
of low-earning self-employed is increased by the implementation of micro-finance pro-
grams that target the poor. These programs induce more low-productivity poor agents to
choose self-employment, which reduces productivity.
Our work is related to a long standing and multifaceted literature on entrepreneur-
ship. Part of the literature focuses on the role of financial constraints that prevent en-
trepreneurs from operating at an optimal scale (Quadrini, 2000; Cagetti and De Nardi,
2006, 2009). We contribute by highlighting the role of labor market frictions (that induce
unemployment risk) in driving self-employment in developing countries. Another part
of the literature deals with misallocation and productivity differences across countries
(e.g., Hsieh and Klenow, 2009, 2014; Banerjee and Moll, 2010; Restuccia and Rogerson,
2013; Midrigan and Xu, 2014). We contribute to this literature by highlighting the role
of selection into entrepreneurship by low-productivity low-wealth agents facing unem-
ployment risk. These individuals constitute a mass of entrepreneurs who lower aggre-
gate productivity and increase misallocation. We connect this mechanism to policies such
as unemployment insurance that make it possible for these agents not to engage in en-
trepreneurship.
Our work is also related to studies of other mechanisms that drive self-employment.7
Hurst and Pugsley (2016) discuss nonpecuniary benefits as a driver of self-employment in
developed economies. Higher transition rates into self-employment for income-constrained
agents suggest that nonpecuniary benefits are less relevant for explaining self-employment
in developing economies. Hombert, Schoar, Sraer, and Thesmar (2014, 2016) discuss the
role of risk in taking on entrepreneurial activities. They show that providing unemploy-
ment benefits to individuals exiting self-employment in France is linked to an increase
in entrepreneurship without a decrease in the average quality of new firms. We see our
results as complementary, in that we examine the implications of similar policies in a dif-
ferent context: that of a developing economy. Garcia-Cabo and Madera (2019) examine
7Our paper is close to unpublished work by Kevin Donovan, developed independently from ours.
76
the role of self-employment as an outside option for workers in the Spanish labor market,
characterized by rigid labor contracts. They also document negative selection into self-
employment by unemployed agents and analyze the consequences of self-employment
promotion policies targeted at the unemployed.
Finally, our work complements recent papers on the role of structural transformation
and wage and unemployment dynamics. During early stages of development, a large
portion of the population engages in low-productivity activities, akin to those of the
subsistence entrepreneurs described above. As the country develops, workers are pulled
from these activities into more “modern” sectors. Storesletten, Zhao, and Zilibotti (2019),
studying the case of China, link this pattern to the unresponsiveness of wages to busi-
ness cycles during early stages of development. The mechanism is similar to the one de-
scribed above for job-guarantee programs, with the unproductive sector absorbing work-
ers in downturns and providing them during booms. It is not until this unproductive
sector has shrunk enough that wages are bid up in the development process. Similarly,
Feng, Lagakos, and Rauch (2018) document a positive relation between unemployment
and GDP per capita. This suggests that unemployment is an especially poor measure of
slack in the labor markets of developing economies, because (in line with our results) self-
employment masks the true level of slack in the market (Breza, Kaur, and Shamdasani,
2017).
The rest of the paper is organized as follows. First we describe the main mechanism
behind self-employment under unemployment risk. This sets up the discussion of the
empirical results that we present in section 3.3. We focus on providing a characterization
of self-employment with the identification of model specification in mind. Third, we de-
scribe the model and its calibration. In section 2.4, we show that the model is consistent
with the observed features of self-employment. Finally, in section 2.5, we use the model
to study job guarantee programs, unemployment insurance, and micro-finance.
77
2.1 Self-employment as an outside option
What drives individuals to choose self-employment? Before we describe our empirical
evidence we sketch a simple model to highlight the main mechanisms at work. We focus
on the forces affecting poor (low-wealth) individuals, who constitute a large share of the
population in developing economies. We show that the combination of unemployment
risk and limited credit access may induce agents to choose self-employment, despite their
low entrepreneurial ability, generating a mass of low-earning self-employed agents. This
mechanism is absent in the presence of strong safety nets (say in the form of unemploy-
ment benefits),8 but it is exacerbated by policies like micro-finance. Safety nets mitigate
the downside of labor income risk and reduce the likelihood that low-productivity agents
will choose self-employment. In contrast, policies similar to micro-finance reduce the min-
imum productivity at which agents opt into self-employment.
The model is as follows. An unemployed agent chooses whether to remain unem-
ployed (U) or to become self-employed (S). The agent has a units of assets and a pro-
ductivity, or entrepreneurial ability, of z. Agents have CRRA utility that depends only on
consumption:(u (c) = c1−σ
1−σ
). There is no borrowing or lending.
If the agent chooses to remain unemployed, she will get a job with probability p ∈
(0, 1], becoming employed (E) and receiving a wage w > 0. Her consumption will then be
cE = a + w. If she does not get a job she will receive unemployment benefits b ∈ [0,w),
and her consumption will be cU = a + b.
If the agent becomes self-employed she can produce consumption goods using her
own assets. Her production depends on her assets and her productivity according to
f (a, z) = zaα, with α ∈ [0, 1]. Consumption for the self-employed is: cS = a + zaα.
The agent will become self-employed when the utility of doing so exceeds the ex-
pected utility of looking for a job: that is, when u(a + f (a, z)
)> p · u (a + w) +
(1 − p
)·
8This mechanism is also absent under risk sharing or when there is no labor income risk, features thatare common in the macro-development literature; see, for instance, Buera et al. (2015).
78
Figure 2.1: Occupational Choice: Unemployment vs. Self-Employment
Assets
Pro
ductivity
Self-Employment Region
Unemployment Region
No Unemployment BenefitsLow Unemployment BenefitsHigh Unemployment Benefits
Note: The figure characterizes the occupational choice of the agent for different levels of unemployment benefits. Linesdepict the threshold value of productivity (z) for each level of assets (a) and a given value of unemployment benefits.The agent chooses self-employment if productivity is above the threshold.
u (a + b). For each level of wealth a, this inequality defines a threshold value for produc-
tivity, above which agents opt into self-employment. Figure 2.1 shows the threshold value
of z for various levels of unemployment benefits (b).
It is instructive to look first at agents as their assets approach zero. The behavior of
these agents is heavily influenced by the level of b. This is because as a goes to zero the
agent’s consumption if unemployed is given by b. When unemployment benefits are low,
unemployment becomes intolerable. In that situation, self-employment is an outside op-
tion that bounds the agent’s consumption away from zero. This mechanism is strongest
when there are no unemployment benefits. In that case, the productivity threshold actu-
ally decreases as the agent becomes poorer, even though the income the self-employed
agent can generate decreases as well. As a consequence, the agent may choose to become
self-employed even if she lacks the entrepreneurial ability (productivity) or the resources
(assets) needed to run a profitable business.9
9Paulson and Townsend (2005) elaborate on many of the same ideas developed in this paper in a shortpolicy note. They show evidence from Thailand during the Asian crisis of 1997, after which “entrepreneurialactivity in Thailand increased ... [and] the number of business households more than doubled,” the authors furthernote that “rising unemployment and falling real wages during the crisis led to changes in the types of people whostarted businesses—and in the types of businesses they started.” (pages 34 and 35).
79
Figure 2.2: Occupational Choice: Unemployment vs. Self-Employment with Micro-Credit
(a) No Unemployment Benefits
Assets
Pro
du
ctivity
Self-Employment Region
Unemployment Region
No Micro-CreditMicro-Credit
(b) High Unemployment Benefits
Assets
Pro
du
ctivity
Self-Employment Region
Unemployment Region
No Micro-CreditMicro-Credit
Note: The figure characterizes the occupational choice of the agent for different levels of micro-credit and unemploy-ment benefits. Lines depict the threshold value of productivity (z) for each level of assets (a) and a given value ofmicro-credit and unemployment benefits. The agent chooses self-employment if productivity is above the threshold.
Unlike poor agents, wealthy agents are not sensitive to the level of unemployment
benefits. Being able to self-insure against income risk, these agents choose self-employment
only when their entrepreneurial income would be sufficiently high relative to their po-
tential labor income. As a consequence, there is a positive selection into self-employment
based on the earning potential of agents, with only high-productivity and high-wealth
agents opting into self-employment.10 The same mechanism is present for poor agents
only when they are insured against unemployment.
The mechanisms we highlight have important implications for the effects of different
policies, especially for policies targeted to poor agents, such as unemployment insurance
or micro-finance. As agents opt into self-employment to escape unemployment, they form
a mass of “disguised unemployed, or forced entrepreneurs” (Breza, Kaur, and Shamdasani,
2017). These agents lower overall productivity by diverting resources from the labor mar-
ket to their own unproductive endeavors. How large this group of agents is depends on
the density at the bottom of the wealth distribution, and, crucially, on the access to insur-
10The selection into self-employment occurs for the same reasons described in Buera, Kaboski, and Shin(2011), where there is no unemployment (p = 1), and no uncertainty over wages. The same pattern is sharedby many models in the macro-development literature. See, for instance, Buera, Kaboski, and Shin (2015) andreferences therein.
80
ance against income risk and the access to credit markets. As Figure 2.1 shows, transfers,
such as unemployment benefits, directly affect the selection into self-employment by pre-
venting unproductive agents from becoming self-employed. Thus the overall productiv-
ity among self-employed agents increases, as does the supply of labor in the economy.11
Other policies, such as micro-finance, also affect the selection into self-employment. To
illustrate this, we extend the simple setup described above to allow self-employed agents
access to kmc units of seed capital, which are given to them to jump-start their business.
This changes self-employed output to: f (a, z |kmc) = z (a + kmc)α. Figure 2.2 shows the
new threshold values for productivity with and without unemployment benefits. Despite
the simplicity of the setup, it is clear that, along with benefiting businesses of productive
entrepreneurs, access to micro-finance changes entry into self-employment by making it
attractive for less-productive agents, potentially reducing allocative efficiency. This mech-
anism is well known in the literature (see, for instance, Buera, Kaboski, and Shin (2017)),
but there has been little emphasis on the role of unemployment risk in determining the
magnitude of the effect on productivity. Absent another form of insuring against unem-
ployment, the access to resources tied to some form of entrepreneurial activity can lead a
considerable mass of agents to opt into self-employment despite having low-productivity
projects.
In section 3.2 we extend the setup discussed above into a quantitative occupational
choice model with unemployment risk and discuss more policy implications. But be-
fore we discuss the model in detail we turn to empirical evidence characterizing the
self-employed in developing economies that provides support for the mechanisms we
highlight.
11The potential of productivity gains from unemployment insurance has been explored before; see, forinstance, Acemoglu and Shimer (1999, 2000). As in our case, the gains come from allowing for longer searchand better selection.
81
2.2 Empirical evidence
In this section we characterize some relevant features of self-employment in devel-
oping countries. We study both Mexican and Indian data, but we focus our analysis on
Mexico.12 Mexico is in fact representative among developing countries in the level of self-
employment, and it offers high-quality data that allow us to explore the composition of
the workforce and transitions in and out of self-employment.
Taken together, our findings are consistent with the prevalence of self-employment out
of necessity in Mexico. By this we mean individuals who opt into self-employment when
facing low-income spells (e.g., caused by unemployment), like those discussed in the pre-
vious section (see Figure 2.1). Mexico has a higher self-employment rate than developed
countries like the U.S., but the self-employed in Mexico are concentrated among the coun-
try’s lowest-earning individuals, most of whom would not be considered productive en-
trepreneurs. The opposite is true in the U.S. The higher Mexican self-employment rate is
shaped in particular by a high transition rate from unemployment to self-employment
(as a result, Mexico has a lower unemployment rate than the U.S.). These transitions are
even more likely for individuals who are income-constrained, indicating that the self-
employment varies in response to how strong these constraints are.
The features of the self-employed we highlight have direct implications for modeling
choices and the effects of development policies. In particular, models of self-employment
without unemployment risk or with complete risk sharing are strongly rejected by the
data, mainly because of their inability to reproduce the concentration of self-employed
among the lowest-earning individuals. These models cannot also reproduce the reaction
of wages and workforce composition to job-guarantee programs. We expand on this in
12Indian data complement our analysis of the Mexican self-employed by allowing us to study the effectsof a major job-guarantee program in India, the NREGA. We test whether self-employment is being drivenby individuals taking up self-employment out of necessity, rather than by individuals who are particularlyattached to, or adept at, their entrepreneurial activities. We find that the implementation of the program islinked to a decrease in self-employment and an increase in unemployment. Consistent with our hypothesis,experimental evidence shows that self-employment masks the real level of slack in the labor market indeveloping countries (Breza, Kaur, and Shamdasani, 2017). We present the results in Appendix 2.7.
82
Labor Status Our Sample General Population U.S.Worker 68.0% 57.9% 80.7%Unemployed 2.6% 3.9% 6.3%Self Employed 29.5% 38.1% 12.9%
Table 2.1: Workforce Composition
Note: The data for the Mexican general population are taken from the world development indicators (WDI). The datafor the U.S. are taken from the current population survey (CPS).
section 2.4.
Our main analysis is based on the Encuesta Nacional de Ocupacion y Empleo (ENOE),
a household survey administered by the National Institute of Statistics and Geography
(INEGI) in Mexico.13 The ENOE includes a rotating panel of responding households who
participate in the survey for up to five quarters. We restrict our attention to males aged
23 to 65 who are head of household and live in one of Mexico’s ten largest municipalities.
We analize data from 1995.Q1 to 2015.Q4. In total we study 250,000 individuals and have
around 1 million observations. We define the self-employed as agents who report working
in their own (or their family’s) business. Table 2.1 shows the composition of the labor force
in our sample, in the whole Mexican economy, and in the U.S. over the period 1995-2015.
Our sample behaves in a similar way to the overall Mexican labor force; we reproduce the
differences mentioned above between the U.S. and Mexico in terms of self-employment
and unemployment.
Our findings match previous studies on Mexican entrepreneurship, which highlight
that “[a] high level of self-employment, combined with the predominance of micro-enterprises,
is a distinctive feature of entrepreneurship in Mexico” (OECD, 2012). In fact, Mexico has an
enterprise birth rate double that of the U.S. and a self-employment rate of around 35
percent; more than 90 percent of Mexican companies have fewer than nine employees, in
comparison with 60 percent in the U.S.
We now turn to transitions in the Mexican labor market. Table 2.2 reports the average
13For further information see http://en.www.inegi.org.mx/proyectos/enchogares/historicas/enoe/.
83
Worker Unemployed Self-EmploymentWorker 90.2% 1.7% 8.1%Unemployed 47.1% 26.7% 26.9%Self-Employment 19.2% 2.0% 79.0%
Table 2.2: Quarterly Transition Rates
Note: The figure characterizes the occupational choice of the agent for different levels of unemployment benefits. Linesdepict the threshold value of productivity (z) for each level of assets (a) and a given value of unemployment benefits.The agent chooses self-employment if productivity is above the threshold.
quarterly transition rates of employed, unemployed, and self-employed individuals. The
high self-employment rate reported in Table 2.1 is explained by high transition rates into
self-employment (8.1 percent of the employed and 26.9 percent of the unemployed tran-
sition to self-employment in a given quarter). On the other hand, the low unemployment
rate is explained by a low transition rate into unemployment of about 2 percent, coupled
with a high transition rate out of unemployment.14 In Appendix 2.10.1 we provide more
evidence showing that the high transition rate from unemployment to self-employment
is not due to observable differences between individuals. To do so, we follow the same
strategy as Katz and Krueger (2017). We find that the transition rate of unemployed agents
to self-employment is 20.9 percentage points higher than thate exhibited by comparable
employed individuals (Table 2.8).15
The observed composition of the labor market (high self-employment coupled with
low unemployment) and the transition rates in the Mexican labor market are both consis-
tent with unemployment being intolerable for individuals. Yet it is still unclear what type
of self-employment is most prevalent in Mexico, and what forces determine the high tran-
14At a quarterly frequency we are unable to observe short term unemployment spells. Crucially for us,these include not only workers who are rehired within the same quarter, but also workers who switch toself-employment after losing their job. These factors inflate the transition rate from employment to self-employment and deflate the transition from unemployment to self-employment. Regardless, the behaviorof the latter type of switchers is consistent with the idea of self-employment out of necessity (as discussedin section 2.1).
15Our results align with those of Katz and Krueger (2017) for the U.S. They find that unemployed indi-viduals are more likely to transition to an alternative work arrangement than agents who are employed. Al-ternative work arrangements (e.g., working for Uber or TaskRabbit) play a similar role as self-employmentin Mexico—namely, offering a self-procured source of income.
84
sition rates into self-employment. In the following two sections we tackle these questions.
Section 2.2.1 further characterizes the type of self-employed individuals who are present
in Mexico. We show that the distribution of the self-employed in Mexico is concentrated
among low-earning individuals, rather than among high-earners as in the U.S., indicating
the prevalence of low-productivity self-employed. In section 2.2.2, we ask whether more
income-constrained individuals are more likely to transition into self-employment. This
informs us of about the mechanisms laid out in section 2.1. We do in fact find that indi-
viduals who have less access to outside sources of income are more likely to transition to
self-employment.
2.2.1 Self-employment is concentrated among low earners
We first characterize the prevalence of different forms of self-employment across de-
veloping and developed countries. The main hurdle in describing the self-employed is
that they encompass agents engaging in different economic activities. Most notably, some
self-employed are productive entrepreneurs who own (and sometimes manage) large
firms, some operate small businesses (e.g., mom-and-pop shops), while others engage in
unproductive endeavors that only provide subsistence income. To overcome this hurdle
we examine the share of self-employed agents by percentile of the earnings distribution
for Mexico and the U.S. This approach allows us to get a snapshot of the concentration of
self-employed of various types without having to adhere to any predetermined grouping.
Figure 2.3 shows the results.16
Self-employment is more prevalent in the tails of the earnings distribution, with both
countries exhibiting a U-shaped relation between the self-employment rate and earnings
despite differences in levels (see Table 2.1). Yet the relation differs between the two coun-
16To compute Figure 2.3 we first run a regression of the form log(earni,t) = α + γt + βXi,t + ηi,t , whereearni,t corresponds to the earnings of individual i at time t, and X is a vector of individual-level controls.We rank ηi,t and classify them in bins of 3 percent of the sample, and then compute the self-employmentrate in each of these bins. The pattern we report is robust when we use raw earnings instead of controllingfor observables. We use data from the Current Population Survey for the U.S.
85
Figure 2.3: Self-Employment Rate by Percentile of the earnings Distribution
10
20
30
40
50
60
Self E
mplo
ym
ent R
ate
0 10 20 30 40 50 60 70 80 90 100Percentile of Earnings
USA Mexico
Note: The figure reports the share of the population classified as self-employed for bins of the earnings distribution.Each bin corresponds to three percent of the population. The blue squares correspond to U.S. data from the CurrentPopulation Survey (CPS). The orange circles correspond to Mexican data from the ENOE. The horizontal dashed linescorrespond to the average self-employment rate in each country.
tries. Self-employment is more salient for individuals at the bottom of the earnings dis-
tribution for Mexico than for the U.S., while the opposite is true at the upper end of the
distribution, where the increase in the self-employment rate is more marked in the U.S.
than in Mexico.
The difference in the relation between self-employment and earnings is consistent
with the mechanisms sketched in section 2.1. The lack of a safety net, coupled with labor
market frictions, can drive low-productivity agents into self-employment as they search
for viable income options, leading to a high self-employment rate among those at the bot-
tom of the earnings distribution. This contrasts with the implications of having limited
access to capital (due to dysfunctional financial markets or information frictions), which
can help explain why self-employed agents have lower earnings in developing countries,
but are by themselves at odds with the higher level of self-employment and its concentra-
tion at the bottom of the distribution. In fact, we show in section 2.4 that a combination
of labor market and capital market frictions is required to generate the U-shaped relation
between self-employment and earnings.
86
2.2.2 Constrained agents transition more into self-employment
In this section we investigate further the potential reasons for an individual to opt
into self-employment. We ask whether individuals who are more resource-constrained
are more likely to become self-employed. To answer this we focus on unemployed indi-
viduals, both because they are more likely to be constrained than employed individuals,
and because most individuals who transition into self-employment in Mexico come from
being unemployed (see Tables 2.2 and 2.8).
To be clear, there are other forces that affect the decision to become self-employed. For
instance, some individuals may prefer self-employment17 or may perceive themselves
(rightly or not) to have a high entrepreneurial ability.18 Nevertheless, we focus on the
empirical relevance of individuals opting into self-employment out of necessity (i.e., as
an outside option from unemployment). There are two main reasons for this. First, as we
explained earlier, individuals who choose self-employment out of necessity do so based
less on their own entrepreneurial ability and more on their access to forms of income
outside of the labor market. This selection in turn changes the distribution of productivity
across the self-employed, producing a larger share of unproductive small enterprises and
reducing aggregate productivity. Second, the decision to become self-employed out of
necessity can be influenced by policy more directly than by the preferences or ability of
the population, as the example in section 2.1 makes clear.
To test whether more constrained individuals are more likely to transition into self-
employment, we use two variables to proxy for access to additional sources of income: the
presence of a second earner in the household (as in Chetty (2008)), and the receipt of remit-
17This was proposed by Hurst and Pugsley (2016) to explain the patterns of self-employment in the U.S.Self-employment gives people independence at work, gives them control over their work schedules, andallows self-determination of tasks. An individual who values those nonpecuniary benefits can then chooseto be self-employed even if doing so decreases their income.
18Higher ability would increase an individual’s expected earnings (relative to a salaried job) and makeself-employment more attractive. Equivalently, the individual can have traits that reduce her prospects inthe labor market (e.g. a low job-finding rate), inducing her to choose self-employment.
87
tances from relatives living abroad.19 We then estimate the effect of being less constrained
on the transition from unemployment. Tables 2.3 and 2.4 show the results. A consistent
message emerges. Individuals with additional sources of income have a lower transition
rate to self-employment. We interpret these results as indicative that constrained agents
do in fact transition more into self-employment.20
Moreover, we observe that less-constrained individuals are more likely to transition
out of self-employment. See the coefficients on the interaction between being self-employed
and having a second earner in the household in Tables 2.9 and 2.10. Self-employed agents
are on average 2.4 percentage points more likely to transition to employment when they
are able to rely on a second earner. This is precisely the relation we would expect if self-
employment out of necessity were prevalent. The less-constrained self-employed can in
principle devote more time and effort to search activities and transition to a salaried job
for which they might be better suited.
Turning to the results in Table 2.3, we estimate that individuals in a household with a
second earner have a 3.2 percentage point higher probability of transitioning to employ-
ment and a 3.9 percentage point lower probability of transitioning to self-employment
(that is a 17 percent decrease, from 22.2 to 18.3 percent) than individuals without a second
earner. We also test whether the individual’s (self-reported) job search activity changes
with the presence of a second earner. Table 2.11 in Appendix 2.10 presents the results. We
find that most job-search activities (e.g., examining job postings, looking for a temporary
job) are not significantly different for individuals with a second earner. Importantly, there
is no difference in whether agents report being making plans to start their own business.
The only significant differences are that individuals in households with a second earner
are, on average, 1.5 years older, and (presumably as a consequence) less likely to use the
19We thank Sylvain Catherine for suggesting the latter exercise.20The results can also be interpreted as an indication that preferences and ability are not the main drivers
of the transition to self-employment. If they were, we should observe that people with external sources ofincome are more prone to become self-employed, as they could enjoy the nonpecuniary benefits of workindependence or try their luck at entrepreneurship, while not worrying (as much) about low income levels.
88
(1) (2) (3) (4)U→E U→S U→U U→I
Second Earner 0.032*** -0.039** 0.007 -0.000[0.010] [0.018] [0.015] [0.000]
Age -0.008*** 0.003*** 0.005*** 0.000[0.000] [0.000] [0.000] [0.000]
Constant 0.835*** 0.209 -0.044 -0.001[0.301] [0.326] [0.098] [0.002]
Observations 8376 8376 8376 8376Mean Dep. Variable 0.505 0.222 0.272 0.000104Schooling Controls Yes Yes Yes YesTime Fixed Effect Yes Yes Yes YesWeighted Yes Yes Yes Yes
Table 2.3: Second Earner and Transitions from Unemployment
Note: The LHS variable is an indicator variable that takes the value of one if the individual experienced the transitionspecified in each column. U denotes unemployment, E salaried work, S self-employment, and I inactivity. SecondEarner is an indicator variable that takes the value of one if the individual’s partner was an income earner in periodt−1. Standard errors are clustered at the city level. Schooling controls are a set of dummies by education level to controlnonparametrically for education. Time fixed effects are at the year-quarter level. The sample consists of individualswho were unemployed in period t − 1. The regressions are run by weighted OLS. ∗, ∗∗, and ∗∗∗ denote significance atthe 10%, 5%, and 1% level.
internet to find a job.
Table 2.4 presents the results using remittances as a proxy for the resources of the in-
dividual. Individuals who receive remittances in times of unemployment transition at a
lower rate to self-employment. The coefficient, –8 percentage points, is economically sig-
nificant, considering that the mean transition rate is 18.8 percentage points in this sample.
Moreover, we would expect the coefficients in this regression to have an upward bias. It is
reasonable to expect that people who need financial assistance from abroad are also those
who have a lower probability of finding a good job, therefore creating an spurious posi-
tive coefficient in column (2) and a negative bias in column (1).The fact that we observe
the opposite (people who receive remittances transition less to self-employment) is reas-
suring. Of course, we cannot rule out other sources of bias since the receipt of remittances
is not created by exogenous variation across individuals.
As we did for second earners, we also check whether receiving remittances has an
effect on search activities or the intent to start a business. Table 2.12 in Appendix 2.10
presents the results. Receiving remittances has a weak effect overall. It is associated with
89
(1) (2) (3) (4) (5)U→E U→S U→U U→I U→S
Remittances 0.058 -0.080*** -0.033 0.055[0.053] [0.021] [0.040] [0.037]
Age -0.012*** 0.002*** 0.002** 0.008*** 0.001***[0.000] [0.000] [0.001] [0.001] [0.000]
Latent Remittances -0.045[0.036]
Constant 1.237*** 0.147 -0.168*** -0.216 0.177[0.262] [0.202] [0.050] [0.227] [0.114]
Observations 8615 8615 8615 8615 25135Mean Dep. Variable 0.463 0.188 0.256 0.0932 0.188Schooling Controls Yes Yes Yes Yes YesTime Fixed Effect Yes Yes Yes Yes YesWeighted Yes Yes Yes Yes Yes
Table 2.4: Remittances and Transitions from Unemployment
Note: The LHS variable is an indicator variable that takes the value of one if the individual experienced the transitionspecified in each column. U denotes unemployment, E salaried work, S self-employment, and I inactivity. Remittancesis an indicator variable that takes the value of one if the individual reported having received remittances in period t−1.Standard errors are clustered at the city level. Schooling controls are a set of dummies by education level to controlnonparametrically for education. Time fixed effects are at the year-quarter level. The sample consists of individualswho were unemployed in period t − 1. The regressions are run by weighted OLS. ∗, ∗∗, and ∗∗∗ denote significance atthe 10%, 5%, and 1% level.
a lower likelihood of using the internet to look for a job, and a lower likelihood of of
searching for temporary employment; however, it is also associated with a higher likeli-
hood of asking directly for a job.
2.3 Model
In this section we describe a quantitative occupational choice model in which agents
face unemployment risk. The objective of the model is to illustrate the role of self-employment
in shaping the response to various policies in developing economies. We extend the base-
line macro-development model in Buera, Kaboski, and Shin (2015) of employed (E) and
self-employed (S) agents by introducing unemployment (U) and allowing for transitions
between occupations. Occupations differ with respect to their income source and whether
or not agents can freely opt into them. With the aim of being parsimonious while captur-
ing the major forces at play, we assume that agents can freely move into unemployment
90
and self-employment, while they can only become employed following an exogenous job
offer, which we interpret as a stand-in for underlying search frictions in the labor market.
We calibrate the model to match salient features of the Mexican labor market, consistent
with the evidence we presented in section 3.3. In section 2.5 we use the model to con-
duct counterfactual experiments designed to evaluate three major policies that affect the
occupational choice of agents.
The model is of a small open economy populated by a continuum of agents. Time is
continuous and goes on forever. Agents are heterogeneous with respect to their occupa-
tion E,U, S and with respect to their labor efficiency (ε ), productivity (z), and asset hold-
ings (a). If employed, an agent’s labor income is given by wε , where w is the economy-
wide wage rate per efficiency unit of labor. Unemployed agents have zero labor efficiency
and receive a constant income b.21 If self-employed, an agent produces final goods using
capital and labor with a technology indexed by the agent’s productivity (which we also
refer to as the agent’s entrepreneurial ability). The agent’s income is determined by the
profits from operating her technology.
As is standard in the literature, agents have limited access to credit markets. Employed
and unemployed agents face a borrowing limit a ≤ 0. Self-employed agents can borrow
to obtain productive capital, but they face a borrowing constraint that depends on their
assets (which are used as collateral): k ≤ λa. These borrowing constraints capture in-
formation frictions and commitment problems, which we do not model explicitly. See,
among others, Cagetti and De Nardi (2006) and Buera et al. (2011) for micro-foundations
of the borrowing constraint.
As we mentioned earlier, any agent can become self-employed or unemployed at will.
In contrast, transitions to employment are governed by an exogenous process that cap-
tures (in a reduced form) the arrival of job offers. In particular, we assume that an agent’s
21It is possible to think about income while unemployed as coming from home production, or fromtransfers from family members or government agencies. In section 2.5 we take the latter view and examinewhat happens if unemployed income b increases.
91
labor efficiency is zero as long as she is not employed. The agent gets to draw a posi-
tive labor efficiency value following the arrival of an exogenous job offer, which follows
a Poisson process with arrival rate γo, which depends in turn on the agent’s occupation
o ∈ U, S. Once the agent draws a new value for her labor efficiency, she gets to accept
it and become employed, or reject it, maintaining her previous occupation. Finally, em-
ployed agents are subject to job destruction shocks with arrival rate γE .
We aim to keep our modeling of the economy as simple as possible, and as close as
possible to the standard modeling of entrepreneurship in the macro-development litera-
ture (e.g., Buera, Kaboski, and Shin, 2015). Yet we depart from previous models in two
important and intertwined ways. First, we include labor income risk by letting the labor
efficiency of employed agents fluctuate. Second, we prevent agents from having access to
employment at will by including an unemployment state with no labor income.22 Without
these features, employment serves as an outside option from self-employment (where in-
come is volatile, following changes in productivity). Consequently, the model is unable to
produce the type of low-earning self-employed agent that characterizes self-employment
in developing economies. In contrast, self-employment serves in our model as an outside
option for unemployed agents, as well as for agents with high entrepreneurial ability. This
allows us to capture the joint distribution of self-employment and earnings, as seen in Fig-
ure 2.3. Moreover, the behavior of agents opting into self-employment plays an important
role in the evaluation of various policies, as we suggested in section 2.1. We expand on
the fit of the model and its policy implications in sections 2.4 and 2.5.
We solve for the stationary equilibrium of the model. Appendix 2.8 presents a version
of the baseline model without unemployment. This alternative model is a useful point of
reference for judging the performance of the model, as we show in section 2.4. Appendix
2.9 discusses the computational implementation of the model’s solution.
22Most of the literature assumes labor income to be common to all agents (given by a market wage), andallows agents to opt into the employment state in a frictionless manner, instead introducing costs to engagein entrepreneurial activities.
92
2.3.1 Stochastic Processes
We assume that labor efficiency, ε , and productivity, z, follow independent Poisson
processes with arrival rates γε and γz respectively. Upon arrival, the agent draws a new
value for the state (either ε or z) from a conditional probability distribution Prε (ε′|ε ) or
Prz (z′|z). When an unemployed or a self-employed agent receives a job offer, events with
Poisson arrival rates γU and γS, she draws a value of labor efficiency from PrU (ε ) or
PrS (ε ) respectively.
2.3.2 Agent’s Problem
The problem of an agent depends on her occupation. We discuss each occupation in
turn. In what follows we denote as V o the value of an agent in occupation o ∈ E,U, S,
taking into account the occupational choice of the agent, and we denote as V o the value
that the agent would receive if she were to remain in occupation o.
Employed agents The employed receive an income of wε and are subject to job destruc-
tion shocks that arrive at a rate γE . If the shock arrives, the agent becomes unemployed.
The agent can also choose to become self-employed at any time. The value for an em-
ployed agent who remains employed is given by V E :
ρV E (a, z, ε ) = maxc
u (c) + V Ea (a, z, ε ) a + γE
(VU (a, z) − V E (a, z, ε )
)(2.1)
+γz∫ (
V E (a, z′, ε
)− V E (a, z, ε )
)dPrz (
z′|z)
+γε∫ (
V E (a, z, ε′
)− V E (a, z, ε )
)dPrε
(ε′|ε
)s.t. a = wε + ra − c a ≥ a
Unemployed agents The unemployed receive an income of b and are subject to job of-
fers that arrive at a rate γU . They are free to reject an offer depending on their current
93
assets and productivity, and on the labor efficiency they would have if employed. The
agent can also choose to become self-employed. The value for an agent who remains un-
employed is given by VU :
ρVU (a, z) = maxc
u (c) + VUa (a, z) a (2.2)
+γU∫
maxV E (a, z, ε ) − VU (a, z) , 0
dPrU (ε )
+γz∫ (
VU (a, z′
)− VU (a, z)
)dPrz (
z′|z)
s.t. a = b + ra − c a ≥ a
Self-employed agents Self-employed agent sreceive income from profits, π (a, z), gen-
erated by their productive activities. Self-employed agents receive job offers at a rate γS.
Upon arrival of an offer, the agent is free to reject it. The agent can also choose to become
unemployed. The value for an agent who continues being self-employed is V S:
ρV S (a, z) = maxc
u (c) + V Sa (a, z) a (2.3)
+γS∫
maxV E (a, z, ε ) − V S (a, z) , 0
dPrS (ε ) .
+γz∫ (
V S (a, z′
)− V S (a, z)
)dPrz (
z′|z)
s.t. a = π (a, z) + ra − c a ≥ a
The optimal consumption decision can be found in all cases from the first order con-
dition of the agent’s problem (see Achdou et al. (2017)). Letting o ∈ E,U, S denote the
occupational state of the agent, we have:
c = u′−1 (
V oa). (2.4)
It is only left to account for the occupational choice of the agents. At every instant the
value of an agent must reflect the upper envelope of the choices available to her. This
94
is akin to a value-matching condition in optimal stopping-time problems (Stokey, 2009).
The following conditions must hold:
V E (a, z, ε ) = maxV E (a, z, ε ) , VU (a, z) , V S (a, z)
(2.5)
VU (a, z) = maxVU (a, z) , V S (a, z)
(2.6)
V S (a, z) = maxVU (a, z) , V S (a, z)
(2.7)
The last two conditions imply that unemployment and self-employment must give the
same value to the agent; this is because the agent can instantaneously move between the
two occupations, so any difference in value is in a sense arbitraged away.
For future reference, let χoo′ be an indicator function for the occupational choice of the
agents. Then for the employed we have:
χEo′ (a, z, ε ) =
1 if V E (a, z, ε ) = V o′ (a, z)
0 otherwise,
where o′ ∈ U, S. For the unemployed and the self-employed we have:
χUS (a, z) =
1 if VU (a, z) = V S (a, z)
0 otherwiseand χSU (a, z) =
1 if V S (a, z) = VU (a, z)
0 otherwise.
Of course χoo = 1 indicates no change in the agent’s occupation.
2.3.3 Self-employed production technology
The profits of a self-employed agent are given by:
π (a, z) = maxk≤λa , n≥0
z(kαn1−α
) ν− wn − (r + δ) k
, (2.8)
95
where α ∈ (0, 1) and ν ≤ 1. The solution to the profit maximization problem when ν < 1
is:
n (a, z) =
(ν (1 − α) z
w
) 11−(1−α)ν
(k (a, z))αν
1−(1−α)ν , (2.9)
with capital demand given by:
k (a, z) = minν
11−ν z
11−ν
(α
r + δ
) 1−(1−α)ν1−ν
(1 − α
w
) (1−α)ν1−ν
, λa. (2.10)
If ν = 1 the solution is:
n (a, z) =
((1 − α) z
w
) 1α
k (a, z) , with k (a, z) = λa1z≥z . (2.11)
The threshold z =(
r+δα
)α (w
1−α
)1−αis the minimum value of z for which there is produc-
tion.
2.3.4 Labor market
The labor market is formally frictionless with efficiency units of labor being trans-
acted at a wage rate w. We assume that unemployed and self-employed agents have no
efficiency units of labor to transact (i.e., ε = 0), and only get them following the arrival
of a job offer. Total labor supply (in efficiency units) is then given by the integral over the
efficiency units of employed agents:
N S =
∫εdGE , (2.12)
where GE is the distribution of employed agents in the economy.
The only sources of labor demand are the businesses of the self-employed. Total labor
demand is thus given by:
N D =
∫n (a, z) dGS , (2.13)
96
where GS is the distribution of self-employed agents in the economy.
It is convenient to sketch the main mechanisms at work in the labor market for the dis-
cussions in sections 2.4 and 2.5. Consider then an increase in the wage rate. First, existing
firms decrease their labor demand. This effect is accompanied by an increase in the num-
ber of self-employed agents who accept job offers because their self-employed income
goes down and their employed income increases. The change in occupational choice fur-
ther decreases labor demand while also increasing labor supply. Provided that the job
offer arrival rate is higher for unemployed agents(γU > γS
)there is an additional effect:
some self-employed agents opt into unemployment to increase their chances of a salaried
job. The net effect is, as expected, a decrease in the net demand for labor.
2.3.5 Equilibrium
A stationary equilibrium for this economy is a set of value functionsV o, V o
o∈E,U,S
,
along with an optimal consumption function coo∈E,U,S, labor and capital demand from
self-employed n, k, prices r,w and a distribution of agents for each occupation Goo∈E,U,S,
such that:
(i) Value functions are consistent with the agent’s optimization. That is, they satisfy
equations (2.1)-(2.3) and equations (2.5)-(2.7).
(ii) Consumption (and thus asset accumulation) is consistent with the agent’s optimiza-
tion. That is, it is given by equation (2.4).
(iii) Capital and labor demand solve the self-employed’s profit maximization problem.
That is, they are given by (2.9) and (2.10) if ν < 1, or by (2.11) if ν = 1.
(iv) Labor market clears: N S = N D, where total labor supply is given by (2.12), and total
labor demand by (2.13).
(v) The interest rate is given by the international interest rate r?.
97
(vi) The distribution of agents is stationary. For this, the densities gE , gU , and gS of
employed, unemployed, and self-employed agents must satisfy the system of Kol-
mogorov Forward Equations (KFE) defined by:23
0 = −∂
∂a
[agU (a, z)
]+
∫χEU (a, z, ε ) gE (a, z, ε ) dε + χSU (a, z) gS (a, z) (2.14)
− χUS (a, z) gU (a, z) − γUPrU (ε ) gU (a, z) 1VE (a,z,ε )>VU (a,z)
− γz∫
Prz (z′|z
)gU (a, z) dz′ + γz
∫Prz
(z |z
′)gU (
a, z′)
dz′
0 = −∂
∂a
[agS (a, z)
]+
∫χES (a, z, ε ) gE (a, z, ε ) dε + χUS (a, z) gU (a, z) (2.15)
− χSU (a, z) gS (a, z) − γSPrS (ε ) gS (a, z) 1VE (a,z,ε )>VS (a,z)
− γz∫
Prz (z′|z
)gS (a, z) dz′ + γz
∫Prz
(z |z
′)gS (
a, z′)
dz′
0 = −∂
∂a
[agE (a, z, ε )
]− γE − χEU (a, z, ε ) gE (a, z, ε ) − χES (a, z, ε ) gE (a, z, ε ) (2.16)
+ γUPrU (ε ) gU (a, z) 1VE (a,z,ε )>VU (a,z)
+ γSPrS (ε ) gS (a, z) 1VE (a,z,ε )>VS (a,z)
− γε∫
Prε(ε′|ε
)gE (a, z, ε ) dε′ + γε
∫Prε
(ε |ε
′)gE (
a, z, ε′)
dε′
− γz∫
Prz (z′|z
)gE (a, z, ε ) dz′ + γz
∫Prz
(z |z
′)gE (
a, z′, ε)
dz′
23The density functions are also such that: 1 =∫ ∫ (∫
gE (a, z, ε ) dε + gU (a, z) + gS (a, z))
da dz. So∫gE (a, z, ε ) da dz dε gives the mass of employed agents, and
∫go (a, z) da dz for o ∈ U, S gives the mass
of unemployed and self-employed agents.
98
2.3.6 Discussion of modeling assumptions
We have already mentioned the rationale behind some of our modeling choices, but it
is worthwhile to further discuss the assumptions we place on the model before moving
to the quantitative implications of the model. In particular, we want to discuss two key
assumptions about the functioning of the labor market. The first one is that labor demand
comes exclusively from the self-employed. This is clearly not the case in reality, and it im-
poses a tight link between labor demand and labor supply. In the model, increases in the
labor supply require reassigning workers to employment, and that reduces the number
of self-employed, in turn reducing labor demand. Because of this link, equilibrium wages
become very responsive to changes in the occupational choices of agents (as we see in
sections 2.5.2 and 2.5.3). This link can be weakened by introducing a corporate sector that
offers an additional source of labor demand (as in Kitao (2008)), or by separating the labor
demand completely from the problem of the self-employed, instead having a new sector
that mixes entrepreneurial output with labor to produce final goods (as in Guvenen, Kam-
bourov, Kuruscu, Ocampo, and Chen (2019)). We choose not to pursue these extensions
because our objective with the model is to highlight the mechanisms behind the mass of
low-productivity self-employed that characterizes developing economies, while keeping
the model as simple as possible.
The second assumption is that there is no endogenous response of job-finding rates(γU, γS
)to changes in the number of job searchers or the productivity (scale) of firms.
As we mentioned above, we chose this modeling of labor market frictions because we are
aiming for parsimony and comparability with other models used in the macro-development
literature. This assumption also simplifies the computational burden of the model.24 Of
course, this assumption has consequences, the main one is the muting of general equilib-
24We see the computational advantages of the model as more than a mere convenience. The way in whichwe pose the model allows practitioners to use standard tools from dynamic programming to solve for themodel in general equilibrium.
99
rium effects that can affect the response to policy changes.25 Nevertheless, these general
equilibrium effects are likely to strengthen the results we provide for the three policies
we consider. We further discuss this issue in section 2.5.
In addition, there are two assumptions about the problem of the self-employed that
we also wish to discuss. The first one is that the self-employed have access to capital at the
global (risk-free) interest rate. This interest rate is lower than the rate that entrepreneurs
in developing countries actually face. As a consequence, self-employment in the model
becomes more attractive and the optimal scale of businesses increases. Even though this
tends to generate larger businesses, the quantitative effect of the lower interest rate is
small for the least productive self-employed. The optimal scale at the bottom of the pro-
ductivity distribution is close to zero in any case. Because we are mostly concerned with
capturing the mass of low-productivity self-employed, we don’t consider this assumption
to be too stringent on the model.
Finally, we assume that all the self-employed operate the same technology, differing
only in productivity, and that there are no installation costs required for agents to be-
come self-employed. Installation costs are generally understood to vary with the type of
technology being adopted by the entrepreneur, as in Midrigan and Xu (2014) or Buera
et al. (2011), with better technologies having higher installation costs. In this case, the low-
asset low-productivity agents are likely to opt for a less good technology, which, we argue,
should have close to zero cost of adoption. Therefore, introducing a menu of technologies
and installation costs would only strengthen our results by making low-productivity self-
employment more attractive for low-wealth agents. Because of this, we choose to abstract
from this margin, keeping the model simple while still being able to capture the presence
of low-productivity entrepreneurs.
25For instance, as we show in section 2.5.2, if there is an increase in unemployment benefits the numberof unemployed workers increases, reducing labor demand. We do not take into account the effect of thisincrease on market tightness, which would spur vacancy creation among firms still in operation. Absentthese effects, all the adjustment in the labor market has to come through the wage rate.
100
2.4 Quantitative analysis
We now turn to the ability of the model to match salient features of self-employment
in developing economies. As we show below, the model is successful in most dimensions.
Further, the data strongly reject an alternative version of the model without unemploy-
ment risk (Appendix 2.8), while our baseline model is shown to be compatible with the
empirical evidence presented in section 3.3 and Appendix 2.7.
To match the data, we calibrate the model by choosing parameters in two ways. A
first group of parameters is externally calibrated, with values taken from the literature
or chosen independently of the equilibrium outcomes of the model. A second group of
parameters is chosen to match targeted moments of the earnings distribution, workforce
composition, and transition rates across occupations from the Mexican data discussed
in section 3.3. Before discussing the parameter values, we define the parameterization of
the stochastic processes governing productivity and labor efficiency. After this is done, we
evaluate the model’s performance in terms of matching targeted and untargeted moments
of the data.
Stochastic processes and discretization of states We discretize the processes for pro-
ductivity (z) and labor efficiency (ε) so that the conditional probability distributions
Prz (z′|z) and Prε (ε′|ε ) are characterized by stochastic matrices of dimensions nz × nz
and nε × nε respectively. To keep parameterization of the processes parsimonious, we use
the method proposed in Rouwenhorst (1995) to discretize AR(1) processes for log(z) and
log(ε). This reduces the number of parameters to choose from nz(nz −1) + nε(nε −1) to just
four, namely the standard deviation and persistence of each process: σz, ρz, σε, ρε . How-
ever, the persistence of the process (which determines the diagonal terms of the transition
matrices) cannot be separately identified from the arrival rate of productivity or labor ef-
ficiency shocks (γz and γε ). We set the arrival rates to 1 and choose the persistence along
with other parameters to match the set of targeted moments (discussed below). Finally,
we set the mean of the processes to z and ε . We choose the values of z and ε jointly with
101
the other internally calibrated parameters discussed below.
Discretizing the processes in this way greatly simplifies the calibration of the model,
although it comes at the cost of higher computational requirements since it makes the ma-
trices involved in the finite difference method less sparse (Appendix 2.9). In consequence,
we choose to set the grid size for z and ε to eleven and thirteen nodes respectively. We
experimented with finer grids and verified that our results do not depend on the partic-
ular size we ch0ose. The other grid that affects the computation of the model is the grid
on assets. We use a 120 node grid with curvature that increases density for low levels of
assets. The limits of the grid are given by the borrowing constraint (a) and an asset barrier
(a). We set a = 10−5, which ensures we don’t face numerical issues, and we set a = 200;
as Figure 2.5b makes clear, this upper bound does not affect the distribution of assets in
the equilibrium of the model. The asset grid is given by:
ai = a +
(i − 1
na − 1
)ηa(a − a) for i ∈ 1, . . . , na. (2.17)
The values of all computational parameters are presented in Figure 2.5b.
Externally calibrated parameters We set a number of parameters to values common
in the literature or that match features of the Mexican economy independently of the
equilibrium. Table 2.5a presents the parameter values we use in our baseline model. The
discount factor is taken from Moll (2014) to match a 5 percent annual discount rate. To
achieve a stationary distribution of assets, we need ρ − r? > 0. We set this gap equal
to 0.05 (at the annual frequency) as in Bianchi (2011), by setting r? = 0.26. The degree
of decreasing returns (ν) is taken from Midrigan and Xu (2014). The curvature of the
utility function (σ) is set to 2, and the power of capital in the self-employed production
technology (α) is set to 1/3, consistent with standard values used in the literature. Finally,
we set the equity constraint of the self-employed (λ) to match a debt-to-capital ratio of 42
percent, consistent with the Mexican data.26Other studies have used lower values for the gap; for instance, ? set it to 0.02.
102
Externally Calibrated Parameters Internally Calibrated ParametersParameter Value Parameter Value
r? International Interest Rate 0 b Unemployment Income w · 10−5
ρ Discount Factor 0.0125 γE Job Destruction Arrival Rate 0.09σ CRRA Parameter 2 γU Job Offer Arrival Rate - U 0.80α Technology - Capital Share 0.3 γS Job Offer Arrival Rate - S 0.60δ Capital Depreciation 0 ε Labor Efficiency- Base Value 0.10ν Technology - Decreasing Returns 0.85 σε Labor Efficiency - Variance 0.09λ Equity Constraint 1.42 ρε Labor Efficiency - Persistence 0.90γε Labor Efficiency - Arrival Rate 1 z Productivity - Base Value 1.00γz Productivity - Arrival Rate 1 σz Productivity - Variance 0.12
ρz Productivity - Persistence 0.90
(a) Model Parameters
Parameter Valuea Borrowing Constraint 10−5
a Asset Barrier 200ηa Asset Grid curvature 2na Asset Grid Size 120nε Labor Efficiency Grid Size 13nε Productivity Grid Size 11
(b) Computational Parameters
Table 2.5: Parameters
Internally calibrated parameters The remaining parameters are internally calibrated to
jointly match a set of eleven moments from the Mexican data. The moments we target
are the standard deviation of log-earnings for the self-employed and the employed, the
composition of the workforce (share of unemployed, self-employed, and employed), and
the quarterly transition rates between occupations. Even though all parameters are cali-
brated jointly, it is instructive to think of the variance of the stochastic processes (σz and
σε ) as matching the standard deviation of earnings, the unemployment income (b), and
the mean of the stochastic processes (z and ε) as matching the composition of the work-
force, and the persistence of the stochastic processes (ρz and ρε ) and the arrival rates of
shocks (γE , γU and γS ) as matching the transition rates. The values of the parameters are
presented in Table 2.5a, and the value of the targeted moments in the data and the model
are presented in Table 2.6, which we discuss below.
103
Std. Dev. log-Earnings Workforce (%) Transitions (%)Data Model Data Model Data Model
0S0 0.44 0.88 0U0 2.6 2.2 U2S 26.9 6.8E 0.25 0.26 S 29.5 28.5 U2E 47.1 52.3
E 68.0 69.3 S2U 2.0 0.8S2E 19.2 14.5E2U 1.7 1.6E2S 8.1 6.1
Table 2.6: Moments for Calibration: Targets and Outcomes
Note: The table reports all the moments targeted in the calibration. Targets are reported in the “Data” columns. Themoments implied by the model are reported in the “Model” columns.
Model performance Overall, the model is able to match the targeted moments, as seen
in Table 2.6. However, there are two important exceptions. The model overestimates the
standard deviation of log-earnings for the self-employed, and it underestimates the tran-
sitions from unemployment to self-employment. The high variance of the earnings of
the self-employed does not overly concern us, given that the data from the ENOE are
likely to undersample high earners, particularly those among the self-employed, biasing
down the estimate of the standard deviation obtained from the data. Moreover, the higher
variance of self-employment earnings plays two roles in the model in matching other rel-
evant moments. First, it makes self-employment more attractive, helping to match the
share of self-employed agents in the economy. Second, it increases the mass of “highly
productive” self-employed, which generates additional labor demand (this link between
self-employment and labor demand is overly tight in the baseline model as explained in
section 2.3.6). On the other hand, we consider the low transition rate from unemploy-
ment to employment to be a shortcoming of the current parameterization of the model.
We discuss its implications in the next section as they become relevant.
The model also fits relevant untargeted moments—most importantly, the distribution
of the self-employed by earnings. Figure 2.4 presents the share of self-employed for each
decile of the earnings distribution. The model replicates the U-shaped relationship be-
tween earnings and the self-employment rate, with the self-employed concentrated at
the lower and upper ends of the earnings distribution. Yet the share of self-employed
104
Figure 2.4: Self-Employment Rate by Decile of the Earnings Distribution
1 2 3 4 5 6 7 8 9 10
Earnings Deciles
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Sh
are
of
Self-E
mp
loye
d A
ge
nts
Baseline ModelNo Unemployment
Note: The figure reports the share of self-employed agents for each decile of the earnings distribution. The orangecircles correspond to the baseline model with unemployment risk. The blue diamonds correspond to the alternativemodel without unemployment risk.
agents for the top decile is overestimated relative to what was found in Figure 2.3. As we
mentioned above, this is in part due to the undersampling of high-earning self-employed
individuals in the data, and in part due to the relatively high value of the variance of
self-employed earnings in the model, which helps to generate more high-productivity
self-employed.
The joint distribution of self-employment and earnings is an important feature of the
data because of its power in distinguishing between different specifications of the model
(in the spirit of ?). Our baseline model with unemployment risk is consistent with the data;
in contrast, the simplified version of the model without unemployment risk, and with
free mobility between employment and self-employment, is not. The main features of
the simplified model are present in most other models of self-employment in the macro-
development literature (e.g., Buera et al., 2011, 2015, 2017; Midrigan and Xu, 2014). We
calibrate the simplified model to match the same moments as our baseline model (except
for those involving unemployment). Figure 2.4 makes clear that the model without unem-
ployment is unable to capture the joint distribution of self-employment and earnings—
specifically, the prevalence of low-earning self-employed agents. In this sense this model
105
Figure 2.5: Model Performance
(a) Self-employment occupational choice
0 5 10 15 20 25 30
Assets
0
0.5
1
1.5
2
En
tre
pre
ne
uria
l A
bili
ty
Self-Employment Region
Unemployment Region
UnemployedEmployed (Av. W)Employed (High W)
(b) Wealth distribution
0 10 20 30 40 50 60 70 80 90 100
Assets
0
0.02
0.04
0.06
0.08
0.1
0.12
0.14
0.16Asset Distribution
GU
GS
GE
G
Note: The figure shows equilibrium outcomes of the baseline model. The left panel presents the occupational choice ofself-employment. Lines depict the threshold value of productivity (z) for each level of assets (a) and a given value oflabor efficiency (zero for the unemployed). The agent chooses self-employment if productivity is above the threshold.The right panel presents the wealth distribution of agents in the model along with the conditional wealth distributionsby occupation.
specification is rejected by the data. We return to this issue in section 2.5.1 where we show
that the simplified model is also at odds with the response of the economy to the imple-
mentation of job-guarantee programs.
The key to generating the mass of self-employed agents at the bottom of the earn-
ings distribution is the occupational choice of the unemployed. Figure 2.5a presents the
productivity thresholds for unemployed and employed agents in the model. The same
mechanisms laid out in section 2.1 translate into our baseline model (see Figure 2.1).
Poor unemployed agents engage in self-employment regardless of their productivity. The
model without unemployment risk cannot generate low-earning self-employed because
the selection into self-employment ensures that only agents with high enough earnings
choose to be self-employed, just like the employed agents in Figure 2.5a. The success of
the model in matching the patterns of self-employment comes from the behavior of the
unemployed, coupled with a distribution of assets concentrated in the left tail (see Figure
2.5b).
106
2.5 Policy analysis
Self-employment is important for determining the response of the economy to various
policies, in particular those intended to increase the productivity of enterprises in devel-
oping economies or those providing insurance in the labor market. As noted in section
2.1, policies and self-employment interact through agents’ occupational choices. Policies
shape the incentives of agents to opt into self-employment, in turn changing the makeup
of firms and workers in the economy. Moreover, the response of the economy to certain
policies can prove helpful in distinguishing between different model specifications and
highlighting the relevant mechanisms at work. We expand on these themes in this section
by examining the response of the model to three distinct policies: job-guarantee programs,
unemployment insurance, and micro-finance.
2.5.1 Job-guarantee programs
Job-guarantee programs are used across developing countries as a tool to provide in-
come and potentially jump-start careers for individuals in high-unemployment regions.
In general, these programs work by increasing labor demand through government-provided
jobs that pay (minimum) market wages and involve low-skilled tasks, typically in cler-
ical or maintenance occupations in government outposts. Job-guarantee programs like
India’s NREGA program (described in section 3.3 and Appendix 2.7) can be massive. The
NREGA program reached 53 million beneficiaries in 2010-2011 alone.
The scope of this type of government intervention raises questions about its implica-
tions for labor markets, in particular for the composition of the workforce and its effects
on market wages. The effect on market wages changes the cost of providing programs
of this nature and is indicative of the level of slack in labor markets. In Appendix 2.7 we
show that the implementation of the NREGA program is associated with a recomposition
of the workforce away from self-employment and toward more employment and more
107
unemployment. In addition, experimental evidence for India on the effects of labor de-
mand shocks on wages shows that there is virtually no response of wages to changes in
labor demand (Breza et al., 2017). The limited effect on wages of increases in labor de-
mand points to the role of self-employment as a form of slack in the labor market. The
intuition is that wages do not react to an increase in labor demand when agents are willing
to opt out of self-employment and into salaried jobs at current wages.
Can the model reproduce the response in workforce composition and wages to an
increase in labor demand? To test this we introduce government demand for labor ngov,
so that total labor demand is
N d =
∫n?(a, z)dGS + ngov . (2.18)
We then solve for the new market-clearing wage.27 We show that the response of the
economy to labor demand shocks, as in job-guarantee programs, is informative about
alternative specifications of the model. In particular, we show that unemployment risk,
and the selection into self-employment it implies, plays a crucial role in the model’s ability
to reproduce the economy’s response to the labor demand shock.
In response to an increase in labor demand by the government, the model implies a
reallocation of the workforce from self-employment into both higher employment and
unemployment. Government demand amounts to 13 percent of the baseline demand for
efficiency units of labor.28 As Imbert and Papp (2015) find, there is a strong crowding-
out effect on private employment (in this case on self-employment). Private demand
for labor decreases 10.7 percent (self-employment decreases 1.7 percent). However, the
overall demand for labor increases (about 2.5 percent), as does the unemployment share
of the workforce (0.1 percent). These movements are qualitatively in line with the find-
ings of Breza et al. (2017). The decrease in self-employment comes mostly from the low-
27In the spirit of the experimental interventions cited above, and the implementation of the NREGAprogram, we do not introduce taxes to finance the government’s labor demand.
28The size of the shock emulates the experiment by Breza et al. (2017).
108
productive self-employed; because of this the productivity distribution improves relative
to the baseline (in the first-order stochastic dominance sense). Figure 2.9 in Appendix
2.10.2 presents more details.
Crucially, the increase in labor demand is not accompanied by an increase in wages.
The market wage (per efficiency-unit of labor) increases 0.5 percent, implying an “elas-
ticity of wage to labor demand”(
∆%w∆%Nd
)of 0.22. This is consistent with the experimental
evidence referenced above that establishes a low response of wages to increases in la-
bor demand. The presence of unemployment risk and low-earning self-employed agents
play a crucial role in generating this result. When we implement the increase in labor de-
mand in the simplified model without unemployment risk (Appendix 2.8), the increase
in wages required to meet the additional demand is an order of magnitude larger than
what is implied by the experimental evidence, implying a (percentage) change in wages
twice as large as the change in labor demand(
∆%w∆%Nd = 2
). In this sense the response of the
economy to job-guarantee programs is informative when determining the correct specifi-
cation of the model. As with the joint distribution of self-employment and earnings, the
data reject the model without unemployment risk in policy-relevant dimensions.
2.5.2 Unemployment insurance
Another policy often used by governments is the implementation of unemployment
insurance or other forms of safety nets. Generally, these programs are intended to provide
insurance to workers in the event of unemployment spells. However, safety net programs
affect the occupational choice of agents, especially of the self-employed. The example in
section 2.1 highlights how access to unemployment insurance can deter unproductive
agents from engaging in self-employment. While unemployment insurance is not typi-
cally thought of as an instrument for improving productivity, it can do so by changing
109
the selection into entrepreneurship and by increasing the labor supply.29
We model unemployment insurance as an increase in the income of unemployed
agents, which is now b + bUI .30 The transfers to the unemployed are financed by (lin-
ear) labor taxes τ. We set bUI to 5 percent of the minimum income among the employed.
We set the value of τ to 0.15 percent, such that the government covers the expenses from
unemployment insurance in equilibrium:
τ
∫w · eεdGE = bUI ·U . (2.19)
Although the policy provides relatively little income to the unemployed (5 percent of
the minimum labor income), it has substantial effects on the composition of the work-
force. As expected, unemployment increases (by 1.1 percentage points), but this change
in unemployment also implies an increase in employment (as the unemployed receive job
offers). Employment increases by 2.5 percentage points. These increases are matched by
a decrease of 3.6 percentage points in the self-employed.
The reason behind the large reaction of the workforce is the effect of policy on the
occupational choice of unemployed agents. See Figure 2.6b. As in the example of section
2.1, the change in occupational choice is concentrated among the poorest agents, who
are now able to increase their minimum productivity threshold to become self-employed.
Consequently, the reduction in self-employment is not uniform. Instead, it is concentrated
among those at the bottom of the earnings distribution, as shown in Figure 2.6a.
29More generous safety nets can also improve productivity by spurring entrepreneurship. See evidencefrom France in Hombert et al. (2014, 2016), where the safety net spurs firm creation by providing new busi-ness owners with insurance against productivity risk. Unlike the case in this paper, the French insuranceprogram does not change selection into self-employment because the unemployed already had access toinsurance. See also the recent work by Robinson (2012) exploring gains from providing insurance againstidiosyncratic productivity risk.
30Our exercise excludes two features of unemployment insurance. First, there are no moral hazard prob-lems in our model, as agents’ search behavior is exogenous, although unemployment insurance doeschange the reservation wage of the unemployed. Second, we assume that the government can tell unem-ployed and self-employed agents apart when implementing the program. This need not be the case. If bothunemployed and self-employed agents received the payments, the program would not have the desiredeffect on occupational choice.
110
Figure 2.6: Model Performance: Unemployment Insurance
(a) Self-employment by deciles of earnings
1 2 3 4 5 6 7 8 9 10
Earnings Deciles
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Sh
are
of
Se
lf-E
mp
loye
d A
ge
nts
Baseline ModelUnemployment Insurance
(b) Self-employment occupational choice
0 5 10 15 20 25 30
Assets
0
0.5
1
1.5
2
En
tre
pre
ne
uria
l A
bili
ty
Self-Employment Region
Unemployment Region BaselineUnemployment Insurance
Note: The figures show equilibrium outcomes of the model under unemployment insurance. The left panel reportsthe share of self-employed agents for each decile of the earnings distribution. The orange circles correspond to thebaseline model. The blue diamonds correspond to the model with unemployment insurance. The right panel presentsthe occupational choice into self-employment of the unemployed. Lines depict the threshold value of productivity (z)for each level of assets (a). The agent chooses self-employment if productivity is above the threshold.
The change in selection into self-employment suggests an improvement in allocative
efficiency in both labor and capital (more productive self-employed and more labor). This
is in fact the case, and the increase in productivity is evidenced by an increase in output
of 2.9 percent. The increase in output is considerable given the quantitatively small un-
employment subsidy being given. As before, the reason behind the increase in output is
the change in the selection into self-employment. Unemployment insurance reduces the
mass of self-employed unevenly, concentrating the decreases among the lower half of the
productivity distribution. This can be seen in Figure 2.7b. The consequence of this uneven
change is an economy with relatively more of the more productive self-employed, as seen
at the right end of Figure 2.7a, which compares the CDF of productivity with and without
insurance. More productive self-employed imply larger firms and more output.
The reason these low-productivity self-employed are better allocated in unemploy-
ment is the imperfection of self-employment as an insurance mechanism. The parameter-
ization of the model prefers lower job-offer arrival rates for those who are self-employed,
compared to those who are unemployed. This means that, in the model, self-employment
111
Figure 2.7: Productivity Changes under Unemployment Insurance
(a) Cumulative distributions
0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2
Entrepreneurial Ability
-2
0
2
4
6
8
10
Diffe
ren
ce
in
CD
F R
ela
tivie
to
Ba
se
line
×10-3
(b) Mass per z-type
0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2
Entrepreneurial Ability
-0.9
-0.8
-0.7
-0.6
-0.5
-0.4
-0.3
-0.2
-0.1
0
Diffe
ren
ce
in
Ma
ss R
ela
tivie
to
Ba
se
line
Note: The figures show changes in the distribution of productivity (z) between the equilibrium of the baseline modeland the unemployment insurance program. The left panel presents the difference in the CDF of productivity among theself-employed relative to the baseline model. Negative values indicate that the new distribution first order stochasticallydominates the baseline distribution. The right panel presents the difference in the mass of self-employed agents for eachz−type. Differences are due to changes in the distribution and overall mass of self-employed agents.
lowers the odds of finding salaried employment. This is not a built-in assumption of the
model but an outcome of the calibration. Also, this is a different statement than sim-
ply asserting that individuals transition to employment from self-employment at lower
rates than from unemployment, which could be the case even for equal job-arrival rates.
Lower job-arrival rates from self-employment are consistent with cross-sectional findings
by Jackson (2020), who reports that engaging in gig-economy jobs in the U.S. reduces the
rate at which individuals find jobs and have lowers their earnings in the long run.
The results we obtain highlight how safety net programs can play a role in increasing
productivity in developing countries by improving allocative efficiency. These programs
not only allow individuals to search for longer and find better jobs; they also prevent
unproductive agents from engaging in entrepreneurial activities for which they are ill-
suited. This in an additional rationale for these types of programs as a source of insurance
against labor income fluctuation.
112
2.5.3 Micro-finance
Finally, we use our baseline model to study the effects of micro-finance. Micro-finance
programs are common in developing economies, generally motivated by dysfunctional
credit markets that prevent entrepreneurs’ access to credit. These financial constraints
curtail the growth of productive entrepreneurs. However, the experimental literature has
found only small average effects following the provision of micro-credit in developing
countries (see, among others, Banerjee, Duflo, Glennerster, and Kinnan (2015) and Baner-
jee, Breza, Duflo, and Kinnan (2019)). As we show below, micro-finance not only allows
productive entrepreneurs to grow their business, but also makes self-employment more
attractive for agents, regardless of productivity. As in the example in section 2.1, receiv-
ing micro-finance credit can reduce the average productivity among entrants into self-
employment.
We model micro-finance as a loosening of the self-employed’s collateral constraint.
The micro-finance program gives an amount kmc of seed capital to the poorest 10 percent
of self-employed agents. For these agents the collateral constraint is:
k ≤ λ · a + kmc. (2.20)
We set kmc to 5 percent of the average k among self-employed in the baseline. We assume
that resources for seed capital come from abroad and that all loans have the same interest
rate (the international rate r?).
The magnitude of the effect of this policy on the composition of the workforce is small,
mostly because it is a more targeted policy than the other two policies we studied. As ex-
pected, there is an increase in self-employment of 0.6 percentage points, which comes
mostly from a decrease in unemployment of 0.4 percentage points. Employment also de-
creases (0.2 percentage points), making up the difference.
Because the policy is targeted at the self-employed with the lowest wealth (also the
113
lowest earnings) there is a (modest) increase in the share of self-employed in the lowest
two deciles of the earnings distribution. There is also a differential effect on the occupa-
tional choice of the unemployed: the productivity threshold for becoming self-employed
is reduced, but only among the poorest. Figure 2.10 in Appendix 2.10.2 presents more
details.
As a consequence of the implementation of the policy, output increases 4.1 percent. But
is this increase due to more capital, or to higher productivity? Figure 2.8 describes what
happens to the productivity distribution after the micro-finance policy is enacted. Micro-
finance makes self-employment more attractive for the poorest agents in the economy,
and it decreases the productivity threshold for becoming self-employed. Thus the en-
try into self-employment is concentrated among the least productive, with even a small
decrease in the mass of mid-productive self-employed (Figure 2.8b). The change in the
selection into self-employment effectively worsens the productivity distribution with re-
spect to the baseline (in the first-order stochastic dominance sense). Figure 2.8a makes
clear that following the implementation of the policy, output increases despite a decrease
in productivity.
We take the results of this model experiment as indicative of the importance of un-
derstanding selection into self-employment as a determinant of the effects of policies like
micro-finance. When self-employment is a refuge for individuals without access to other
forms of income, policies that make engaging in entrepreneurial activities more attractive
can have unintended consequences for the composition of the self-employed, potentially
worsening the distribution of productivity.
2.6 Concluding remarks
Our main objective in this paper is to highlight the role of self-employment in devel-
oping economies in shaping the response of the economy to different policies (includ-
114
Figure 2.8: Productivity Changes under Micro-Finance
(a) Cumulative distributions
0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2
Entrepreneurial Ability
-0.005
0
0.005
0.01
0.015
0.02
0.025
0.03
Diffe
ren
ce
in
CD
F R
ela
tivie
to
Ba
se
line
(b) Mass per z-type
0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2
Entrepreneurial Ability
-0.3
-0.2
-0.1
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
Diffe
ren
ce
in
Ma
ss R
ela
tivie
to
Ba
se
line
Note: The figures show changes in the distribution of productivity (z) between the equilibrium of the baseline modeland the micro-finance program. The left panel presents the difference in the CDF of productivity among the self-employed relative to the baseline model. Negative values indicate that the new distribution first order stochasticallydominates the baseline distribution. The right panel presents the difference in the mass of self-employed agents for eachz−type. Differences are due to changes in the distribution and overall mass of self-employed agents.
ing job-guarantee programs, unemployment insurance, and micro-finance). In order to
understand this response, we show that it is key to take into account how the policies
change the selection of individuals into self-employment, particularly those who are un-
employed. We see self-employment as critical for understanding the reaction of the econ-
omy because it plays a role both for productive entrepreneurs starting businesses and
for poor agents who take on entrepreneurial activities as a last resort in their search for
sources of income.
Moreover, self-employment is in itself a distinctive feature of developing economies.
Self-employment is prevalent in developing economies, with rates much higher than
those in richer countries. In addition, self-employment is concentrated among low-earning
individuals (unlike in developed economies), and it is more likely to be taken up by those
who are income-constrained (individuals who become self-employed out of necessity
rather than out of preference or aptitude). These features cannot be reproduced by the
workhorse macro-development used in the literature to study the economy-wide impacts
of development policies. We show that the introduction of unemployment risk, combined
115
with financial frictions and lack of a social safety net, is key to reconciling the model with
the features of self-employment in developing economies.
Unemployment risk shapes the selection of agents into self-employment, and in turn
the response of the economy to various types of policies. Unemployment risk allows the
model to reproduce the limited wage response of the economy to the implementation
of job-guarantee programs. Unemployment risk also plays a crucial role in determining
the effects of unemployment insurance and micro-finance on productivity. Here is where
the role of selection becomes more relevant. Unemployment insurance prevents low-
productivity individuals from engaging in entrepreneurial activities, increasing produc-
tivity as a result. On the contrary, the availability of micro-finance makes self-employment
more attractive as a source of income for low-assets and low-productivity individuals; as
a result, productivity worsens, despite the positive effects of micro-finance on the produc-
tive self-employed.
2.7 Evidence from India
We complement the analysis from Mexico that we presented in the previous sections
with evidence from the National Rural Employment Guarantee Act (NREGA) program
in India. The NREGA is a program that provides short-term jobs at market wages in ru-
ral India. The program was initially implemented in the poorer districts in India in 2006,
and then extended in 2007 and 2008. The schedule in which the program was imple-
mented across districts allows us to exploit regional variation to determine the effect on
self-employment of a large workfare program. The exercise is similar to that of Imbert
and Papp (2015), who study whether NREGA crowded out private sector employment.
In our regressions we match data from the implementation of NREGA with microdata on
time use and occupations from The National Sample Survey Office (NSSO).
Our exercise aims to test whether the creation of public salaried work positions (an in-
116
(1) (2) (3) (4)SE SE SE U
NREGA -0.012 -0.038*** -0.015* 0.010**[0.008] [0.005] [0.008] [0.004]
Observations 395662 395662 395662 395662Avg LHS 0.719 0.719 0.719 0.0516District Fixed Effect No Yes Yes YesIndividual Controls Yes Yes Yes YesYear-Quarter Fixed Effect No No Yes YesConstant Yes Yes Yes Yes
Table 2.7: Change in self-empolyment due to implementation of NREGA
Note: NREGA is the dif-dif coefficient that takes the value of one for all the district-year-quarter triplets in whichthe program is active. All the columns cluster the standard errors at the district level. Columns 1 to 3 analyze theeffects on self-employment and differ on whether there are district and time fixed effects. Column four runs the sameregression of column 3 but using unemployment as the dependent variable.
crease in labor demand) reduces self-employment, while simultaneously increasing un-
employment. We consider this type of response to be consistent with (a share of) indi-
viduals taking up self-employment out of necessity. In this case there would be no at-
tachment to self-employment, and individuals would move out of self-employment and
into the new salaried positions. Moreover, additional wage-earning individuals can al-
low households to spend more time searching for jobs (making unemployment tolerable).
On the contrary, if self-employment was driven by preferences for or productivity in en-
trepreneurial activities, we would expect a decrease in unemployment with no changes
in self-employment (also accompanied by an increase in wages in salaried work).
We estimate a dif-dif regression using the implementation of the NREGA across dis-
tricts in India. Table 2.7 summarizes the results of the exercise. The main finding is that
in districts where the program was instituted first, the share of time dedicated to self-
employment went down, and unemployment went up.31 The results hold even when
controlling for district and time fixed effects, and individual-level controls. Both the re-
31We measure self-employment with the share of time dedicated to an individual’s own business, insteadof measuring it as a dichotomous state (as we did with the Mexican data). This change is motivated bythe differences between life in rural India and urban Mexico. It is common for individuals in our Indiansample to be employed part of the week, and self-employed or unemployed for another part. Despite thisdifferences, we actually see it as encouraging that the behavior of self-employment is consistent betweenthe two countries.
117
sult on self-employment and on unemployment are consistent with self-employment be-
ing driven (partly) by individuals who are not particularly attached, or adept, to their
entrepreneurial activities.
The exercise in this section differs with the previous in that it does not depend on
individual variation, relying instead on variation at the regional level. Because of this
reason we see this exercise as a good complement to the evidence of the previous sections.
By comparing changes in self-employment across regions the results are not affected by
differences in individual unobservable characteristics. The fact that this exercise (with a
different design and data source) provides evidence consistent with the one from Mexico
is encouraging. Nevertheless, we are cautious in interpreting our results. We only take
this evidence as suggestive of the mechanism we highlighted in Section 2.1.32
Finally, the results in Table 2.7 also relate to previous experimental results on labor
rationing and slackness in local labor markets. In particular, our finding with the NREGA
program are aligned with those of Breza et al. (2017), who randomize market-level tran-
sitory positive labor demand shocks across Indian villages to test the slackness of local
labor markets. They find that, following their intervention, self-employment falls with-
out an increase in the market wage. Their results are consistent with self-employed acting
to hide the true slack of the market by harboring unemployed agents in need of income.
We explore the effects of job-guarantee programs in our model, and also find a small re-
action of wages coupled with reductions in self-employment in response to increases in
labor demand (Section 2.5.1).
32There are various problems with our data that we cannot control for. For instance, misreporting of anindividual’s occupation, or presence of assortative mating. It is also hard to determine how comparablethe public jobs offered by NREGA are to alternative positions. It is possible that our results are driven byNREGA jobs being considered superior.
118
2.8 Model without unemployment risk
In this section we describe a simplified model without unemployment risk. The key
difference from the model in Section 3.2 is that agents do not lose their labor efficiency
when they opt into self-employment. As before an agent is free to become self-employed
at any point, but now the agent is also free to become employed in response to changes
in her labor efficiency, entrepreneurial ability or assets. There is no change in the stochas-
tic process for labor efficiency, ε , and productivity, z, neither in the profit maximization
problem of the self-employed, or in the definition of total supply and demand for labor.
2.8.1 Agent’s Problem
Because agents can change instantly across occupations, the occupational choice prob-
lem reduces to maximizing instantaneous income. The value of an agent is then:
ρV (a, z, ε ) = maxc
u (c) + Va (a, z, ε ) a + γε∫
V(a, z, ε′
)dPrε
(ε′|ε
)+ γz
∫V
(a, z′, ε
)dPrz (
z′|z)
s.t. a = maxweε, π (a, z)
+ ra − c a ≥ a (2.21)
with π (a, z) given as in equation (2.8).
The optimal consumption decision is found as in Section 3.2:
c = u′−1 (Va) . (2.22)
Finally agents are classified as employed if weε ≥ π (a, z) and as self-employed otherwise.
2.8.2 Equilibrium
An stationary equilibrium for this economy is a value function V , along with an
optimal consumption function c, labor and capital demand from self-employed n, k,
119
prices r,w and a distribution of agents G such that:
(i) The value function satisfies (2.21).
(ii) Consumption (and thus asset accumulation) are consistent with the agent’s opti-
mization. That is, it is given by equation (2.22).
(iii) Capital and labor demand solve the self-employed’s profit maximization problem.
That is, they are given by (2.9) and (2.10) if ν < 1, or by (2.11) if ν = 1.
(iv) Labor market clears: N S = N D, where total labor supply is given by (2.12), and total
labor demand by (2.13).
(v) The interest rate is given by the international interest rate r?.
(vi) The distribution of agents is stationary. This is obtained if the distributions satisfy
the Kolmogorov Forward Equation (KFE):
0 = −∂
∂a[ag (a, z, ε )] − γz
∫Prz (
z′|z)g (a, z, ε ) dz′ + γz
∫Prz
(z |z
′)g
(a, z′, ε
)dz′
− γε∫
Prε(ε′|ε
)g (a, z, ε ) dε′ + γε
∫Prε
(ε |ε
′)g
(a, z, ε′
)dε′ (2.23)
120
2.9 Computational appendix
2.9.1 Solution to HJB equations
The model is solved using an implicit finite difference method as the one shown in
Achdou et al. (2017). The occupational choice is solved through a splitting method, solv-
ing first for an auxiliary value V , the value that applies if the agent continues in the same
occupation, and then solving for the occupational choice.
Consider grids over assets, entrepreneurial ability and labor efficiency:
~a = [a1, . . . , ana ] ~z =[z1, . . . , znz
]~ε = [ε1, . . . , εnε ]
with na, nz and nε elements respectively, and constant distance between grid points of ∆a,
∆z and ∆ε . Let i denote the index of the asset dimension, j of the entrepreneurial ability,
and k of the labor efficiency.
For notational convenience we will treat all value functions as depending on all three
states, it is understood that VU and V S do not vary across ε . Denote V oi jk = V o
(ai, z j, ε k
)and let the backward and forward difference of the value function approximate the deriva-
tive:
V oa
(ai, z j, ε k
)≈
V oi+1, j k − V o
i jk
∆a= ∂aV o
i jk,F V oa
(ai, z j, ε k
)≈
V oi jk − V o
i−1, j k
∆a= ∂aV o
i jk,B .
The problem to solve is:
ρV Ei jk = u
(cE
i jk
)+ ∂aV E
i jk ·(yE
i jk + rai − cEi jk
)+ γE
(VU
i j − V Ei jk
)(2.24)
+ γznz∑
j ′=1
(V E
i j ′k − V Ei jk
)Prz
(z j ′ |z j
)+ γε
nε∑k ′=1
(V E
i jk ′ − V Ei jk
)Prε (ε k ′ |ε k )
121
ρVUi j = u
(cU
i j
)+ ∂aVU
i j ·(yU
i j + rai − cUi j
)+ γU
nε∑k ′=1
(V E
i jk ′ − VUi j
)PrU (ε k ′) 1
VEijk ′
>VUij
(2.25)
+ γznz∑
j ′=1
(VU
i j ′ − VUi j
)Prz
(z j ′ |z j
)
ρV Si j = u
(cS
i j
)+ ∂aV S
i j ·(yS
i j + rai − cSi j
)(2.26)
+ γSnε∑
k ′=1
(V E
i jk ′ − V Si j
)PrS (ε k ′) 1
VEijk ′
>VSij
+ γznz∑
j ′=1
(V S
i j ′ − V Si j
)Prz
(z j ′ |z j
)
together with:
V Ei jk = max
V E
i j,k, VUi j , V
Si j
(2.27)
VUi j = max
VU
i j , VS
i j
(2.28)
V Si j = max
VU
i j , VS
i j
(2.29)
The implicit method solves the following equation on V o,n+1i j k given a value for V o,n
i jk . For
employment the equation is:
V E,n+1i j k − V E,n
i jk
∆+ ρV E,n+1
i j k = u(cE,n
i jk
)+ ∂aV E,n+1
i j k · sE,ni jk + γE
(VU,n+1
i j − V E,n+1i j k
)(2.30)
+ γznz∑
j ′=1
(V E,n+1
i j ′k − V E,n+1i j k
)Prz
(z j ′ |z j
)+ γε
nε∑k ′=1
(V E,n+1
i j k ′ − V E,n+1i j k
)Prε (ε k ′ |ε k )
For o ∈ U, S the equation is:
122
V o,n+1i j − V o,n
i j
∆+ ρV o,n+1
i j = u(co,n
i j
)+ ∂aV o,n+1
i j · so,ni j +
nε∑k ′=1
γo,ni jk ′
(V E,n+1
i j k ′ − V o,n+1i j
)Pro (ε k ′)
+ γznz∑
j ′=1
(V o,n+1
i j ′ − V o,n+1i j
)Prz
(z j ′ |z j
)(2.31)
Note that the (known) value at iteration n is used to compute consumption, and the drift
of the assets, which we will call savings for convenience:
so,ni jk = yo
i jk + rai − co,ni jk where co,n
i jk = u′−1
(∂aV o,n
i jk
)It is also used to define if the agent is willing to change after a job offer. We have:
γU,ni jk = γU
1VE,nijk ′
>VU,nij
γS,ni jk = γS
1VE,nijk ′
>VS,nij
Next it is necessary to determine whether to use the forward or backward approx-
imation to the first derivatives of the value function. We follow the “upwind scheme”
presented in Achdou et al. (2017).
Since consumption can be defined with the backward or forward difference approxi-
mation we get:
so,ni jk,B = yo
i jk + rai − u′−1
(∂aV o,n
i jk,B
)so,n
i jk,F = yoi jk + rai − u
′−1(∂aV o,n
i jk,F
)The idea is to use the backward difference when the implied drift is negative, and the
forward difference when the drift is positive. Yet there are cases for which so,ni jk,F < 0 <
so,ni jk,B, in these cases we set savings equal to zero, so the derivative is not used, in any
case the FOC of the problem gives the exact derivate of the value function as: ∂aVo,ni jk =
u′(y j k + rai
).33
33Additional care is needed because of the non-convexities introduced by the occupational choice of
123
Consumption is then:
co,ni jk = u
′−1(∂aV o,n
i jk,B
)1
so,nijk,B
<0 + u
′−1(∂aV o,n
i jk,F
)1
so,nijk,F
>0 +
(yo
i jk + rai)1
so,nijk,F
<0<so,nijk,B
,
and the drift term for assets is replaced by:
∂aV o,n+1i j k · so,n
i jk = ∂aV o,n+1i j k,B
[so,n
i jk,B
]−+ ∂aV o,n+1
i j k,F
[so,n
i jk,F
]+
=V o,n+1
i j k − V o,n+1i−1, j k
∆a
[so,n
i jk,B
]−+
V o,n+1i+1, j k − V o,n+1
i j k
∆a
[so,n
i jk,F
]+
Grouping terms we get the following expression for employment:
V E,n+1i j k − V E,n
i jk
∆+ ρV E,n+1
i j k = u(cE,n
i jk
)+ γEVU,n+1
i j
+ xEi jkV E,n+1
i j k + xE−i j k V E,n+1
i−1, j k + xE+i j k V E,n+1
i+1, j k
+ γznz∑
j ′=1
Prz(z j ′ |z j
)V E,n+1
i j ′k + γεnε∑
k ′=1
Prε (ε k ′ |ε k ) V E,n+1i j k ′
where
xEi jk =
[sE,n
i jk,B
]−
∆a−
[sE,n
i jk,F
]+
∆a− γE − γz − γε
xE−i j k = −
[sE,n
i jk,B
]−
∆a
xE+i j k =
[sE,n
i jk,F
]+
∆a
agents. It is possible that both so,nijk,B
< 0 and that so,nijk,F
> 0 for the same state. In this case we take the drift
that provides the highest change in value by comparing u(co,nijk,B
)+ ∂aVo,n
ijk,B· so,n
ijk,Bwith u
(co,nijk,F
)+ ∂aVo,n
ijk,F·
so,nijk,F
. We omit this from the notation for readability.
124
For unemployment and self-employment:
V o,n+1i j − V o,n
i j
∆+ ρV o,n+1
i j = u(co,n
i j
)+
nε∑k ′=1
γo,ni jk ′Pro (ε k ′) V E,n+1
i j k ′
+ xoi jV
o,n+1i j + xo−
i j V o,n+1i−1, j + xo+
i j V o,n+1i+1, j
+ γznz∑
j ′=1
Prz(z j ′ |z j
)V o,n+1
i j ′
where
xoi j =
[so,n
i j,B
]−
∆a−
[so,n
i j,F
]+
∆a−
nε∑k ′=1
γo,ni jk ′Pro (ε k ′) − γz
xo−i j = −
[so,n
i j,B
]−
∆a
xo+i j =
[so,n
i j,F
]+
∆a
Boundary Conditions
A final loose end before writing up the linear system in matrix form is what to do with
the boundaries of the different grids. At the lower boundary of the asset grid the agent is
subject to a no-borrowing constraint. Hence it has to be the case that the agent does not
try to borrow. The drift has to be non-negative at that point, which implies that xo−1 j k = 0
for all(j, k
). At the upper boundary a similar constraint can be imposed, so that xo+
na j k = 0.
This should arise naturally if the upper boundary is high enough. Notice that imposing
these restrictions implies that V n+10 j and V n+1
na+1, j are not part of the system.
125
System Solution
The equations above describe a system of na × nz (2 + nε ) equations, its best to define
the value function a stack of three value functions, one for each occupation:
V =[VU ; V S; V E
]T
V o = vec[V o
i jk
]
The system is:1
∆
(V n+1 − V n
)+ ρV n+1 = un + AnV n+1
where un =[uU,n; uS,n; uE,n
]and uo,n = vec
[u(co,n
i jk
)]with consumption computed as ex-
plained above.
Matrix An is given by:
An = Bn + C + D
Bn =
BnUU 0 Bn
UE
0 BnSS Bn
SE
BEU 0 BnEE
C =
C 0 0
0 C 0
0 0 CE
D =
0 0 0
0 0 0
0 0 D
The matrices Bn
oo are sparse and they only contain elements in the diagonal, upper di-
agonal and lower diagonal. Consider Xo =[xo
i jk
], X−o =
[xo,−
i j k
]and X+
o =[xo,+
i j k
], all
three dimensional matrix that contain the coefficients x (note that x is already adjusted
for the boundaries). Then we have: diag(Bn
oo)
= vec (Xo), diag+ (Bn
oo)
= vec(X+
o
)and
diag−(Bn
oo)
= vec(X−o
), where the upper diagonal and lower diagonal are adjusted not to
include the zero terms of the boundaries.
The matrices Bnoo′
depend on the type of transition. For the transition from employ-
126
ment to unemployment we have:
BEU = γE
Ina ·nz...
Ina ·nz
so that BEU is of size na · nz · nε × na · nz. For the transition from unemployment and self-
employment to employment:
BnoE = γo
[Pro (ε1) diag
(vec
(1
VEij1>Vo
ij
))· · · Pro (
εnε)
diag(vec
(1
VEijnε
>Voij
)) ]
where we abuse notation by letting diag (·) give a diagonal matrix when it is evaluated in
a vector.
Matrices C and D are also sparse and they are independent of the iteration. Their
construction takes advantage of the fact that the elements of C only vary with j and the
elements of D only vary with k. We first construct C = γzPrz ⊗ Ina and CE = γz Inε ⊗ C.
Finally, D = γεPrε ⊗ Ina ·nz .
This problem can now be expressed as:
TnV n+1 = tn
where:
Tn =( 1
∆+ ρ
)Inanz (2+nε ) − An tn = un +
1
∆V n
Algorithm
(i) Compute matrices C and D. These matrices do not change with equilibrium prices
or iterations.
(ii) Take as given w.
127
(iii) Solve for earnings in each state: yoi jk for each combination of (a, z, ε ) and occupation.
These values don’t change with iterations.
(iv) Guess a value for V n, a nanz (2 + nε ) vector. It is easier to store it as three separate
matrices of dimensions na × nz, na × nz and na × nε × nz.
(a) We find it better to find the initial condition by solving for a fixed point of
the problem without occupational choice (this same algorithm without the last
step).
(v) Compute the backward and forward drift: so,ni jk,B and so,n
i jk,F for i = 2, . . . , na and
i = 1, . . . , na − 1 respectively, and all(j, k, o
).
so,ni jk,B = yo
jk + rai − u′−1
(∂aV o,n
i jk,B
)so,n
i jk,F = yojk + rai − u
′−1(∂aV o,n
i jk,F
)These values are stored in six matrices (two per occupation, one with backward drift
and the other one with forward drift).
(vi) For all(i, j, k, o
)compute consumption as:
co,ni jk = u
′−1(∂aV o,n
i jk,B
)1so,n
ijk,B<0 + u
′−1(∂aV o,n
i jk,F
)1so,n
ijk,F>0 +
(yo
jk + rai)
1so,nijk,F
<0<so,nijk,B
These values are stored in three matrices of dimensions na×nz, na×nz and na×nε×nz.
(vii) Compute the utility vector as: un =[uU,n; uS,n; uE,n
]and uo,n = vec
[u(co,n
i jk
)].
(viii) Compute the adjusted shock arrival rates:
γU,ni jk = γU1VE,n
ijk>VU,n
ijkγS,n
i jk = γS1VE,nijk
>VU,nijk
γE,ni jk = γE
(ix) Compute the matrices Xo =[xo
i jk
], X−o =
[xo,−
i j k
]and X+
o =[xo,+
i j k
].
128
(x) Compute matrix Bn =
BnUU 0 Bn
UE
0 BnSS Bn
SE
BnEU 0 Bn
EE
, where diag(Bn
oo)
= vec (Xo), diag+ (Bn
oo)
=
vec(X+
o
)and diag−
(Bn
oo)
= vec(X−o
), where the upper diagonal and lower diagonal
are adjusted not to include the zero terms of the boundaries. The matrices Bnoo′
are
defined above.
(xi) Compute the matrix An = Bn + C + D.
(xii) Compute the matrix T and vector t:
Tn =( 1
∆+ ρ
)I3nanε nz − An tn = un +
1
∆V n
(xiii) Compute V n+1/2 as:
V n+1/2 =(Tn)−1 tn
(a) We use the Biconjugate gradients stabilized (l) method, preconditioned with
LU Factorization. See Matlab functions “ilu” and “bicgstabl.”
(xiv) Divide the vector V n+1/2 into three matrices of na×nz, na×nz and na×nε ×nz: VU,n+1/2,
V S,n+1/2, and V E,n+1/2.
(xv) Compute VU,n+1, V S,n+1, and V E,n+1 as follows:
VU,n+1i j k = max
VU,n+1/2
i j k , V Si jk
V S,n+1i j k = max
VU,n+1/2
i j k , V S,n+1/2i j k
V E,n+1i j k = max
VU,n+1/2
i j k , V Si jk , V E,n+1/2
i j k
129
(a) Define the following matrices as indicators of the occupation choice:[χoo
′
i j k
]
χUSi j =
1 if VU,n+1i j = V S
i j
0 otwχSU
i j =
1 if V S,n+1i j = VU,n+1/2
i j
0 otw
χEUi jk =
1 if V E,n+1i j k = VU,n+1/2
i j
0 otwχES
i jk =
1 if V E,n+1i j k = V S
i j
0 otw
These functions are 1 if the agent changes occupations at(i, j, k
).
(b) Define now the vectors χoo′
= vec(χoo
′)
to be used later. χ is a vector of length
nanz (2 + nε ).
2.9.2 Solution to KFE equations
Before solving the KFE the transition matrix A has to be modified to include the en-
dogenous transitions between unemployment and self-employment. For this we use the
indicators χ constructed as part of the value function iteration.
Now, consider a transition matrix P:
P =
PUU PUS AUE
PSU PSS ASE
PEU PES AEE
note that since there are not endogenous transitions to employment the last column of
matrices are just as in matrix A. The other columns are modified only if there are endoge-
nous transitions. Note that each matrix Poo′
is of size nanεnz × nanεnz.
(i) Make all matrices Poo′
= Aoo′
and Poo = Aoo.
(ii) For matrix P make zero any (column) entry related to an endogenous transition,
130
since these states are not reached. For all m and q in 1, . . . , nanεnz:
P∗Umq = 0 if χUS (q)
= 1
P∗Smq = 0 if χSU (q)
= 1
P∗Emq = 0 if χEU (q)
= 1 or χES (q)
= 1
where ∗ ∈ U, S, E.
(iii) For matrix P adjust entries to take into account endogenous transitions coming from
other occupation o into occupation o′
. This implies moving the columns of Po∗ that
were set to 0 because of transitions into P∗o′
. For all m and q in 1, . . . , nanεnz:
P∗Sm,q−lq = P∗Sm,q−lq + A∗Umq if χUS (q)
= 1
P∗Umq = P∗Umq + A∗Smq if χSU (q)
= 1
P∗Umq = P∗Umq + A∗Emq if χEU (q)
= 1
P∗Sm,q−lq = P∗Sm,q−lq + A∗Emq if χES (q)
= 1
where lq maps the index of the agent after paying the lk units of adjustment cost.
(iv) Finally as explained in Moll’s example for stopping time (multiple assets with ad-
justment costs) the diagonal elements with transitions have to be adjusted:
PUUmm =
−1
∆if χUS (m) = 1
PSSmm =
−1
∆if χSU (m) = 1
PEEmm =
−1
∆if χEU (m) = 1 or χES (m) = 1
131
Moll says: “To see why the −1/∆ term shows up, consider the time-discretized pro-
cess for g:
gt = PTgt −→ gt+∆t = (∆P + I)T gt
where I is the identity matrix. The transition matrix P = ∆P + I needs to have
all entries in the adjustment region Cmm = 0 and hence ∆P + I = 0. Without the
adjustment, the matrix P is singular.
The system to solve is:
PTg = 0
A simple way to solve the system is to make one of the elements of g to be equal to an
arbitrary number, and replace such row of PT by a row of zeros with a one in the diagonal.
Call this matrix PT and let ι = [0, . . . , 0, 0.1, 0, . . . , 0]T then solve for:
g =[PT
]−1ι
Normalize g so that it sums to 1: g = g/sum(g). Finally define g as:
gi =gi
∆ai
132
2.10 Additional graphs and tables
2.10.1 Mobility across occupations
In what follows we dig deeper into how the labor market status of an individual af-
fects transitions. To do so, we follow the same strategy as Katz and Krueger (2017) in
their study of alternative work arrangements in the U.S.. The first question we ask is
whether unemployment makes an individual more likely to transition into self-employed.
To answer this we focus on the universe of individuals who are either employed or self-
employed in period t, and check whether the transitions to self-employment are larger for
those agents who were unemployed in the previous period.
This exercise differs from the conditional transition rates reported in Table 2.2. The re-
gression we conduct allows us to control for the (observable) characteristics of individu-
als, thus comparing transition rates across similar individuals (in terms of age, education
and location), instead of computing transitions among individuals with the same labor
market status (e.g. unemployed). Of course, our results do not control for all characteris-
tics of the individuals (in particular, we do not observe wealth in our data), neither can
we control for unobservable traits that make some individuals more employable, or more
inclined to start their own business. We thus take this evidence as only suggestive of the
mechanisms we study.
Table 2.8 reports the regression results. The transition rates of unemployed agents to
self-employment are 20.9 percentage points higher than those exhibited by (observation-
ally) comparable agents who had a salaried job. This result holds after controlling for age,
education, and after adding time and city fixed-effects.34 While we are not able to con-
trol for all the relevant factors affecting transitions into self-employment, we interpret the
higher transition rate from unemployment as suggestive of the role of self-employment
34Our results align with those of Katz and Krueger (2017) for the U.S.. They find that unemployed individ-uals are more likely to transition to an alternative work arrangement job than agents who are employed. Al-ternative work arrangements (e.g. working for Uber or Task Rabbit) have a similar role as self-employmentin Mexico, namely offering a self-procured source of income.
133
(1) (2) (3) (4)SE SE SE SE
Ut−1 0.209*** 0.209*** 0.208*** 0.208***[0.003] [0.003] [0.003] [0.003]
St−1 0.717*** 0.717*** 0.706*** 0.706***[0.012] [0.012] [0.012] [0.012]
Age 0.002*** 0.002***[0.000] [0.000]
Constant 0.080*** 0.109*** -0.027 -0.038[0.005] [0.005] [395.990] [167.520]
Observations 1033397 1033397 1033397 1033397Mean Ent 0.285 0.285 0.285 0.285Schooling Controls No No Yes YesCity Fixed Effect No No No YesTime Fixed Effect No Yes Yes YesWeighted Yes Yes Yes Yes
Table 2.8: Transitions to Self-Employment
Note: The LHS variable is an indicator variable that takes the value of one if the individual is self-employed andzero if the individual is employed. Ut−1 and St−1 are indicator variables that take the value of 1 if the individualwas unemployed or self employed in the previous quarter respectively. Age is the age in years. Standard errors areclustered at the city level. Schooling controls are a set of dummies by education level to control non-parametrically foreducation. Time fixed effects are at the year-quarter level. The sample consists of individuals who are either employedor self-employed in period t. We run the regressions by weighted OLS. ∗, ∗∗, and ∗∗∗, denote significance at the 10%,5%, and 1% level.
as an outside option for individuals who need an income source, as opposed to self-
employment representing entrepreneurial activities for which the individual is better
suited (relative to working in a salaried job). In Section 2.2.2 and Appendix 2.7 we provide
more evidence consistent with this interpretation.
The second question we ask is whether opting into self-employment hurts an individ-
ual’s chances to find a job. The effect of self-employment on the transitions into employ-
ment matters to determine how persistent the effects of individual occupational choices
are, and how policies that affect those choices affect in turn the labor market. To answer
this question we focus on the universe of agents who are either unemployed or self-
employed in period t − 1, and follow them to determine whether or not they become
employed. As before this allows us to compare the transition rates of self-employed indi-
viduals with (observationally) comparable unemployed individuals.
Table 2.9 presents the regression results. We do in fact find that self-employed indi-
134
(1) (2) (3) (4) (5)E E E E E
St−1 -0.268*** -0.268*** -0.255*** -0.254*** -0.340***[0.021] [0.021] [0.020] [0.020] [0.014]
Age -0.006*** -0.006*** -0.004***[0.000] [0.000] [0.000]
Second Earner 0.022[0.018]
St−1× Second Earner 0.024**[0.011]
Constant 0.463*** 0.417*** 0.704*** 0.684*** 0.589[0.015] [0.014] [0.103] [0.111] [1203.540]
Observations 327250 327250 327250 327250 145945Mean Emp 0.221 0.221 0.221 0.221 0.221Schooling Controls No No Yes Yes YesTime Fixed Effect No Yes Yes Yes YesWeighted Yes Yes Yes Yes Yes
Table 2.9: Transitions to Employment
Note: The LHS variable is an indicator variable that takes the value of one if the individual is employed in period t.St−1 and Second Earner are indicator variables that take the value of 1 if the individual was self-employed and if theindividual’s couple was an income earner in the previous quarter respectively. Age is the age in years. Standard errorsare clustered at the city level. Schooling controls are a set of dummies by education level to control non-parametricallyfor education. Time fixed effects are at the year-quarter level. The sample consists of individuals who were eitherunemployed or self-employed in period t−1. We run the regressions by weighted OLS. ∗, ∗∗, and ∗∗∗, denote significanceat the 10%, 5%, and 1% level.
viduals are 34 percentage points less likely to transition to employment than comparable
unemployed individuals. Even if the actual effect of self-employment is not as large, this
estimate indicates that opting into self-employment can have long-lasting implications for
an individual, particularly for low-productivity self-employed who are now less likely to
abandon this state and move to employment. We will revisit this when analysing the
quantitative fit of the model in Section 2.4.
An important caveat for the results in Table 2.9 is that we are not controlling for
selection into self-employment on the basis of entrepreneurial ability or preference for
self-employment. We also lack the full occupational history of individuals, so we can-
not condition on the attachment to self-employment of each individual. However, we
can partially address some of these shortcomings by focusing on individuals who were
unemployed to begin with (in period t − 2), and who then either remain unemployed
or transition to self-employment (in period t − 1). This lets us compare individuals that
135
start in a common state, and who then differ on whether or not they transition through
self-employment. When we perform this analysis the same result emerges, with individ-
uals who become self-employed being 14.4 percentage points less likely to transition to
employment in period t. The regression results can be found in Table 2.10.
(1) (2) (3) (4) (5)E E E E E
St−1 -0.066*** -0.069*** -0.084*** -0.086*** -0.144***[0.014] [0.014] [0.017] [0.017] [0.050]
Age -0.009*** -0.009*** -0.007***[0.001] [0.001] [0.001]
Second Earner 0.035[0.057]
St−1× Second Earner -0.024[0.058]
Constant 0.383*** 0.456*** 0.854*** 0.863*** 1.327***[0.017] [0.064] [0.226] [0.228] [0.075]
Observations 7320 7320 7320 7320 3205Mean Emp 0.355 0.355 0.355 0.355 0.355Schooling Controls No No Yes Yes YesTime Fixed Effect No Yes Yes Yes YesWeighted Yes Yes Yes Yes Yes
Table 2.10: Transitions to Employment from Unemployment
Note: The LHS variable is an indicator variable that takes the value of one if the individual is employed in period t.St−1 and Second Earner are indicator variables that take the value of 1 if the individual was self-employed and if theindividual’s couple was an income earner in the previous quarter respectively. Age is the age in years. Standard errorsare clustered at the city level. Schooling controls are a set of dummies by education level to control non-parametricallyfor education. Time fixed effects are at the year-quarter level. The sample consists of individuals who were unemployedin period t − 2, and were not employed in period t − 1. We run the regressions by weighted OLS. ∗, ∗∗, and ∗∗∗, denotesignificance at the 10%, 5%, and 1% level.
Finally, Tables 2.11 and 2.12 present results for regressions of different (self-reported)
search activities of the unemployed.
136
(1)
(2)
(3)
(4)
(5)
(6)
(7)
(8)
(9)
Ask
edJo
bPo
stPu
blic
Ag
Tem
pSE
Plan
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tern
etN
ewsp
aper
Nee
dto
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kA
geSe
cond
Earn
er-0
.033
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09-0
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-0.0
020.
002
-0.0
58**
*-0
.022
0.00
01.
564*
**[0
.023
][0
.010
][0
.008
][0
.003
][0
.001
][0
.019
][0
.017
][0
.000
][0
.528
]C
onst
ant
0.20
3***
0.02
1**
0.02
0**
0.00
8***
0.00
10.
105*
**0.
069*
**0.
000
41.0
63**
*[0
.022
][0
.009
][0
.008
][0
.002
][0
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][0
.018
][0
.016
][.]
[0.4
97]
Obs
erva
tion
s11
214
1121
411
214
1121
411
214
1121
411
214
1121
411
214
Tabl
e2.
11:S
econ
dEa
rner
and
Job-
Sear
chA
ctiv
itie
s
Not
e:Th
eLH
Sva
riab
leis
anin
dica
tor
vari
able
that
take
sth
eva
lue
ofon
eif
indi
vidu
ali
perf
orm
edth
egi
ven
activ
ityto
sear
chfo
ra
job
inth
epr
evio
usqu
arte
r.Th
elas
ttw
oco
lum
nsco
rres
pond
tow
eath
eror
nott
hein
divi
dual
decl
ares
toha
vea
need
tow
ork,
and
diffe
renc
esin
age.
Seco
ndEa
rner
isan
indi
cato
rvar
iabl
etha
tta
kest
heva
lueo
fone
ifth
eind
ivid
ual’s
coup
lew
asan
inco
mee
arne
rin
peri
odt−
1.S
tand
ard
erro
rsar
eclu
ster
edat
thec
ityle
vel.
All
regr
essi
onsi
nclu
desc
hool
ing
cont
rols
(ase
tofd
umm
ies
byed
ucat
ion
leve
lto
cont
roln
on-p
aram
etri
cally
for
educ
atio
n),a
ndtim
efix
edef
fect
sat
the
year
-qua
rter
leve
l.Th
esa
mpl
eco
nsis
tsof
indi
vidu
als
who
wer
eun
empl
oyed
inpe
riod
t−1.
The
regr
essi
ons
are
run
byw
eigh
ted
OLS
.∗,∗∗,a
nd∗∗∗,d
enot
esi
gnifi
canc
eat
the
10%
,5%
,and
1%le
vel.
137
(1)
(2)
(3)
(4)
(5)
(6)
(7)
(8)
(9)
Ask
edJo
bPo
stin
gPu
blic
Ag.
Tem
pSE
Plan
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tern
etN
ewsp
aper
Nee
dto
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kA
geR
emit
tanc
es0.
183*
0.02
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004
-0.0
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*-0
.004
**-0
.035
***
0.09
20.
045
-0.2
50[0
.103
][0
.023
][0
.012
][0
.002
][0
.002
][0
.004
][0
.089
][0
.051
][2
.385
]C
onst
ant
0.15
7***
0.00
7***
0.00
8***
0.00
7***
0.00
4**
0.03
5***
0.04
0***
0.04
3***
43.7
66**
*[0
.007
][0
.002
][0
.002
][0
.002
][0
.002
][0
.004
][0
.004
][0
.004
][0
.212
]O
bser
vati
ons
8200
8200
8200
8200
8200
8200
8200
8200
8200
Tabl
e2.
12:R
emit
tanc
esan
dJo
bSe
arch
Act
ivit
ies
Not
e:Th
eLH
Sva
riab
leis
anin
dica
tor
vari
able
that
take
sth
eva
lue
ofon
eif
indi
vidu
ali
perf
orm
edth
egi
ven
activ
ityto
sear
chfo
ra
job
inth
epr
evio
usqu
arte
r.Th
ela
sttw
oco
lum
nsco
rres
pond
tow
eath
eror
nott
hein
divi
dual
decl
ares
toha
vea
need
tow
ork,
and
diffe
renc
esin
age.
Rem
ittan
ces
isan
indi
cato
rva
riab
leth
atta
kes
the
valu
eof
one
ifth
ein
divi
dual
repo
rted
havi
ngre
ceiv
edre
mitt
ance
sin
peri
odt−
1.St
anda
rder
rors
are
clus
tere
dat
the
city
leve
l.A
llre
gres
sion
sin
clud
esc
hool
ing
cont
rols
(ase
tof
dum
mie
sby
educ
atio
nle
velt
oco
ntro
lnon
-par
amet
rica
llyfo
red
ucat
ion)
,and
time
fixed
effe
cts
atth
eye
ar-q
uart
erle
vel.
The
sam
ple
cons
ists
ofin
divi
dual
sw
how
ere
unem
ploy
edin
peri
odt−
1.Th
ere
gres
sion
sar
eru
nby
wei
ghte
dO
LS.∗
,∗∗,a
nd∗∗∗,d
enot
esi
gnifi
canc
eat
the
10%
,5%
,and
1%le
vel.
138
2.10.2 Model: additional graphs and tables
Shocks Preferencesε Labor Efficiency - Base Value ρ Discount Factorσε Labor Efficiency - Variance σ CRRA Parameterρε Labor Efficiency - Persistence Technologyγε Labor Efficiency - Arrival Rate α Capital Sharez Productivity - Base Value δ Capital Depreciationσz Productivity - Variance ν Decreasing Returnsρz Productivity - Persistence Assetsγz Productivity - Arrival Rate λ Equity ConstraintγU Job Offer Arrival Rate - Unemployed a Borrowing ConstraintγS Job Offer Arrival Rate - Self-employed a Asset BarrierγE Job Destruction Arrival Rate Income
b Unemployed Income
Table 2.13: Model Parameters
Figure 2.9: Productivity Changes under Job Guarantee
(a) Cumulative Distributions
0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2
Entrepreneurial Ability
-0.01
-0.009
-0.008
-0.007
-0.006
-0.005
-0.004
-0.003
-0.002
-0.001
0
Diffe
ren
ce
in
CD
F R
ela
tivie
to
Ba
se
line
(b) Mass per z−type
0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2
Entrepreneurial Ability
-0.5
-0.45
-0.4
-0.35
-0.3
-0.25
-0.2
-0.15
-0.1
-0.05
0
Diffe
ren
ce
in
Ma
ss R
ela
tivie
to
Ba
se
line
Note: The figures shows changes in the distribution of productivity (z) between the equilibrium of the baseline modeland the job guarantee program. The left panel presents the difference in the CDF of productivity among the self-employed relative to the baseline model. Negative values indicate that the new distribution first order stochasticallydominates the baseline distribution. The right panel presents the difference in the mass of self-employed agents for eachz−type. Differences are due to changes in the distribution and overall mass of self-employed agents.
139
Figure 2.10: Model Performance - Micro-Finance
(a) Self-Employment by deciles of earnings
1 2 3 4 5 6 7 8 9 10
Earnings Deciles
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Sh
are
of
Se
lf-E
mp
loye
d A
ge
nts
Baseline ModelMicro-Credit
(b) Self-Employment Occupational Choice
0 5 10 15 20 25 30
Assets
0
0.5
1
1.5
2E
ntr
ep
ren
eu
ria
l A
bili
tySelf-Employment Region
Unemployment Region BaselineMicro-Credit
Note: The figures show equilibrium outcomes of the model under micro-finance. The left panel reports the share ofself-employed agents for each decile of the earnings distribution. The orange circles correspond to the baseline model.The blue diamonds correspond to the model with micro-finance. The right panel presents the occupational choice intoself-employment of the unemployed. Lines depict the threshold value of productivity (z) for each level of assets (a).The agent chooses self-employment if productivity is above the threshold.
140
Chapter 3
Information Frictions in K: Micro
Measurement and Macro ImplicationsWith Andres Drenik and Pablo Ottonello
3.1 Introduction
A long tradition in economics and finance examines how asymmetric information af-
fects asset markets. As information frictions affect the valuation, liquidity, and trading of
assets, the last decade witnessed a surge of theories that identify these frictions as playing
a central role in macroeconomic dynamics.1 Motivated by these theories, our goal in this
paper is to measure how relevant information frictions are to asset markets.
We develop a methodology to identify the extent of information frictions in asset mar-
kets and apply it to data from physical capital markets. Our key observation is that in
a broad class of models of trade in asset markets, information frictions affect the rela-
tionship between listed prices and selling probabilities. On the one hand, under full in-
formation, high-quality assets attract more buyers than low-quality assets, which trans-
lates into higher prices and trading probabilities. On the other hand, under asymmet-
ric information, sellers of high-quality assets signal their type and separate from sellers1See, for example, Guerrieri and Shimer (2014), House and Leahy (2004), Hendel and Lizzeri (1999),
Eisfeldt (2004), Kurlat (2013), and Bigio (2015)
141
of low-quality assets. This implies that high-quality assets trade at high prices but low
selling probabilities. We apply our methodology to the capital markets, using a unique
dataset on a panel of nonresidential structures listed online for trade. We show that the
patterns of prices and duration are consistent with the presence of asymmetric informa-
tion. First, capital units that are more expensive because of their observable characteristics
(e.g., location, size) tend to have lower duration, as predicted by models of trading under
a full information model. Second, capital units that are expensive beyond their observable
characteristics tend to have a longer duration, as predicted by models of trading under
asymmetric information. Combining model and data, we estimate that asymmetric in-
formation can explain 21% of the +30% dispersion in the price differences of units with
similar observed characteristics. We quantify the effects of information frictions on allo-
cations, prices, and liquidity, and show that the estimated degree of information frictions
can to lead to 15% lower output due to low trading probabilities of high-quality capital.
The paper begins by laying out a model of trading in asset markets subject to informa-
tion frictions that allows us to illustrate our methodology. The environment is aimed at
capturing key aspects of our data, and focuses on a physical capital market in which sell-
ers post prices and buyers search among listed units to produce. Sellers are agents who
hold units of capital but cannot currently produce. Buyers are agents who can produce
consumption units using capital as input. Gains from trade arise from these different pro-
duction opportunities. Capital units are heterogeneous in their quality, i.e., in terms of the
flow of consumption units they generate in production. Sellers choose a price at which to
list and sell their assets in a decentralized market and face an endogenous probability
determined by the relative mass of buyers and sellers. We show that the relationship be-
tween posted prices and probability of selling critically depends on the degree of asym-
metric information on capital quality. When capital quality is public information, high-
quality capital attracts more buyers and has a higher selling probability than low-quality
capital. When capital quality is the private information of sellers, high-quality capital
sellers choose to signal their type and separate from sellers of low-quality assets. They
do so by choosing to list high-quality capital at such high prices that low-quality assets
would not choose to mimic their pricing behavior; higher prices attract fewer buyers and
142
are associated with lower trading probabilities. However, insofar as sellers can receive
business opportunities in the future and start producing with their capital, high-quality
sellers have a lower marginal cost of not trading than low-quality sellers. This separat-
ing equilibrium under asymmetric information resembles that of the classical model of
Spence (1973), in which low types have a high marginal cost of effort and choose not to
mimic the education levels of high types. In asset markets, the equivalent marginal effort
exerted by high types is selling with a lower probability.
Based on this framework, we show that the extent of asymmetric information in asset
markets can be identified from microlevel data on listed prices and time-to-sell of indi-
vidual assets in a narrowly defined market.2 The first important data elements are listed
prices. If a researcher observes price differences between assets listed for trade within a
narrowly defined market, those differences could reflect heterogeneous quality that is the
private information of sellers. However, it could also reflect heterogeneity in asset quality
that is known by all market participants, but unobserved by the researcher. Therefore, a
second important element is the covariance between listed prices and duration. Under the
hypothesis that there is no asymmetric information between these assets, one should ob-
serve a positive relationship between listed prices and time to sell in the data. This means
that if one instead observes that higher prices tend to have a larger duration while listed,
one can reject the hypothesis of full information in our framework. The more price differ-
ences are driven by differences in quality that are the private information of sellers, the
higher the covariance between listed prices and duration should be. These different pre-
dictions mean that information frictions can be identified from the relationship between
prices and selling probability across assets within a narrowly defined market.
We apply our methodology to data on physical capital markets. For this, we use a
dataset that allows us to construct a novel joint measurement of individual market prices
and duration of capital units listed for trade. In particular, our dataset contains the history
of nonresidential structures (retail and office space) listed for rent and sale in Spain by one
of Europe’s main online real estate platforms, Idealista, with rich information on each
2In our model, assets within a market are perfect substitutes for the buyer. Therefore, by a narrowlydefined market in the data we mean a group of listed assets that exhibit a high degree of substitutability forthe buyer.
143
unit, including the listed price, exact location, size, age, and other characteristics. Given
the data’s panel structure, for each unit we can compute the duration on the platform
and the search intensity received, measured by the number of clicks received in a given
month.
We begin the empirical analysis by providing a test of the model’s predictions. To
this end, we first isolate the component of a property’s price that reflects the character-
istics that are public information from the component that reflects the characteristics not
observed by a researcher using these data (henceforth “the econometrician”), and poten-
tially also by buyers. We estimate a hedonic regression of (log) prices per square foot
on the set of characteristics included in each listing within a narrowly defined market
(e.g., a neighborhood and compute the predicted prices from the hedonic regression and
residual prices. We then study the comovement between predicted and residual prices
with duration on the market. The data show (i) a negative relationship between predicted
prices and duration and (ii) a positive relationship between residual prices and duration.
The first empirical fact validates the prediction of the model under full information: Since
predicted prices are obtained from observable characteristics, the theory predicts that on
average, properties with better characteristics (which are reflected by a higher predicted
price) should have a shorter duration on the market. The second fact provides evidence
rejecting the hypothesis that there is no asymmetric information. That is, if residual prices
would only reflect characteristics that are observed by market participants but not by the
econometrician (e.g., listings that include pictures of the property), one would expect to
observe a negative relationship between residual prices and duration, as observed for pre-
dicted prices and duration. We instead observe a positive relationship between residual
prices and duration, which is consistent with the theory’s prediction about capital quality
under asymmetric information.
We also provide an additional set of empirical results showing that our findings would
be hard to rationalize with other theories of trading in asset markets that do not explicitly
incorporate information frictions. First, we examine whether theories of price dispersion
in markets with search frictions (e.g., Burdett and Judd, 1983) can rationalize our empiri-
cal findings. In principle, these theories generate a positive relationship between residual
144
prices and duration: Sellers of homogeneous properties are indifferent between selling
quickly at a low price or waiting in order to sell at a higher price, and thus randomize their
choices. However, given the quantitative relation between residual prices and duration in
the data, we show that any seller facing such price-duration trade-off will maximize the
expected discounted revenues by choosing the highest price we see in the data. Second,
we analyze whether heterogeneous sellers’ preferences can rationalize the empirical fact.
To do this, we repeat the analysis by computing the expected discounted revenues for
a very broad set of preferences (discount factors from 0 to 0.99, and attitude toward risk
from risk neutral to extreme forms of risk aversion). We find that all types of sellers would
maximize their expected net present value by choosing the highest price observed in the
data. Finally, we explore whether heterogeneous holding costs that sellers must pay can
explain this fact, and conclude that in order for differential holding costs to explain the
differences in expected discounted revenues in the data, they must be extremely large.
It is worth mentioning that in addition, none of these alternative theories can rationalize
the negative relationship between predicted prices and duration simultaneously with a
positive relationship between residual prices and duration.
In the last part of the paper, we map the model to the data in order to quantify the
extent of asymmetric information in the market for physical capital. Based on our identi-
fication strategy, we combine data on the standard deviation of residual prices and their
covariance with duration to disentangle how much of the dispersion of residual prices
reflects the characteristics of properties that are only known by the seller. Our calibra-
tion exercise shows that 21% of residual prices can be attributed to heterogeneous quality
that is private information of the seller. To quantify the effects of asymmetric information,
we compare the estimated model’s predictions with the prediction of a model in which
there is no private information. Asymmetric information has large effects on capital un-
employment: The average unemployment rate of capital is 18% higher with asymmetric
information. This is the result of asymmetric information reducing average trading prob-
abilities, which increases the average unemployment rate. There is an additional effect
that reduces aggregate utilization of capital: Asymmetric information reduces more the
trading probabilities of high-quality capital, which increases the average quality of the
145
pool of unemployed capital. This large effect on trading probabilities is translated into
entrepreneurs’ valuations due to an illiquidity discount. Therefore, the unconditional av-
erage price of a unit of capital is 16.7% lower due to asymmetric information. The overall
welfare effect of information frictions is equivalent to an output loss of 18.4%. The mag-
nitudes of the effects on allocations and prices are on the same order of magnitude of the
estimated effects of search frictions (e.g., Gavazza, 2016).
Related Literature Our paper contributes to five branches of the literature. First is the
literature on asymmetric information in asset markets. Classic theories show how infor-
mation frictions can affect the quality of assets traded (Akerlof, 1970) and the financing
investment opportunities (see, for example, Stiglitz and Weiss, 1981; Myers and Majluf,
1984). We contribute to this literature by measuring these frictions in asset markets. We
do so, by developing a methodology that builds on the theories of the asymmetric infor-
mation in the presence of trading frictions pioneered by Guerrieri et al. (2010) and further
studied by Delacroix and Shi (2013), Guerrieri and Shimer (2014), and Lester et al. (2018),
among others. We show that the effect on allocations of asymmetric information identi-
fied by these theories on allocations is large and relevant from a policy perspective.
Our second contribution is to the literature that measures asymmetric information.
Important contributions to this literature include work by Chiappori and Salanie (2000),
Ivashina (2009), and Einav et al. (2010), who measure asymmetric information in insur-
ance and financial markets, and work by Kurlat and Stroebel (2015), who measure asym-
metric information in housing markets. Our paper complements these studies, by devel-
oping a methodology to measure asymmetric information that exploits the relationship
between prices and trading probabilities –which typically characterize asset markets– but
that can be applied more broadly to other frictional markets.
Our third contribution is to the literature in trading frictions in asset markets. This
includes the large body of work on financial markets (for a recent survey, see Lagos
et al., 2017); housing markets (see, for example, Wheaton, 1990; Krainer, 2001; Caplin and
Leahy, 2011; Piazzesi et al., 2015); and physical capital markets (see, for example, Kur-
mann and Petrosky-Nadeau, 2007; Gavazza, 2011; Cao and Shi, 2017; Ottonello, 2017).
146
Our paper contributes to this literature by showing the relevance of the interaction be-
tween asymmetric information and trading frictions. In particular, asymmetric informa-
tion can increase the duration of capital reallocation, leading to a potential scope of Pareto-
improving market interventions.3
Finally, our paper contributes to the large body of research that measures resource
misallocation (see, for example, Hsieh and Klenow, 2009). We contribute to this literature
by studying a novel form of misallocation that stems from agents who own high-quality
capital that signals their type by choosing to list capital at high prices, which are vis-
ited less frequently by buyers and have lower matching rates. This form of misallocation
would typically not be measured in existing firms, but rather in unemployed capital.
Layout The rest of the paper is organized as follows. Section 3.2 presents the theoretical
framework. Section 3.3 presents the data and empirical facts. Section 3.4 maps the model
to the data and quantifies informational asymmetries. Section 3.5 presents countefactual
analysis. Section 3.6 concludes.
3.2 Theoretical Framework
We construct a model of trading in asset markets subject to information frictions that
allows us to illustrate our methodology. The environment is aimed at capturing key as-
pects of our data, and focuses on a physical capital market in which sellers post prices
and buyers search among listed units to produce. We show that the relationship between
posted prices and probability of selling critically depends on the degree of asymmetric in-
formation about capital quality, with capital of higher quality and price tending to match
at higher rates under full information and at lower rates under asymmetric information.
3Empirical studies have shown that capital reallocation is large and procyclical (see, for example, Rameyand Shapiro, 1998, 2001; Eisfeldt and Rampini, 2006; Eisfeldt and Shi, 2018, and references therein). Relatedto these findings, recent work has studied the implications of secondary asset markets. See, for example,Lanteri (2018) for endogenous irreversibility and Gavazza and Lanteri (2018) for endogenous illiquidity.
147
3.2.1 Environment
Time is discrete and infinite, and there is no aggregate uncertainty.
Goods Two goods are traded: final goods and capital goods. Capital goods are hetero-
geneous in two dimensions: an observed quality ω ∈ Ω ≡ [ω1, . . . , ωNω ], with ωi < ω for
i < j, and an unobserved quality a ∈ A ≡ [a1, . . . , aNa], with ai < a j for i < j. As de-
scribed in detail below, the unobserved quality a is the private information of the owner
of the capital. Qualities in the economy are distributed jointly according to a probability
distribution G(ω, a), which is public information.
Markets Final goods are traded in a Walrasian market. Capital goods are traded in a
decentralized market with search frictions. Sellers list their capital units in the decen-
tralized market, with their quality ω perfectly observed by all market participants (be-
low, we discuss the identification of the model when part of ω could be unobserved by
the econometrician), and choose at what price q to post their units. Buyers dedicate la-
bor to search and match, and can direct their search toward a submarket with a specific
price q and a specific observed quality ω. The flow of new matches in submarket (ω, q)
is given by M(kst (ω, q), hs
t (ω, q)), where kst (ω, q) and hs
t (ω, q) denote, respectively, capital
posted by sellers in submarket (ω, q) and period t and hours worked by buyers search-
ing in submarket (ω, q) and period t. We assume thatM(ks, hs) = minm(ks)η(hs)1−η, ks,
where η ∈ (0, 1) and m > 0.4 In each submarket (ω, q), the market tightness, denoted
θt(ω, q) ≡hst (ω,q)
kst (ω,q)
, is defined as the ratio between buyers’ hours of search and the mass
of capital posted by sellers.5 Visiting submarket (ω, q) in period t, sellers face a proba-
bility p(θt(ω, q)) ≡M(ks
t (ω,q),hst (ω,q))
kst (ω,q)
of selling capital, and buyers match a mass of capital
µ(θt(ω, q)) ≡M(ks
t (ω,q),hst (ω,q))
hst (ω,q)
per hour of search.
4The assumed functional form of the matching function is convenient for tractability and is used fre-quently in related literature on labor search (e.g., Shimer, 2005).
5Following the directed search literature (see, for example Moen, 1997; Menzio and Shi, 2011), in sub-markets that are not visited by any sellers, θt(ω, q) is an out-of-equilibrium conjecture that helps determineequilibrium. See footnote 7 below for more details.
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Agents, preferences, and technologies The economy is populated by a unit mass of en-
trepreneurs (also referred to as buyers) and a unit mass of capitalists (also referred to as
sellers). Entrepreneurs have access to a technology to produce final goods using capital,
given by yt(ω, a) = ωakt(ω, a), where yt(ω, a) denotes its output in terms of final goods
in period t and kt(ω, a) denotes capital of type (ω, a) used as inputs for production in pe-
riod t. Each period, entrepreneurs are also endowed with hours of work to dedicate to
search activities in capital markets. They have preferences over consumption of the final
good described by∑∞
t=0 βt cit − χhit , where cit denotes the consumption of agent i in pe-
riod t and hit the hours of work dedicated to search activities. Capitalists are agents who
own capital goods but do not have access to a production technology, which gives rise
to gains from trade between capitalists and entrepreneurs. They have preferences over
consumption of the final good, described as∑∞
t=0 βtcit . Each period a capitalist faces a
probability ϕK ∈ (0, 1) of developing a business idea and becoming an entrepreneur. This
assumption implies that capitalists with high-quality unobserved quality have a higher
reservation value for these units, which is a frequent assumption in asymmetric informa-
tion models of asset markets (e.g., Akerlof, 1970). To focus on a stationary equilibrium,
and without loss of generality, we also assume that each period entrepreneurs have an
i.i.d. probability ϕE = ϕK of becoming capitalists, which can be seen as the exit rate of
businesses.
Information and timing Capital quality a is the private information of the owner of the
unit of capital. That is, buyers cannot distinguish capital units of different qualities a at a
given price. The timing each period is as follows:
(i) Capitalists list prices for their capital units, which are perfectly observed by all
agents.
(ii) Entrepreneurs purchase capital, choosing their search effort for capital units at dif-
ferent prices.
(iii) Entrepreneurs produce final goods using capital accumulated in current and previ-
ous periods.
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(iv) Entrepreneurs exit and become capitalists with probability ϕK , and capitalists re-
ceive business ideas and become entrepreneurs with probability ϕE .
This setup requires that we specify the entrepreneur’s beliefs about the type of capital,
given a listed price. We assume that all entrepreneurs have the same beliefs. We describe
beliefs by the mapping λa(ω, q) : A × R+ → [0, 1], which denotes the probability that a
unit of capital is of unobserved type a, given the price of capital q and the observed type
ω. We also denote by ae(ω, q) ≡∑
a∈A aλa(ω, q) the expected unobserved quality at the
price q and observed quality ω, under beliefs λa(ω, q).
3.2.2 Optimization
Entrepreneurs An entrepreneur arrives to a period with capital holdings described by
the matrix
k ≡
k(ω1, a1) ... k(ωNω , a1)
... ... ...
k(ω1, aNa ) ... k(ωNω , aNa )
, where k(ω, a) denotes capital with observed quality ω ∈ Ω
and unobserved quality a ∈ A. The problem of an entrepreneur, in recursive form, is
given by
VE(k) = maxh(ω,q)≥0ω∈Ω,q∈R+
c − χ∑ω∈Ω
∫q∈R+
h(ω, q) + βVE(k′) (P1)
s.t. c +∑ω∈Ω
∫q∈R+
qµ(θ(ω, q
))h(ω, q) dq =
∑ω∈Ω
∑a∈A
ωak(ω, a)′, (3.1)
k(ω, a)′ = k(ω, a) +
∫q∈R+
πa(ω, q)µ(θ(ω, q
))h(ω, q) dq, ∀(ω ∈ Ω, a ∈ A), (3.2)
where k(ω, a)′ denotes capital of quality (ω, q) accumulated in the current period; h(ω, q)
the hours worked searching for capital in submarket (ω, q); πa(ω, q) the probability of
matching a unit of capital of quality a when searching in submarket (ω, q); VE(k) the
expected lifetime utility for an entrepreneur from capital stocks k; VK (k) the expected
lifetime utility for a capitalist from capital stock k (further described below); and VE(k) ≡
(1 − ϕK )VE(k) + ϕKVK (k). Let h(ω, q; k) and q(ω, a; k) denote the policy functions associ-
ated with problem P1.
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Capitalists The problem of a capitalist, in recursive form, is in turn given by
VK (k) = maxs(ω,a),q(ω,a)
c + βVK (k′) (P2)
s.t. c =∑ω∈Ω
∑a∈A
s(ω, a)p(θ(ω, q(ω, a)))q(ω, a)k(ω, a), (3.3)
k(ω, a)′ = [(1 − s(ω, a)) + s(ω, a)(1 − p(θ(ω, q(ω, a))))]k(ω, a), ∀(ω ∈ Ω, a ∈ A)
(3.4)
where s(ω, a) ∈ 0, 1 is an indicator variable that takes the value of one if the capitalist de-
cides to participate in the decentralized market selling capital type (ω, a); q(ω, a) denotes
the submarket choice of a capitalist of type (ω, a); and VK (k) ≡ (1− ϕE)VK (k) + ϕEVE(k).6
Equation (3.3) is the capitalist’s budget constraint, which links consumption to the rev-
enues from selling capital, given the choice of prices. Equation (3.4) is the capitalist’s
capital accumulation constraint. Capitalists in this setup must take into account that their
choice of prices can signal their capital quality, which will be reflected in the equilibrium-
tightness function θ(ω, q). Let s(ω, a; k) and q(ω, a; k) denote the policy functions associ-
ated with problem P2.
Linearity of recursive problems A tractable feature of the model is that the entrepreneur’s
and capitalist’s recursive problems are linear in capital holdings, which follows from the
linearity of preferences, production, capital accumulation, and search technologies.
Proposition 1 Entrepreneurs’ and capitalists’ recursive problems are linear in capital stocks, i.e.,
value functions can be expressed as VE(k) =∑ω∈Ω
∑a∈AνE(ω, a)k(ω, a) and
VK (k) =∑ω∈Ω
∑a∈AνK (ω, a)k(ω, a). The marginal value of capital holdings satisfies the recur-
6Allowing the capitalist to list in multiple submarkets for a capital unit of quality a would lead to thesame equilibrium.
151
sive problems:
νE(ω, a) = ωa + βνE(ω, a), (P3)
νK (ω, a) = maxs(ω,a),q(ω,a)
s(ω, a)p(θ(ω, q(ω, a)))q(ω, a) + s(ω, a)(1 − p(θ(ω, q(ω, a))))βνK (ω, a),
(P4)
where νE(ω, a) ≡ (1−ϕK )νE(ω, a)+ϕK νK (ω, a) and νK (ω, a) ≡ (1−ϕE)νK (ω, a)+ϕEνE(ω, a).
Proposition 1 implies that the value of a unit of capital of a given type does not depend
on other capital holdings of its owner. For an entrepreneur, the value for a unit of capital
of type (ω, a) is given by the utility flow generated by its production plus its continuation
value, which takes into account the probability of exiting production. For a capitalist, the
value of a unit of capital of type (ω, a) is given by the expected utility flow from selling
the unit plus its continuation value, which takes into account the probability of receiving
a business idea and becoming an entrepreneur. As a consequence of Proposition 1, policy
functions do not depend on capital stocks, i.e., h(ω, q; k) = h∗(ω, q), s(ω, a; k) = s∗(ω, a),
and q(ω, a; k) = q∗(ω, a).
Operating with recursive problems P3 and P4, one can solve for the marginal value of
capital for entrepreneurs and capitalists:
Corollary 1 The marginal value of capital is given by
νK (ω, a) =1
ρ[rK (ω, a)(1 − β(1 − ϕK ))︸ ︷︷ ︸
expected revenuefrom selling capital
+ βϕEpn(ω, a)ωa︸ ︷︷ ︸expected revenue from
future potential production
], (3.5)
νE(ω, a) =1
ρ[ωa(1 − β(1 − ϕK )pn(ω, a))︸ ︷︷ ︸
expected revenuefrom production
+ βϕErK (ω, a)︸ ︷︷ ︸expected revenue from
future potentially selling capital
], (3.6)
where, rK (ω, a) ≡ s∗(ω, a)p(θ(ω, q∗(ω, a)))q∗(ω, a) denotes the current revenue per unit of cap-
ital type (ω, a) for capitalists posting in an optimal submarket; pn(ω, a) ≡ (1 − s∗(ω, a)) +
s∗(ω, a)(1 − p(θ(ω, q∗(ω, a)))) the associated probability of not selling capital type (ω, a); and
ρ ≡ 1 − β(1 − ϕK ) + pn(ω, a)(β2(1 − ϕK − ϕE) − β(1 − ϕE)) a discount rate that converts the
152
period expected revenue into an expected lifetime value.
Corollary 1 shows that the expected discounted lifetime utility from a unit of capital for
capitalists and entrepreneurs is both a function of the revenues from selling capital and
the revenues from production. In the case of capitalists, their value from a unit of capital
depends on the expected revenue of selling that unit of capital, scaled by the probability
of continuing to be a capitalist, plus the revenue that capitalists have if they do not sell
the unit of capital but instead develop a business idea, become entrepreneurs, and start
producing with the unit of capital. In the case of entrepreneurs, their value from a unit
of capital depends on the revenue from producing with that unit of capital, scaled by
the probability of continuing to be an entrepreneur, plus the revenue from exiting the
entrepreneurial activity and having to sell that unit of capital. Given that higher capital
quality translates into higher production, this property of the value functions implies
that capital quality strictly increases the value of capital for entrepreneurs, and weakly
increases it for capitalists:
Corollary 2 The value functions of entrepreneurs and capitalists are, respectively, increasing and
non-decreasing in unobserved capital quality, i.e., ∂νE(ω,a)∂a > 0 and ∂νK (ω,a)
∂a ≥ 0.
Free entry and equilibrium market-tightness function Proposition (1) characterizes
the value of entrepreneurs’ existing units of capital. In addition, Problem (P1) shows that
entrepreneurs have free entry to purchase capital in all submarkets. Their optimality con-
dition with respect to hours dedicated to search activities in all submarkets implies that
hs(ω, q)(µ(θ(ω, q
))(q − ve
E(ω, q)) + χ)+ = 0, (3.7)
where veE(ω, q) ≡
∑a∈Aπa(ω, q)νE(ω, a) denotes the expected value of purchasing capital
at price q (which use the linearity result in Proposition 1). This condition requires that in
open submarkets in which entrepreneurs are willing to search, the expected cost per unit
of capital in that submarket(q + χ
µ(θ(ω,q))
)is equal to the expected value of the capital
unit, veE(ω, q).
For submarkets visited by a positive mass of capitalists, condition (3.7) determines the
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equilibrium market-tightness function θ(ω, q). Following the directed search literature,
we also assume that (3.7) also determines the market-tightness function in submarkets
not visited by capitalists in equilibrium.7 This assumption implies that the equilibrium
market-tightness function faced by capitalists is given by
θ(ω, q) = µ−1
(χ
veE(ω, q) − q
)(3.8)
for all q < veE(ω, q), and θ(ω, q) = 0 for all q ≥ ve
E(ω, q), meaning that capital units listed
above the entrepreneurs’ value of capital remain unmatched.
3.2.3 Equilibrium under Full Information
We first consider the case in which trading occurs with full information. This corre-
sponds to the case withA = a. In this setup, with only one possible unobserved quality,
entrepreneurs’ beliefs are λ a(ω, q) = 1. A competitive equilibrium in the economy under
full information can then be defined as follows.
Definition 1 (Equilibrium under full information) An equilibrium under full information
consists of value functions ν∗E
: Ω → R and ν∗K
: Ω → R; policy functions s∗ : Ω → 0, 1 and
q∗ : Ω→ R+; and a market-tightness function θ∗ : Ω × R+ → R+ such that:
(i) ν∗E
satisfies (P3) for all ω ∈ Ω and a = a.
(ii) ν∗K
satisfies (P4) for all ω ∈ Ω and a = a; s∗ and q∗ are the associated policy functions.
(iii) The market-tightness function satisfies (3.8).
The following result derives the equilibrium price of capital and market tightness for
each type of capital under full information.
7 As argued by Menzio and Shi (2011), a justification of this assumption comes from considering a se-quential game in which capitalists choose with a tremble their posted prices and then entrepreneurs choosein what submarkets to search. Because of the tremble, the tightness is well defined for all pairs (ω, q). Aswe make the tremble arbitrarily small, θ(ω, q) converges to (3.8).
154
Proposition 2 Under full information, there exists a unique equilibrium in which the price of
capital and market tightness for capital quality ω are given by qFI(ω, a) = ηνE(ω, a) + (1 −
η)βνK (ω, a) and θFI(ω, a) ≡ θ(ω, qFI(ω, a)) =(m(1 − η)χ−1(νE(ω, a) − βνK (ω, a))
) 1η .
This result is graphically represented in Figure 3.1 for the case Ω = ωL, ωH, with
ωL < ωH. Dashed lines represent the isocost curves of entrepreneurs, with the one corre-
sponding to the high quality ωH simply being shifted upward by the difference in quality
with ωL. Solid lines denote the isorevenue curve of capitalists, with the one for the capi-
talist with high-quality capital having a lower slope. This is the result of requiring a lower
“compensation” in terms of higher probability of sale for a given reduction in prices, since
the outside option of capitalists is increasing in the quality of its capital. In equilibrium,
capitalists choose the submarket that maximizes their utility subject to the entrepreneurs’
indifference condition. Proposition 2 shows that under full information, the price of a unit
of capital and its matching rate are increasing in the quality of capital, which implies the
following result.
Corollary 3 In an equilibrium under full information, capital units with higher prices have
higher matching rates. That is, if ω′ > ω, then qFI(ω′, a) > qFI(ω, a) and p(θFI(ω′, a)
)>
p(θFI(ω, a)
).
To see the intuition behind this result, replace the equilibrium price of capital in the
equilibrium market-tightness function (3.8) to obtain
(1 − η)(ωa + β[νE(ω, a) − νK (ω, a)]) =χ
µ(θ(ω, q)
) . (3.9)
Equation (3.9) requires that in equilibrium, the net benefit for entrepreneurs from pur-
chasing a unit of capital in the decentralized market relative to producing it must be
equal to its search cost. As in standard models of directed search, the surplus (given by
ωa + β[νE(ω, a) − νK (ω, a)]) is “split” according to the elasticity of the matching function.
Thus, since the price of capital scales with its productivity less than proportionally (η < 1),
the net gain of purchasing capital is increasing in its productivity. By non-arbitrage, the
search cost must be higher for capital units with higher productivity, meaning that sellers
of these units match at a higher rate.
155
θFIL θFI
H
qFIL
qFIH
θ
q
Isorevenue capitalist - ωL Isocost entrepreneur - ωLIsorevenue capitalist - ωH Isocost entrepreneur - ωH
Figure 3.1: Competitive Equilibrium under Full Information
3.2.4 Equilibrium under Asymmetric Information
An equilibrium under asymmetric information is defined as follows:
Definition 2 A perfect Bayesian equilibrium consists of value functions ν∗E
: Ω × A → R and
ν∗K
: Ω×A → R; policy functions s∗ : Ω×A → 0, 1 and q∗ : Ω×A → R+; a market-tightness
function θ∗ : Ω × R+ → R+; and a belief function λ∗a : A × Ω × R+ → [0, 1], such that:
(i) ν∗E
satisfies (P3) for all (ω, a) ∈ Ω × A.
(ii) ν∗K
satisfies (P4) for all (ω, a) ∈ Ω × A, and s∗ and q∗ are the associated policy functions.
(iii) The market-tightness function satisfies (3.8), given beliefs λa(ω, q).
(iv) The belief function is derived from capitalists’ strategies using Bayes’ rule where possible.
Next, we consider the equilibrium under complete asymmetric information. This case
corresponds to Ω = ω and Na > 2. The last assumption is made in order to focus on the
156
appropriate equilibrium selection mechanism (when Na = 2 our selection mechanism still
chooses the same type of equilibrium, but its requirements are stronger than needed). An
important property of any equilibrium under asymmetric information is the following
consequence of the single-crossing condition:
Lemma 1 In an equilibrium under asymmetric information, if a > a′ then θ(ω, q(ω, a)) ≤
θ(ω, q(ω, a′)) for given ω.
This result is driven by the fact that the low-type capitalist has a higher marginal cost of
not trading. A high type can never choose a higher probability of trading than the low
type, because if the low type weakly prefers a low trading probability to a high trading
probability, the high type would strictly prefer it.
In the setup considered, there are many equilibria, each supported by appropriate
out-of-equilibrium beliefs. Of particular interest are separating equilibria, which satisfy
the following additional condition.
Definition 3 A separating equilibrium under asymmetric information is an equilibrium in which
different types post different prices: If a 6= a′ then q(ω, a) 6= q(ω, a′) for all pairs (a, a′) ∈ A.
An implication of this definition is that prices reveal the quality of each unit of capital. In
a separating equilibrium, two conditions must be satisfied for any pair (a, a′) ∈ A with
a > a′. First, it must be that the lower type a′ does not want to mimic the higher type a,
p(θ(ω, q(ω, a′)))q(ω, a′) +(1 − p(θ(ω, q(ω, a′)))
)βν(ω, a′)
≥ p(θ(ω, q(ω, a)))q(ω, a) +(1 − p(θ(ω, q(ω, a)))
)βν(ω, a′), (3.10)
and that the higher type a does not want to mimic the lower type a′,
p(θ(ω, q(ω, a)))q(ω, a) +(1 − p(θ(ω, q(ω, a)))
)βν(ω, a)
≥ p(θ(ω, q(ω, a′)))q(ω, a′) +(1 − p(θ(ω, q(ω, a′)))
)βν(ω, a). (3.11)
The definition of a separating equilibrium does not impose any constraints on off-
equilibrium beliefs. For example, any equilibrium satisfying (3.10) and (3.11) could be
157
supported with these off-equilibrium beliefs: After observing any off-equilibrium choice
q(ω, a), the entrepreneur believes that the deviation was made by the lowest quality a1.
With such beliefs and the optimal response of the entrepreneur, no capitalist has an in-
centive to deviate. The following result imposes more structure on these beliefs by con-
sidering the equilibrium that satisfies the D1 criterion of Cho and Kreps (1987). What this
criterion does is to first find the set of types that are more likely to deviate relative to
the equilibrium choices. After requiring that entrepreneurs have beliefs consistent with
this set after observing the deviation, the D1 criterion eliminates equilibria in which a
capitalist’s payoff of the deviation under the worst entrepreneurs’ consistent belief is not
equilibrium dominated.
Proposition 3 There exists a unique equilibrium that satisfies the D1 criterion. This is a separat-
ing equilibrium, in which the tightness function θAI(ω, a) ≡ θ(ω, qAI(ω, a)) and prices qAI(ω, a)
satisfy:
(i) For i = 1,
qAI(ω, ai) = argmaxq(ω,ai)
p(θ(ω, q(ω, ai)))q(ω, ai) +(1 − p(θ(ω, q(ω, ai)))
)βν(ω, ai).
(ii) For all ai ∈ A and i ≥ 1,
p(θAI(ω, ai))qAI(ω, ai) +(1 − p(θAI(ω, ai))
)βν(ω, ai)
= p(θAI(ω, ai+1))qAI(ω, ai+1) +(1 − p(θAI(ω, ai+1))
)βν(ω, ai).
(iii) For all ai ∈ A,
θAI(ω, ai) ≡ θ(ω, qAI(ω, ai)) = µ−1
(χ
ν(ω, ai) − qAI(ω, ai)
).
This result was originally established by Guerrieri et al. (2010) in a search model with
adverse selection under a different equilibrium selection mechanism. We show that a sim-
ilar equilibrium is obtained in a signaling model. The intuition behind this result can be
158
θAILθAI
H
qAIL
qAIH
θ
q
Isorevenue capitalist - aL Isocost entrepreneur - aLIsorevenue capitalist - aH Isocost entrepreneur - aH
Figure 3.2: Competitive Equilibrium under Asymmetric Information
seen in Figure 3.2 for the case A = aL, aH, with aL < aH. In a separating equilibrium,
the outcome in the submarket for the lowest quality capital is the same as the one ob-
tained under full information (see Figure 3.1). However, the outcome in the submarket
for higher-quality capital is distorted by the fact that higher-quality capitalists maximize
expected utility subject to the constraint that lower-quality capitalists do not have a strict
preference for participating in their submarket and given entrepreneurs’ belief function.
Although multiple separating equilibria are supported by different sets of beliefs (see the
proof of Proposition 3 in the Appendix), the unique separating equilibrium that satis-
fies the D1 criterion is the one depicted in Figure 3.2. In such an equilibrium, the higher-
quality capitalist chooses the allocation that renders the lower-quality capitalist just indif-
ferent between mimicking and not, because it minimizes the signaling “effort” imposed
by the lower trading probability. Thus, the following simple result follows from the sepa-
rating equilibrium, with important implications that can be tested in the data.
Corollary 4 In the unique separating equilibrium with asymmetric information that satisfies
the D1 criterion, capital units with higher prices have lower matching rates: If a > a′, then
159
qAI(ω, a) > qAI(ω, a′) and p(θAI(ω, a)) < p(θAI(ω, a′)).
The model predicts that owners of capital units that possess characteristics that are
not possible to announce in a listing signal their type by choosing a high price, which
is associated with low trading probabilities and is not easy to mimic by owners of low-
quality capital, given their higher marginal cost of not trading. For this reason, while
the market tightness faced by the lowest type is the same under full and asymmetric
information (θAI(ω, a′) = θFI(ω, a′)), the tightness faced by the higher type a > a′ is lower
under asymmetric information than under full information (θAI(ω, a) < θFI(ω, a)). This
implies an important qualitative change in the relationship between prices and duration
on the market created by asymmetric information and signaling.
3.2.5 Identification
In the previous subsections, we have shown how prices and trading probabilities re-
spond differently to changes in the observed and unobserved components of the quality
of a unit of capital. Given the implications that asymmetric information has on the alloca-
tion, a natural question is: Can we use micro-data on prices and duration on the market to
estimate the quantitative relevance of information frictions in the capital market? A priori,
one could think that by using data on observables (e.g., location, size, number of rooms,
etc.) as proxies for the observed component of the quality of capital ω, one could estimate
the dispersion of the unobserved component a by looking at the dispersion of residual
prices (i.e., the residual of a regression of prices on observables). However, suppose in-
stead that a component of ω is in fact observed by market participants, but not “by the
econometrician.” More formally, suppose that ω is a function of characteristics observed
only by market participants z and a vector of characteristics observed by everyone x (in-
cluding the econometrician). Then, this exercise will not provide the right answer. Here,
we show that despite the potential presence of factors unobserved by the econometrician,
we can still recover two key objects: the aggregate dispersion of the z and a components
and their relative magnitudes. In other words, we develop a methodology to recover the
importance of asymmetric information using micro-data on prices and duration.
160
Our theoretical identification analysis is conducted under the assumption that the
elasticity of the matching function η = 0.5. In this special case, the model has a closed-
form solution that allows us to show our identification result and facilitates exposition
of the intuition. In the analysis of the extended model for the quantitative analysis, we
provide a numerical exploration of the identification argument to show that it is valid
there.
First, we present the assumptions we make in order to identify the presence of asym-
metric information in the data:
Assumption 4 A unit of capital with observable characteristics x and unobserved components z
and a produces exp(x′δ)za efficiency units of capital.
Assumption 5 (z, a) ⊥⊥ x.
Assumption 6
*.,
log z
log a
+/-∼ N *.
,
0
0
,
σ2z σz,a
σz,a σ2a
+/-.
The first assumption imposes restrictions on how the quality of a unit of capital gets
transformed into efficiency units.8 The second assumption requires that the components
of quality that are unobserved by the econometrician are independent of the observable
characteristics x. However, as will become clear below, this assumption is not necessary
for identification. In fact, one could allow for correlation between z and x, and a and x
and still identify the parameters of interest with the use of additional moments from the
data. However, by disposing from this assumption, one would need to impose structure
on such correlations. In the spirit of tractability, we abstract from this possibility. The last
assumption is more operational, and assumes that the unobserved heterogeneity is jointly
log-normally distributed.9
8This specific assumption is not needed. What is important is that x, z and a get transformed into effi-ciency units of capital in a monotonic way. That is, a certain feature of a unit of capital always increases ordecreases the efficiency units of the unit.
9The means of both components are not separately identified from the average observable productivity.Thus, we include a constant term in the vector x and normalize the mean of both unobserved componentsto zero. This is without loss of generality, because the presence of asymmetric information is measured bythe covariance matrix of z and a, and not by their means.
161
We assume that the other parameters from the model are calibrated using aggregate
data, including the discount factor β, the parameters of the matching function m and η,
the search cost χ, the outside option of the seller φ, and the decreasing returns in the pro-
duction function α. Thus, the goal is to separately identify the parameters of the covari-
ance matrix (σ2ω, σ2
a, and σω,a) and the vector δ affecting the transformation into efficiency
units of capital, using the micro-data.
The identification argument proceeds by first showing that ratios of prices and (ex-
pected) duration across units of capital only depend on ratios of different x’s, z’s, and
a’s.
Proposition 4 If η = 0.5, then for any two units of capital (x, z, ai) and (x, z, ai+1), the unique
equilibrium that satisfies the D1 criterion features prices, and ratios of prices and expected duration
given by
q(x, z, ai) = exp(x′δ)zai
(1 −
1
2Θi
(a1
a2, . . . ,
ai−1
ai, φ, β
)),
q(x, z, ai+1)
q(x, z, ai)= Q
(exp(x′δ)exp(x′δ)
,zz,
ai+1
ai;
ai
ai−1, . . . ,
a2
a1, φ, β
)and
E(D(x, z, ai+1)
)E
(D(x, z, ai)
) ≡ 1/p(θ(x, z, q(x, z, ai+1))
)1/p
(θ(x, z, q(x, z, ai))
) = D
(exp(x′δ)exp(x′δ)
,zz,
ai+1
ai;
ai
ai−1, . . . ,
a2
a1, φ, β
),
with ∂Q(·)∂ x/x > 0, ∂Q(·)
∂ z/z > 0, ∂Q(·)∂ai+1/ai
> 0, ∂D (·)∂ x/x < 0, ∂D (·)
∂ z/z < 0 and ∂D (·)∂ai+1/ai
> 0.
Proposition 4 shows that while the vector δ is identified by the first moment of the distri-
bution of prices, the remaining parameters are identified by the second moments of the
joint distribution of prices and durations. First, notice that the vector δ can be obtained
from a regression of (log) prices on observable characteristics. This is the result of As-
sumption 5. Second, given any two units of capital, the ratio of their prices and expected
duration are only functions of the ratio of qualities x, z, and a. They also depend on pa-
rameters δ, φ, and β, but these are separately identified or calibrated (see Section 3.4 with
the quantitative model). Third, the ratios of prices and duration depend on the z and x
components of these two units only, while they depend on the a components of all units
162
of lower quality. This is because prices fully reflect the components that are observed by
market participants (x and z), while distortions created by asymmetric information ac-
cumulate over types. That is, asymmetric information distorts the relative allocation of
capital units of quality a1 and a2, which in turn affects the relative allocation of capital
units of quality a2 and a3, and so on.
More importantly, Proposition 4 shows that the ratio of both the z and the a com-
ponents have similar effects on the ratio of prices, but opposing effects on the ratio of
(expected) duration. This is the key identifying result. While larger gaps between the z
and the a components of two units both increase price dispersion, a larger gap in the z
component decreases relative duration, and a larger gap in the a component increases rel-
ative duration. These opposite relationships allow for identification of the dispersion and
importance of the a component. While the joint dispersion of both components (σ2z + σ2
a)
is disciplined by aggregate price dispersion, the relative dispersion of the z and a com-
ponents (σ2z/σ
2a) is disciplined by measures that summarize the comovement between a
unit’s price and its corresponding duration.
Finally, aggregate duration dispersion is informative of the covariance σz,a. While
higher dispersion in both the z and a components of quality increase the dispersion of
duration, a higher σz,a decreases it. The intuition comes from the fact that duration is de-
creasing in z and increasing in a. Thus, to the extent that both components are positively
correlated, their effects on expected duration are neutralized and the dispersion of du-
ration should be small. On the other hand, if they are negatively correlated, their effects
would tend to go in the same direction and the dispersion of duration should be high.
In principle, there could be many data moments that are informative about the disper-
sion of prices, duration, and the comovement between them. We propose the following
three standard moments: i) the standard deviation of (log) prices, ii) the standard devia-
tion of (log) duration, and iii) the covariance between (log) prices and duration. Figure 3.3
plots the relationship between these three moments and the parameters of the log-normal
distribution of (z, a), and illustrates the intuition behind our methodology. Although these
three moments are affected by the three parameters of interest, the figure shows how σa
and σz can be identified using data on the covariance between prices and duration, and
163
how the covariance σz,a can be recovered using data on the standard deviation of duration
on the market.
The figure also illustrates an important prediction of the model. As σz → ∞ (or as
σa → 0), the covariance between prices and duration becomes negative, since the model
behaves asymptotically as in the extreme full information case. On the other hand, as
σz → 0 (or as σa → ∞), the covariance becomes positive, since the equilibrium behaves
as in the full asymmetric information case. In the following empirical section, we exploit
these results to devise a simple test for the presence of asymmetric information.
0 0.2 0.4 0.6 0.8-0.5
0
0.5
1
1.5
2
0 0.2 0.4 0.6 0.8-1
-0.5
0
0.5
1
1.5
2
-0.1 -0.05 0 0.05 0.10
0.5
1
1.5
Figure 3.3: Illustration of Identification
3.3 Empirical Evidence
In this section, we first present and describe the micro data on commercial real estate
from Spain. We then document the extent to which differences in capital prices can be
explained by observable characteristics. Next, using micro-data on residual prices and
measures related to search intensity, we provide suggestive evidence that rejects the null
hypothesis of full information in the market of physical capital. Finally, we present evi-
dence showing that other potential mechanisms cannot be the main drivers behind the
patterns observed in the data.
164
3.3.1 The Data
Our data consist of a panel of nonresidential structures (retail and office space) listed
for sale and rent. The source of these data is Idealista, one of Europe’s leading online
real estate intermediaries.10 The frequency of the panel is monthly, and it includes the
universe of capital units that were listed on this platform between 2005 and 2018. The data
contain information during the period of time each listing was active online. The dataset
includes roughly 8.9 million observations for Spain, where an observation corresponds to
a property–month pair. Overall, these observations come from over 1.15 million different
capital units.
For each property, we observe a wide range of characteristics that we link to its price.
In particular, we observe the address of the property, its construction year, its area, stan-
dardized self-reported condition of the unit, the number of rooms, and whether the prop-
erty has heat or air conditioning. Table 3.1 presents some descriptive statistics on these
characteristics.11 The table includes four columns, which are the mean and standard devi-
ation for properties listed for rent and sale, respectively. Our main variable of interest for
each capital unit is its price, which we observe for each property at a monthly frequency.
The average sale price per square foot is $162 (expressed in constant 2017 dollars), and
monthly rents are around $1 per square foot per month. The properties are relatively old,
with the average age around 26 years. The properties have similar sizes regardless of the
operation.
For each capital unit, we also observe three key variables related to its time-to-sell and
the attention it receives on the platform. First, based on the identifier of each property,
we compute the number of months the unit is listed on the platform, which we refer
to as duration. Table 3.1 shows that units for rent and sale remain on the platform 7.7
and 9.2 months on average, respectively. Second, we compute each capital unit’s search
volume in each month, measured by the number of views and clicks each listing received
10Idealista is the leading online platform in the real estate market in Spain (see Comparison ofusers and Comparison of platform). Other papers in the literature have made use of data from onlineplatforms in the real estate market (see, for example, (Piazzesi et al., 2015)).
11For those variables that change over time, we first take the average of the variable for each listing andreport the average of that variable across listings.
165
Mean Rent Std. Rent Mean Sale Std. Sale
Price 1.09 0.77 162.28 129.74Duration 7.70 7.56 9.21 8.25
Construction Date 1986.61 19.67 1986.96 20.01Area 2588.87 3977.47 2948.43 4507.27New 0.00 0.06 0.04 0.21Needs Restoration 0.08 0.28 0.15 0.36Good Condition 0.91 0.28 0.81 0.39Rooms 2.60 2.80 2.38 3.20Restrooms 1.32 1.30 1.20 1.54Heating 0.38 0.49 0.28 0.45AC 0.77 0.42 0.71 0.46
Emails 2.90 2.09 2.99 2.05Views 1460.25 2264.15 875.37 1333.88Clicks 72.31 97.51 46.96 59.26
Number of Obs. 6.1e+05 6.1e+05 3.8e+05 3.8e+05
Table 3.1: Descriptive Statistics
Note: Price is the price per square foot in constant 2017 dollars. Duration is the number of months a prop-erty lasted in the database. Construction date is the year in which the property was built. Property area ismeasured in square feet. “New” is a categorical variable that takes the value of 1 if the property is new.“Needs Restoration” is a categorical value that takes the value of 1 if the owner declares the property needsreparations. “Good Condition” takes the value of 1 if the property does not need reparations. “Rooms” isthe number of separate rooms the property has, similar for “Restrooms”. Heating and AC are categoricalvariables that take the value of 1 when the property has some heating and air conditioning technologies.Emails is the number of times per month a property received an email from a potential customer. Viewsis the number of times a property appeared in the screen of a potential customer per month. Clicks is thenumber of times per month a potential customer clicked on the property listing to see its details.
and the number of emails the seller receives from potential buyers through the platform.
Each listing for rent and sale was on average viewed 1,460 and 875 times, respectively.
Similarly, listings for rent and sale received 72 and 46 clicks per month, respectively, and
2.9 and 3 emails per month, respectively.
Appendix 3.7.1 provides more details on the data. In particular, Section 3.7.2 describes
how the online platform works. Section 3.7.3 studies the representativeness of the dataset,
showing that the data from the online platform are consistent with aggregate patterns
observed in Spain during the period of analysis in terms of the aggregate evolution of
prices and the timing of sales.
166
Variation over Time and Space. Here, we describe the coverage of the data and the ob-
served variation in prices of listed capital. An important observable dimension of capital
prices is the time dimension. Figure 3.5 shows that, as is well known, the price of capital
units experienced large fluctuations over the last 15 years during the boom and bust in the
real estate market in Spain. In the markets for both sale and rent, prices declined by more
than 50% from the peak in 2007 to the trough in 2012. Since then, prices have remained
stable. Another key observable dimension that explains differences in capital prices is lo-
cation. Figure 3.4 shows remarkable differences in sale prices across regions at different
levels of aggregation. Panel (a) shows the average price across the 50 provinces in Spain;
Panel (b) zooms in on the province of Madrid and shows the average price across munic-
ipalities in that province; Panel (c) zooms in on the city of Madrid and shows the average
price across neighborhoods in the city. These maps demonstrate that locations vary sig-
nificantly in their capital prices. Finally, Figure 3.8 in Appendix 3.7.4 shows the evolution
of average time to sell over time, which was around 6 months during the boom of the real
estate market and then increased to more than 10 months during the subsequent bust.
Discussion of the Data. The dataset has many advantages. First, it contains panel data
for a large amount of nonresidential real estate, with wide geographical and temporal
coverage. Second, it contains information on the duration of a listing online. Third, it
provides information about the search behavior of potential buyers (monthly number of
clicks and emails received). However, the dataset does not contain information on trans-
acted prices. We believe that this should not be a concern for various reasons. First, Fig-
ure 3.5 in the Appendix compares indices of listed prices from Idealista with indices of
transacted prices from the National Registry of Property in Spain. We show that the in-
dices have similar patterns.12 Second, below we show that listed prices are strongly asso-
ciated with duration on the platform and the attention the listing receives (measured by
clicks and emails received). Third, previous papers with access to both listed and trans-
acted prices have shown that the modal property sells at its listed price and that the aver-
12Our index leads the index of transacted prices. This is expected since our index consists of listed pricesand it will take properties some months to exit the database, be registered as sales and recorded in nationalstatistics.
167
214 − 293 193 − 214
177 − 193 167 − 177
157 − 167 148 − 157
134 − 148 118 − 134
112 − 118 94 − 112
(a) Spain
309 − 438 229 − 309
208 − 229 187 − 208
168 − 187 150 − 168
120 − 150 102 − 120
85 − 102 6 − 85
No data
(b) Province of Madrid
398 − 1028
324 − 398
276 − 324
257 − 276
234 − 257
213 − 234
203 − 213
175 − 203
157 − 175
101 − 157
No data
(c) City of Madrid
Figure 3.4: Capital Prices Across Locations
Note: Each map shows average prices by location expressed in constant 2017 dollars per square foot. Thetop panel shows average prices across provinces in Spain. The lower-left panel zooms in on the province ofMadrid to show substantial heterogeneity across municipalities within this province. The lower-right mapshows that, after zooming in on the municipality of Madrid, there is still significant geographical dispersionof prices across neighborhoods.
age property sells within 1.6% of its listed price (see, e.g., Guren, 2018).
Another concern is that duration contains measurement error due to sellers’ failure to
delete the listing after a sale. This should not be a concern. First, Idealista is a paid service,
so it is costly for the seller to keep a listing dormant after the property has been sold.
Second, a large fraction of listings are associated with professional sellers (i.e., real estate
agents). Finally, to alleviate any remaining concerns, we exploit the fact that the platform
asks sellers why they decided to close the listing. Figure 3.7 in Appendix 3.7.4 compares
the histogram of duration for two groups of listings: those that closed the listing because
the property was rented out or sold and those that do not provide any explanation. Those
168
(a) Capital for Sale (b) Capital for Rent
Figure 3.5: Evolution of Prices of Capital Units
Note: The left panel shows the evolution of mean prices at the daily frequency from 2006 to 2017. The rightpanel shows an equivalent index for rental units. Prices are denominated in constant 2017 dollars per squarefoot. To compute these price indices, we averaged the prices of all active listings in a given day.
histograms are virtually identical.
3.3.2 Key Data Moments
We now use our data to test the main predictions of the model. The theory predicts that
if the quality of properties is known to all market participants, then their price should be
negatively correlated with duration on the market. In addition, the theory predicts that if
instead the quality of properties is private information of the seller, then their price should
be positively correlated with duration on the market. In order to conduct these tests, we
must first isolate the component of a property’s price that reflects the characteristics that
are public information from the component that reflects the characteristics not observed
by the econometrician, and potentially by buyers. Thus, we proceed by first measuring the
component of a listed priced that can be predicted based on the property’s characteristics
included in the listing. That is, we estimate hedonic regression to obtain the predicted
price based on observable characteristics and the residual price. Then, we analyze how
both the predicted and the residual price comove with duration on the market.
169
Obtaining a Measure of Residual Prices
To quantify the role of observable characteristics of a listing in explaining its price, we
estimate the following hedonic pricing model for the (log) price per square foot:
log(qilt) = νlt + γXi + εilt (3.12)
where qi jt is the price (in 2017 dollars) of a capital unit i in location l, listed in month
t, νlt are location and time fixed effects, Xi is a set of observable characteristics included
in the listing, and εilt is a random error term.13 Table 3.2 presents the results of this ex-
ercise, showing the R2 of the regression and the standard deviation of residual prices.
To understand how much of the variation in prices is predicted by different groups of
characteristics, we estimate multiple regressions including such groups one at a time.
Table 3.2 shows that in the raw data, the standard deviation of prices is 68% and 77% in
the market for rent and sale, respectively. Of this variation, time fixed effects can account
for 5% and 14% of the variation of prices in each type of transaction. This is perhaps
surprising, given the collapse of the real estate market in Spain. However, this result is
explained by the fact that in the real estate market, location is a key factor for determining
the value of a property. Once we include location and time fixed effects, the R2 of the
regression increases to 53% and 59%, respectively. If we include interactions of the time-
location fixed effects with the type of property (office, retail space, or warehouse), area,
and age of the property, the R2 further increases to 75% and 78%. Finally, in the last row
of the table, we include the additional characteristics described in Table 3.1.14
A major conclusion from Table 3.2 is that although the empirical model has a high
predictive power for listed prices, between 20% and 25% of the variation in prices is not
13Location fixed effects are defined, for each unit, at the finest geographical level possible in the platform:the neighborhood level in the case of big cities like Madrid or Barcelona, and the city level in smaller cities.Results are similar if we focus only on cities that have available neighborhood information.
14In this analysis, we have focused on the average listed price during the lifetime of the listing. Thereis another source of price dispersion: price changes during the life of the listing. Table 3.1 in Appendix3.7.4 shows that between 5% and 7% of listings change price in a given month. Despite these price changesover time, most of the variation in prices across listings is accounted for by the average price of the listing.Table 3.2 in Appendix 3.7.4 continues the analysis of Table 3.2 by further including a listing fixed effect andestimating the regression using the entire panel dataset. Results show that less than 6% of the variation inprices can be accounted for by properties that change their price during the lifetime of the listing.
170
explained by characteristics included in the listings. Moreover, the standard deviation of
the residuals in the benchmark specification, in which we include all available controls, is
around 45% of the variation observed in the raw data. Figure 3.6 shows the distribution of
price residuals, which illustrates the relevance of the dispersion in prices not accounted
for by the characteristics in the listings. We refer to the dispersion of the residuals from
the regression of log prices on all fixed effects and controls of the characteristics in the
listings as residual dispersion.
Std Rent Std Sale R2 Rent R2 Sale
Raw data 0.68 0.77 0.00 0.00Time 0.67 0.71 0.05 0.14Time x Location 0.47 0.49 0.53 0.59... x Type 0.45 0.48 0.57 0.61... x Area 0.35 0.37 0.74 0.76... x Age 0.34 0.36 0.75 0.78
Benchmark 0.34 0.36 0.75 0.78
Table 3.2: Price Variation Accounted for by Listed Characteristics
Note: This table shows the R2 and standard deviation of residuals of different variations of equation (3.12).Time and location are fixed effects. Type (office, retail space, or warehouse), area, and age are sets of fixedeffects for each of these characteristics. The row labeled Raw Data presents statistics for the demeaned rawlog prices. The following rows include the mentioned fixed effects in the regression. The last row includesadditional controls for the variables listed in Table 3.1.
Relationship between Prices and Duration
The last part of the analysis consists of documenting that residual prices and predicted
prices have relationships with duration of opposite signs. By predicted prices, we refer to
the component of a property’s price that is linked to its observable characteristics. Since
such characteristics are observed in the listing, the theory predicts that on average, prop-
erties with better characteristics (which are reflected by a higher predicted price) should
have a shorter duration on the market. By residual prices, we refer to the component
of a property’s price that is cannot be explained by its observable characteristics. These
residual prices can reflect the quality that is private information of the seller, but can also
reflect characteristics that are observed by market participants, but not by the econome-
171
(a) Price Residuals – Sale (b) Price Residuals – Rent
Figure 3.6: Distribution of Price Residuals
Note: This figure shows the differences in log prices per square feet with respect to its mean for the raw dataand price residuals after including the fixed effects in Table (3.2). The left panel shows the distributions forsales and the right panel for rentals.
trician (e.g., listings that include pictures of the property, which convey information not
included in the hedonic regression). A priori, the theory does not offer a prediction about
the relation between residual prices and duration. If most of the residual price is the re-
sult of characteristics not observed by the econometrician, then this relationship should
be negative. If, instead, a large component of residual prices is the result of sellers’ choices
to signal their private information, we should expected a positive relationship.
Figure 3.7 plots these relationships. Panel (a) shows that units with higher predicted
prices tend to have a shorter duration on the market, which is consistent with model
predictions under Full Information. Panel (b) shows that units with higher price residuals
tend to have a higher duration, on the market. Table 3.3 presents the same results in a
regression framework. In column (1), we regress (log) duration on (log) prices and obtain
a negative and statistically significant relation. If the price of a property increases by 1%,
expected duration decreases by 0.06%. In the second column, we split the (log) price into
two components—predicted and residual prices—and run the same regression. While we
obtain a negative and statistically significant relationship between duration and predicted
prices, we obtain a positive and statistically significant relationship between duration and
residual prices. In the last two columns, we split the analysis by type of operation (rent or
172
sale), and results are similar across regressions.15
Table 3.5 and Figure 3.10 in Appendix 3.7.4 reproduce the same analysis by replacing
duration with the average monthly clicks received by a listing (as a proxy for search inten-
sity). Results are consistent with those found for duration. Properties with high predicted
prices receive more clicks on average, which is consistent with a shorter duration. On the
other hand, properties with high residual prices receive fewer clicks on average, which is
consistent with a longer duration. This last set of results is important, because it shows
that listed prices do play an important role in attracting or repelling potential buyers by
affecting their search behavior.
(a) Predicted Prices (b) Residual Prices
Figure 3.7: Relationship between Prices and Duration
Note: Panel (a) shows the relationship between predicted prices and duration. Panel (b) shows the relation-ship between residual prices and duration. Price residuals and predicted prices are obtained after runninga regression of log prices on a set of fixed effects and observable characteristics. Figures show a binned scat-ter plot of each relationship, after controlling for location-time-type (offices, retail space, and warehouses)fixed effects.
The different relations that residual and predicted prices have with duration suggest
an important role of information. When higher prices stem from listed characteristics,
such as the location of the unit—which can be perfectly observed by buyers—they tend
to be associated with shorter time to sell. When high prices cannot be easily linked to
15The reason behind the inclusion of time-location fixed effects in the regression is to allow for the pro-cess of duration on the market to differ over time and location (e.g., the match efficiency could be marketspecific). However, the theory predicts that if a better observable location contributes positively to the qual-ity of the property, it should also have a positive effect on the trading probability. Therefore, the inclusionof fixed effects is absorbing part of this effect as well. Tables 3.3 and 3.4 in the Appendix show the resultsexcluding the location-time fixed effects. Results are robust to the exclusion of fixed effects.
173
(1) (2) (3) (4)log(Dur) log(Dur) log(Dur) log(Dur)
log(Price) -0.068***(0.001)
log(Predicted Price) -0.137*** -0.230*** -0.118***(0.006) (0.009) (0.009)
log(Residual Price) 0.033*** 0.029*** 0.038***(0.003) (0.004) (0.004)
Constant 2.014*** 2.143*** 1.801*** 2.528***(0.002) (0.011) (0.001) (0.042)
Observations 1090875 1090857 643713 447117R2 0.010 0.202 0.199 0.262Fixed Effects Yes Yes Yes YesSub Sample Full Full Rent Sale
Table 3.3: Prices and Duration
Note: This table presents the results of a regression of log duration on the two components of prices, residualand predicted prices. Because the left-hand-side variable is the log duration of a listing, we choose the right-hand-side variable to be the mean price over the lifetime of the listing. The first column shows a regressionof duration on prices. Column 2 regresses duration on predicted, residual prices, and location×time×typefixed effects. Columns 3 and 4 split the sample by operation (sale versus rent). Standard errors are clus-tered at the location-time level. *, **, and *** represent statistical significance at the 10%, 5%, and 1% level,respectively.
observable characteristics, then they are associated with longer time to sell.
Under the null hypothesis of full information, according to our model, residual prices
reflect characteristics of properties not observed by the econometrician. Then, we should
expect a negative relation with duration, as is the case with predicted prices. The fact that
we estimate a positive relation provides evidence that the extent of asymmetric informa-
tion cannot be zero. This conclusion is more formally supported in the estimation exercise
of the model, which allows us to provide a quantitative magnitude of the deviation from
full information.
Additional supporting evidence
3.3.3 Alternative explanations
In this subsection, we discuss alternative theories that could generate a positive re-
lation between residual prices and duration. In each case, we present evidence showing
174
that such alternative explanations are implausible, either because they have trouble rea-
sonably matching the magnitude of the relation between residual prices and duration,
and/or because they fail to simultaneously rationalize the relation between predicted
prices and duration.
Search theories of price dispersion
The positive relation between residual price and duration suggests a trade-off between
price and time-to-sell, giving rise to a natural explanation from the search literature. If
properties and agents are homogeneous, price dispersion obtains from sellers’ indiffer-
ence when choosing the price of their listed units: Higher prices are associated with less
search from buyers and more time to sell, and lower prices are associated with more
search and shorter time to sell. The key is that the trade-off between prices and time to
sell is such that they provide an equivalent expected revenue to the seller. This explana-
tion is akin to that of labor- and product-market models such as Burdett and Judd (1983)
and Burdett and Mortensen (1998).
To analyze the possibility that such theories explain the positive relation between
residual prices and duration, we exploit the data to compute the expected net present
values of listed properties at their residual prices and trading probabilities implied by the
relation in Panel (b) of Figure 3.7. That is, we compute
pq(1 − β(1 − p))
,
where q is the residual price, p is the selling probability, and β is the discount factor. The
formula is just a geometric sum corresponding to the expected net present value of listing
a price q and with a selling probability p. Note that we abstract from price changes in
this calculation and use the mean price instead, since the frequency of price changes is
small.16
Figure 3.8 shows the results for both types of transactions. The blue circle lines corre-
16The trading probability in a given month is computed from the duration of each property by q = 1−e−λ,where λ = 1/duration is the hazard rate.
175
(a) Sale (b) Rent
Figure 3.8: Net Present Value of Price-Duration Trade-off
spond to our benchmark calculation, in which we use the observed duration and mean
listed prices, and a discount factor of β = 0.99 to compute the net present value. The
data show that models of frictional price dispersion cannot explain the positive relation-
ship between residual prices and duration. In the data, the relationship is such that sellers
cannot be optimally choosing to randomize: The expected net present value is monoton-
ically increasing in the listed price. Any seller facing such price-duration trade-off will
maximize expected revenue by choosing the highest price we see in the data.
Heterogeneous Sellers
Another potential explanation for the positive relation is that residual prices do not
reflect heterogeneity in the properties’ unobserved characteristics, but rather heterogene-
ity in sellers’ preferences. Before we computed the net present value of a listing for a
risk-neutral and relatively patient seller (which makes the preference for a higher price
stronger). Here, we explore how our previous conclusion is affected by different prefer-
ences.
The orange diamond series in Figure 3.8 corresponds to an alternative calculation in
which we make sellers extremely impatient (β = 0). The rationale for this calculation
is that we may be ignoring heterogeneity in sellers’ discount factors which leads us to
conclude that some properties have higher returns when in reality low-price sellers are
176
setting lower prices in order to sell faster, given their low discount factor. By setting the
discount factor to 0, the calculation disproportionally affects properties that have lower
trading probabilities and high prices, flattening the net present value profile. However,
even in this extreme scenario, the relation between prices and duration in the data is such
that we still find that the net present value is monotonically increasing in the listed price.
If, under the preferences of the most impatient seller, a higher residual price with lower
selling probability is preferred, then the higher residual price would also be preferred
under any other possible discount factor.
The green series with triangles shows a case in which the realization of duration is
worse ex-ante than the one that is realized ex-post. The rationale for this exercise is as
follows. If sellers are heterogeneous with respect to their risk aversion, then some sellers
may post lower prices as a measure to insure themselves. To evaluate the quantitative
effect of this argument, we compute the NPV under extreme risk aversion: Sellers form
expectations of trading probabilities under a “worst-case” scenario. We create quantiles
of the price residual, and within each quantile we compute the standard deviation of
duration across listings. Then, to compute the trading probability of each property, we
use the realized duration plus 2 standard deviations of the duration within the quantile to
which each property belongs. If the distribution of durations is more dispersed (riskier)
for higher prices, then this exercise will shift the net present value of more expensive
properties, flattening the NPV profile. The green series in Figure 3.8 show that this is
indeed the case, but the quantitative magnitude is small: The NPV profile is still upward
sloping. Finally, the red square series combines both sources of seller heterogeneity: It
computes the NPV with both a zero discount factor and an adverse duration realization.
Even in this case, the NPV profile is upward sloping.
The conclusion of this analysis is that seller heterogeneity cannot rationalize the pos-
itive relationship between residual prices and duration. If it could, the NPV analysis
should show that sellers with different preferences should have different NPV-maximizing
prices. We find that for a very broad set of preferences (discount factors from 0 to 0.99,
and attitude toward risk from risk neutral to extreme forms of risk aversion), all sellers
would maximize their expected net present value by choosing the highest price observed
177
in the data.
The last piece of evidence against the role of sellers’ preferences is the negative relation
between the predicted prices and duration we estimate. According to Proposition 2 in our
model, sellers with homogeneous properties but different discount factors will optimally
choose different prices: The optimal price is increasing in the seller’s discount factor, since
a higher price is associated with a lower trading probability, which is relatively less costly
for more patient sellers. Importantly, this prediction applies in the case with full informa-
tion. If predicted prices reflect the component of a property’s quality that is observable
to market participants, then a model with heterogeneous sellers’ discount factor should
predict a positive relation between predicted prices and duration. However, we instead
estimate a negative relationship. Our claim is not that heterogeneity in sellers’ preferences
is not important, but that such heterogeneity cannot be the main driver of the data.
Heterogeneous Holding Costs
There is one additional source of sellers’ heterogeneity that is not considered by our
previous analysis of preference heterogeneity: the presence of heterogeneous holding
costs. These are understood as costs that sellers must pay each period until the property is
sold, such as maintenance costs, taxes, debt service costs, etc. If sellers face different costs,
then some sellers might be forced to list properties at low prices in order to sell their prop-
erty faster, as would occur in a fire sale. This would generate the positive relation between
residual prices and duration. We explore this possibility by computing the size of this cost
that would render sellers indifferent between listing at the highest price without a cost or
at their chosen price with a cost. That is, we compute the necessary holding cost of each
listing relative to the holding cost of a seller who listed his property at the highest price.
We then present the size of this cost as a share of the listed price. The question we seek to
answer with this exercise is: How large must the cost be in order to rationalize the choice
of a lower residual price?
To compute the (unobserved) cost, c, we solve the following equation:
phqh − c j(1 − ph)
1 − β(1 − ph)=
p jqj − c j(1 − p j)
1 − β(1 − p j),
178
where qh and ph are the price and selling probability of the property with the highest
residual price, respectively, and qj and p j are the price and probability we observe for
property j. In order to rationalize the preference for a lower price and a higher trading
probability, the cost must be higher when the difference between prices is larger and when
the difference in durations is smaller. We estimate how large these costs must be in order
to rationalize the choice of sellers for the case of sales. We present the cost normalized
by the price of the most expensive property (in relative terms). Figure 3.9 presents the
results. We can see that in order for differential holding costs to explain the differences
in returns in the data, they must be extremely large. To illustrate, the cost of holding 1
square foot of a property for 1 additional month would have to be larger than the price
at which the owner can sell that unit. We conclude that it is unlikely that the bulk of the
positive relation between residual prices and duration is explained by the presence of
heterogeneous holding costs.
Figure 3.9: Required Holding Costs
3.4 The Relevance of Information Frictions in the Capital
Market
In this section, we calibrate the model to quantify the extent of asymmetric informa-
tion in the market for physical capital. We then explore the effects of information frictions
on allocations, prices, and liquidity by comparing equilibria with asymmetric and full
179
information.
3.4.1 Quantifying Frictions: Model and Data
Calibration We calibrate the model under the assumption that the data are generated
from a separating equilibrium in steady state. We choose to calibrate the model to a
monthly frequency. There are two groups of parameters. The first group is set outside
of our calibration exercise: β, η, χ, ϕK , and ϕE . The subjective discount factor β is chosen
to match an annualized interest rate of 4%. The elasticity of the matching function η is
set to 0.86 following Ottonello (2017), who estimates it using data from Idealista. Without
loss of generality, we normalize the search cost χ to one.17 We set ϕE to 0.008 to match
an annual firm exit rate of 9% (EUROSTAT). The assumption here is that when firms exit,
they list their commercial real estate for sale. Finally, we set the number of types z and a
to 100 each. These parameters are summarized in Table 3.4.
Parameter Description Valueβ Monthly discount factor 0.997η Elasticity matching function 0.860χ Search Cost (normalized) 1.000ϕK = ϕE Transition prob. 0.008Nz Number of z types 100Na Number of a types 100
Table 3.4: Externally Set Parameters
We jointly calibrate a second group of parameters—δ, σ2a, σ2
z , and m—by matching im-
portant identifying moments in the data. For this, we choose a set of moments as targets
of the calibration of the model: the standard deviation of log residual prices, the covari-
ance between residual prices and duration, the unconditional average duration, and the
coefficients of a regression of log prices on the characteristics of properties (see equation
(3.12)). For a given set of parameters, we compute the equilibrium choices of prices and
transaction probabilities for each type of capital. Then, we simulate the evolution of multi-
ple units of capital, generate a sample of listed units as in Idealista, and perform the same17We can show the following result. Take any combination (m1, χ1). Then, for any given value χ2, the
equilibrium allocation, prices, and transaction probabilities with m2 =(
m1
χ1−η1
)χ
1−η2 are the same.
180
analysis as the one performed with the microdata from Idealista. Finally, we compute
those identifying moments with the simulated data and use a minimum-distance estima-
tor to choose parameter values that match the moments in the data. Since the model is
meant to capture the equilibrium within a specific market, we choose to calibrate it to a
neighborhood in the city center of Madrid. Appendix 3.8 provides more details of this
procedure.
Although there is no one-to-one mapping from parameters to moments, we provide
intuition of the identification of the model parameters. The average transaction probabil-
ity is pinned down by the matching efficiency m. The vector δ transforms the characteris-
tics of a property into the dividend it produces. Since dividends are reflected in the price
of a property, those parameters are identified by the parameters of the hedonic regression
of prices on the characteristics of units of capital. Finally, the key parameters σ2a and σ2
z
are jointly identified by the standard deviation of residual prices (those obtained after es-
timating the hedonic regression) and the covariance of residual prices and duration. The
intuition is that the dispersion of prices is increasing in both σ2a and σ2
z . However, as we
showed before, the covariance responds differently to changes in σ2a than to changes in
σ2z . The higher σ2
a is, the larger the component of residual prices driven by quality that is
private information of the seller. According to the predictions of the model, there should
be a more positive covariance between residual prices and duration. On the other hand,
the higher σ2z is, the larger the component of residual prices driven by observable qual-
ity. In this case, there should be a more negative covariance between residual prices and
duration. These two opposing forces allow us disentangle the relative magnitudes of σ2a
and σ2z .
Table 3.5 reports the calibrated parameters. The value of the matching efficiency im-
plies that on average, properties stay on the market for 10 months. The presence of large
trading frictions allows sellers of high-quality capital to signal their type by spending
more time on the market. The values of σ2z and σ2
a imply large quality heterogeneity
across units of capital. Without including variation in observable characteristics, the stan-
dard deviation of (log) quality is 0.67. Of this overall heterogeneity, 21% is attributed to
heterogeneous quality that is private information of the seller.
181
Param. Description Value Target Data Modelm Match efficiency 1.050 Avg. log duration 1.802 2.523σ2
z Var. z 0.280 Var. log prices 0.124 0.122σ2
a Var. a 0.030 Var. log duration 0.643 1.065σza Cov. z and a 0.000 Cov. log prices and duration 0.017 0.012
Table 3.5: Internally Calibrated Parameters
Goodness of Fit Figure 3.10 presents the joint distribution of prices and duration, in
both the data and the model. The overall fit is good. Although the model generates ex-
cess mass at high durations, the distribution of prices is well approximated (additional
results on the goodness of fit are presented in Appendix 3.8). Additionally, in Table 3.6
we reproduce the regression results reported in Table 3.3 for this specific market. There is
a positive relationship between residual prices and duration. This is expected, since we
targeted the covariance between these two variables. However, the regression results also
report a negative relationship between predicted prices and duration, in both the data
and the model. This is an additional test of the quantitative exercise, since it was not part
of the set of targeted moments.
(a) Data (b) Model
Figure 3.10: Joint Distribution of (log) Prices and DurationNote: These figures plot the joint distribution of (log) prices and duration in the data (Panel (A)) and in themodel (Panel (B)). Lighter colors denote a higher concentration of observations in given price-duration pair.
182
Data Modellog(Dur) log(Dur)
Intercept 3.119 2.780( 0.579) ( 0.314)
Predicted price -0.231 -0.045( 0.102) ( 0.055)
Residual price 0.141 0.097( 0.040) ( 0.021)
N 3247 19332R2 0.005 0.001
Table 3.6: Regression coefficientsNote: This table presents the results of a regression of log duration on the two components of prices, residualand predicted prices. Predicted and residual prices are obtained from a first regression of (log) prices onthe observable characteristics of capital (denoted by the vector X). The first column estimates the regressionwith data from Idealista. The second column estimates the regression with simulated data generated fromthe model.
3.5 Counterfactual Analyses
In this section, we perform a series of counterfactual analyses to quantify the effects in-
formation frictions have on allocations, prices, and liquidity. We begin by deriving a set of
equilibrium objects that will guide the discussion of the role of asymmetric information.
Capital Unemployment As previously shown, information frictions generate lower av-
erage trading probabilities. Therefore, one of the variables affected by asymmetric infor-
mation is the stock of unemployed capital. To derive the implications for capital unem-
ployment, we begin with the law of motion of the stock of unemployed capital of quality
(ω, a):
k′K
(ω, a) = kE(ω, a)ϕK (1 − p(ω, a)) + kK (ω, a)(1 − ϕE)(1 − p(ω, a)).
The stock of unemployed capital in the following period contains: (1) units of capital
that are employed in the current period, whose owner experiences a negative shock and
becomes a capitalist, and are not sold at the beginning of the following period, and (2)
units of capital that are unemployed in the current period, whose owner does not become
an entrepreneur, and are not sold at the beginning of the following period. The steady
183
state unemployment rate thus becomes:
u(ω, a) =ϕK (1 − p(ω, a))
p(ω, a) + (ϕK + ϕE)(1 − p(ω, a)).
Finally, we can compute the steady state aggregate stock of unemployed capital as
E(u(ω, a)ωa
)= E
(u(ω, a)
)︸ ︷︷ ︸Avg. unemployment
rate
E (ωa) + Cov(u(ω, a), ωa
)︸ ︷︷ ︸Composition of
unemp. capital
.
Asymmetric information affects the stock of unemployed capital via two effects. First,
asymmetric information reduces average trading probabilities, and therefore increases
the average unemployment rate across units of different qualities. Second, there is a com-
position effect. Because asymmetric information reduces more the trading probabilities
of units of capital of higher quality, the pool of unemployed capital is composed of units
with higher average quality than the unconditional average quality in the economy.
Illiquidity Discounts The reduction in trading probabilities caused by asymmetric in-
formation has implications for the valuation of assets. To see this, recall that the price of
an asset of quality (ω, a) is given by
p(ω, a) = vE(ω, a) −χ
µ(θ(ω, a)),
thus reflecting the valuation of the asset by the entrepreneur and the total search costs
incurred to purchase the unit of capital. In turn, we can express the value of the unit of
capital to the entrepreneur as
vE(ω, a) =ωa
1 − β
(1 −
βϕK(1 − p(ω, a)
)1 − β(1 − ϕK − ϕE)
(1 − p(ω, a)
)︸ ︷︷ ︸Illiquidity discount
)
−βϕK χθ(ω, a)
(1 − β)(1 − β(1 − ϕK − ϕE)
(1 − p(ω, a)
))︸ ︷︷ ︸Search costs
.
184
As in Duffie et al. (2005), the fact that current entrepreneurs might become sellers in the
future means that the value of a unit of capital for an entrepreneur today is affected by
trading frictions. First, the value of capital includes the net present value of dividends, re-
duced by an illiquidity discount. Entrepreneurs value less units of capital that take longer
to sell. Second, since future sale prices are discounted by buyers’ total search costs, a lower
buyers’ trading probability increases such costs and reduces the sale price. Therefore, a
higher market tightness θ(ω, a) decreases the illiquidity discount, but increases buyers’
search costs.
Counterfactual 1: Quantifying the Effects of Asymmetric Information Having esti-
mated the parameters of the model, we quantify the effects of asymmetric information on
equilibrium allocations, prices, and liquidity. To do so, we compare the model’s predic-
tions with a counterfactual scenario in which there is no private information. The latter
corresponds to a version of the model in which the a component of quality is perfectly
observed by all market participants.
Results are reported in Table 3.7. The first column reports equilibrium objects in the es-
timated model and the second column reports them for the counterfactual scenario with
full information. Of the aggregate stock of efficiency units of capital of 1.3 (the stock of
units of capital is normalized to 1), 0.24 are misallocated due to information frictions. The
average unemployment rate of capital is 18% with asymmetric information, and close
to zero with full information. The contribution of the composition effect to capital un-
employment is small: The stock of unemployed capital (in efficiency units) is only 4%
higher, because higher-quality capital is more likely to be unemployed. These results are
further illustrated by the second panels in Figures 3.11 and 3.12, which show the equi-
librium trading probabilities of properties with different (z, a) qualities. In the case with
asymmetric information, the gradient of the trading probability with respect to the un-
observed quality a is negative and steep. Instead, with full information, this gradient is
positive and not as steep.
Table 3.7 further reports that information frictions decrease the unconditional aver-
age price of units of capital by 16.7% relative to the scenario with full information. The
185
reduction in prices is almost entirely brought about by a decrease in the entrepreneurs’
valuations of assets (the contribution of the reduction of buyers’ search costs is negligi-
ble). In turn, entrepreneurs’ valuations are severely affected by the illiquidity discount:
Asymmetric information leads to an illiquidity discount of 16.4%. With full information,
this discount is close to zero. These results are further illustrated in the first panels in Fig-
ures 3.11 and 3.12, which show the equilibrium prices of properties with different (z, a)
qualities.
Finally, Table 3.7 presents the comparison of welfare across scenarios. In our model,
welfare is given by total dividends produced by employed capital net of the search costs
buyers pay in order to search and match with sellers. The latter are determined by the
search cost χ and the mass of buyers searching in the market: χE(θ(ω, a)kK (ω, a)
). In
the estimated model, the welfare losses generated by information frictions are equivalent
to 18.4% of welfare in the counterfactual with full information. In the estimated model,
search costs are negligible. The fact that sellers face low trading probabilities means that
buyers are meeting sellers with high probabilities, so they do not incur large search costs.
With full information, search costs are slightly larger, but still represent only 0.02% of
total welfare. To sum up, we find that the effects of information frictions in the market for
physical capital are large. The magnitudes of the effects on allocations and prices are on
the same order of magnitude of the estimated effects of trading frictions (e.g., Gavazza,
2016).
3.6 Conclusion
In this paper, we documented that information asymmetries play a key role in as-
set markets. This conclusion emerges from a new methodology to measure information
frictions and from applying this methodology to microlevel data on the physical capital
market. The methodology builds upon theories of asymmetric information in markets
with trading frictions, which predict that information affects the relationship between
prices and trading probabilities. The empirical analysis shows that the patterns between
listed prices and duration are consistent with the presence of asymmetric information.
186
Asym. Info. Full Info.
E(u(ω, a)ωa
)0.2419 0.0018
E(u(ω, a)
)0.1786 0.0016
Cov(u(ω, a), ωa
)0.0090 -0.0003
E(q(ω, a)
)318.7825 382.7327
E(vE(ω, a)
)318.7829 382.9802
E(χ/µ(ω, a)
)0.0004 0.2475
Avg. Illiquidity Disc. 0.1641 0.0016
Welfare 1.0624 1.3023
Output 1.0624 1.3026
Search Costs 0.0000 0.0003
Table 3.7: The Role of Information: Asymmetric vs Full Information
Note: This table reports the results of counterfactual analysis. The first column reports statistics on capi-tal unemployment, prices, and welfare in the calibrated model with asymmetric information. The secondcolumn reports similar statistics under the counterfactual scenario in which the a component of qualitybecomes the common knowledge of all market participants.
Figure 3.11: Prices and Trading Probabilities: Asymmetric Information
187
Figure 3.12: Prices and Trading Probabilities: Full Information
Combining theory and data, we estimate that information frictions are large and have a
significant effect on output, prices, and liquidity.
In future research, our methodology could be used to inform models of asymmetric
information and business cycles. In this area, an important additional element to consider
would be the presence of financial frictions that interact with information and trading
frictions. For instance, if capital is used as collateral, asymmetric information could be a
first order factor shaping firms’ and households’ access to financial markets. In addition,
one could study how asymmetric information affects the production of new capital, and
how policies can affect the choice of quality in aggregate investment. These extensions
are planned for future research.
188
3.7 Appendix
3.7.1 Empirical Appendix
3.7.2 The online platform
This subsection describes how the platform works. When entering the website, the
buyer encounters the screen shown in Figure 3.1. The platform asks the client to choose
a type of transaction (buy, rent, or find a shared space), the type of property (retail store,
office, etc.), and the location.
Figure 3.1: Main Website
Once those options are selected, suppose the client wants to find a unit in Madrid
(Figure 3.2). There, the website shows the number of properties available for sale by area
in the city.
189
Figure 3.2: Options Madrid
After choosing a narrower location within the city (not shown here), the client finds a
scrolling list of the available units that meet her requirements, as shown in Figure (3.3).
There, the user can include more filters depending on her requirements for layout and
amenities.
190
Figure 3.3: Available listings in a narrow location in Madrid
When the user finds a unit that may be to her taste and clicks on it, a window pops up
with the details shown in Figure 3.4 plus text details not shown here. The main informa-
tion the listing contains is the unit description with pictures, price, change in price, area,
date of construction, and other amenities and equipment.
191
Figure 3.4: A listing on the website
3.7.3 Representativeness of the dataset
In this subsection, we analyze the representativeness of the dataset, showing that our
data is consistent with aggregate patterns observed in Spain over this period. We provide
two pieces of evidence about our data. First, we show that in our data, the price index
exhibits the patterns of aggregate data. Second, we show that the patterns of sales follow
those of aggregate sales of structures in Spain.
Figure 3.5 shows the index of listed prices for properties for sale in our sample and the
index of transacted prices of retail space in Spain (the latter come from official transaction
records). Both indexes are normalized to one at their respective peak. We highlight the fact
that the fall in prices we observe is consistent, and very similar in size to that observed for
retail space in Spain during the recent financial crisis. Moreover, our index leads the ag-
gregate index, which is expected since our index consists of listed prices. This is expected,
since our index consists of listed prices and it will take properties some months to exit the
192
database, be registered as sales, and be recorded in national statistics.
Figure 3.6 shows the index of sales for properties for sale in our sample and the aggre-
gate sales index of real estate in Spain. Both indexes are normalized to take the value of 1
in the first month of 2007. The index for our data is constructed by computing the share
of units that exit the database with respect to the number of active posts in that month. In
the case of the aggregate number, we normalize the number of sale transactions recorded
by the Statistical Agency. In doing this, we assume that the total stock of units during this
period is fairly constant (we do not have information on the size of the stock). Although
our index is noisier than the national estimates, the patterns of the two series are close to
each other.
0.5
0.6
0.7
0.8
0.9
1.0
2005q1 2010q1 2015q1 2020q1Date
Aggregate Data Idealista Madrid
Idealista Barcelona
Figure 3.5: Price Index: Dataset versus Aggregate DataNote: The solid line shows the price index for properties for sale in Barcelona and Madrid in our dataset. The
dashed line shows the aggregate retail space price index gathered from the National Registry of Property
(Registradores de Espana). All indices are normalized to their respective peak.
193
0.0
0.5
1.0
1.5
2005m1 2010m1 2015m1 2020m1Date
Idealista Data Aggregate Data
Figure 3.6: Sales Rate: Dataset versus Aggregate DataNote: The solid line shows the sales rate for properties in our dataset. The dashed line shows the aggregate
sales index of real estate gathered from the Statistical Agency of Spain (INE). Both indices take the value of
one in January 2007.
194
3.7.4 Additional Figures and Tables
Figure 3.7: Distribution of Duration: Confirmed SalesNote: This figure compares the histogram of duration for two subgroups of listings: those that, after remov-
ing the listing from the platform, explained that they did so because the property was rented out or sold,
and those that did not provide an explanation.
6
8
10
12
14
2006 2008 2010 2012 2014 2016
Date
(a) Capital for Sale
6
7
8
9
10
11
2006 2008 2010 2012 2014 2016
Date
(b) Capital for Rent
Figure 3.8: Evolution of Average Duration
Note: The left panel shows the evolution of mean time to sell (in months) at monthly frequency from 2006to 2017. The right panel shows an equivalent index for rental units. Time to sell is measured as the timedifference between the entry and exit dates of each listing. Each observation contains the average time tosell for listings that entered the online platform in a given month.
195
7.00
7.20
7.40
7.60
7.80
log
price
45 50 55 60 65 70Participation
(a) Price and Labor-Force Participation
7.10
7.20
7.30
7.40
7.50
7.60
7.70
log
price
0 10 20 30 40Unemployment
(b) Prices and Unemployment
Figure 3.9: Capital Prices and Regional Business Cycles
Note: This figure shows the relationship between log prices of posts for sale in a given province in a given
quarter year with economic variables, in this case labor-force participation and unemployment rate. The
figure presents a binned scatterplot, in which we choose 100 quantiles of the relationship between the
economic variable of interest and log prices and compute the average for observations in that quantile.
Rent Office Sale Office Rent Warehouse Sale Warehouse
Frequency of Price Changes 0.07 0.07 0.05 0.07Frequency of Price Increases 0.02 0.02 0.02 0.02Frequency of Price Decreases 0.05 0.05 0.04 0.05Absolute Size of Price Changes 0.15 0.12 0.16 0.15Absolute Size of Price Increases 0.19 0.15 0.19 0.18Absolute Size of Price Decreases 0.14 0.11 0.15 0.14
Table 3.1: Frequency of Price Changes for Capital
Note: This table presents price adjustment statistics by property type and operation. In order to compute thetable, we first compute statistics about price changes within each property and then take averages acrossproperties in a given time period. Finally, we compute the average over time. The first row shows thefrequency of price changes, which is the average share of properties that exhibit a price change in a givenmonth. The following two rows show the share of listings with price increases and decreases. The absolutesize of price changes is computed as the absolute value of the log difference in prices over consecutivemonths (ignoring the zeros).
196
Sale Rent
Statistic IQR R2 IQR R2
Raw Data 0.666 0.000 0.802 0.000
Benchmark 0.284 0.776 0.198 0.845
Property Fixed Effect 0.119 0.946 0.116 0.937
Table 3.2: Price Variation Accounted for by Listed Characteristics in New Entrants
Note: This table extends Table (3.2) by including a property fixed effect, which gathers inference from prop-
erties that change their prices while they are active in the dataset. We find that after including property
fixed effects, non-parametrically absorbing all of the property’s time-invariant price determinants, the IQR
is roughly 11% and the R2 is roughly 0.94.
(1) (2) (3)
log Dur log Dur log Dur
log(Price) -0.012***
(0.002)
log(Predicted Price) -0.032*** -0.118***
(0.006) (0.009)
log(Residual Price) 0.035*** 0.038***
(0.004) (0.004)
Observations 447141 447141 447117
R2 0.000 0.001 0.262
Subsample Full Full Full
Fixed Effects No No Location-Time
Table 3.3: Regression of Prices on Duration - SaleNote: This table presents the results of a regression of log duration on the two components of prices, residual
and predicted prices. The sample includes listings for sale only. Because the left-hand-side variable is the
log duration of a listing, we choose the right-hand-side variable to be the mean price over the lifetime of the
listing. The first column shows a regression of duration on prices. Column 2 regresses duration on predicted
and residual prices. Column 3 additionally includes location×time×type fixed effects. *, **, and *** represent
statistical significance at the 10%, 5%, and 1% level, respectively.
197
(1) (2) (3)
log Dur log Dur log Dur
log(Price) -0.116***
(0.002)
log(Predicted Price) -0.186*** -0.230***
(0.008) (0.009)
log(Residual Price) 0.032*** 0.029***
(0.005) (0.004)
Observations 643734 643734 643713
R2 0.009 0.015 0.199
Subsample Full Full Full
Fixed Effects No No Location-Time
Table 3.4: Regression of Prices on Duration - RentNote: This table presents the results of a regression of log duration on the two components of prices, residual
and predicted prices. The sample includes listings for rent only. Because the left-hand-side variable is the
log duration of a listing, we choose the right-hand-side variable to be the mean price over the lifetime of the
listing. The first column shows a regression of duration on prices. Column 2 regresses duration on predicted
and residual prices. Column 3 additionally includes location×time×type fixed effects. *, **, and *** represent
statistical significance at the 10%, 5%, and 1% level, respectively.
198
(a) Predicted Prices (b) Residual Prices
Figure 3.10: Relationship between Prices and Clicks
Note: Panel (a) shows the relationship between predicted prices and average monthly clicks. Panel (b) showsthe relationship between residual prices and average monthly clicks. Price residuals and predicted pricesare obtained after running a regression of log prices on a set of fixed effects and observable characteristics.The figures show a binned scatter plot of each relationship, after controlling for location-time-type (offices,retail space, and warehouses) fixed effects.
(1) (2) (3) (4)Clicks Clicks Clicks Clicks
log(Price) 3.437***(0.113)
log(Predicted Price) 28.218*** 41.899*** 8.710***(0.991) (1.683) (0.648)
log(Residual Price) -31.318*** -40.048*** -19.907***(0.828) (1.102) (0.521)
Constant 52.649*** 6.464*** 75.808*** 1.649(0.224) (1.845) (0.231) (3.078)
Observations 1070976 1070810 632581 438064R2 0.028 0.369 0.399 0.341Subsample Full Full Rent Sale
Table 3.5: Prices and Clicks
Note: This table presents the results of a regression of log average monthly clicks on the two componentsof prices, residual and predicted prices. Because the left-hand-side variable is the average monthly clicks alisting received, we choose the right-hand-side variable to be the mean price over the lifetime of the listing.The first column shows a regression of clicks on prices. Column 2 regresses clicks on predicted and residualprices, and location×time×type fixed effects. Columns 3 and 4 split the sample by operation (sale versusrent). Standard errors are clustered at the location-time level. *, **, and *** represent statistical significanceat the 10%, 5%, and 1% level, respectively.
199
3.8 Quantitative Analysis
3.8.1 Goodness of Fit
-1 0 1 2 3 4 5 6 7
-1
0
1
2
3
4
5
6
7
Figure 3.11: Regression Coefficients: Data vs Model
200
Figure 3.12: Histogram of Prices: Data vs Model
Figure 3.13: Histogram of Predicted Prices: Data vs Model
201
Figure 3.14: Histogram of Residual Prices: Data vs Model
Figure 3.15: Histogram of Duration: Data vs Model
202
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