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The Impact of Consumer Credit Access onUnemployment
Kyle F. HerkenhoffNBER Working Paper (2018)
Macroeconomics Reading GroupMorteza Ghomi
March 6, 2019
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Outline
Introduction
ModelHouseholdsSaving and Lending InstitutionsFirms
Stochastic Steady StateCalibration1977 vs. 2010
Exploring the Model’s MechanismsIR Experiment
Main Quantitative ExperimentFixed vs. Fluctuating accessTrend vs. Cycle
Conclusion
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Introduction
I Unemployed households’ access to unsecured revolving creditmore than tripled over the last three decades
I Low asset unemployed households replace approximately 15%of lost income through unsecured borrowing
I 40% of households self-report defaulting on non-mortgagepayments in response to job loss
I The ability to borrow significantly prolongs unemploymentdurations and raises replacement wages (Herkenhoff et al2015)
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Main Question
”How growth and fluctuations in households’ access to creditmarkets since the 1970s have affected the way employment evolvesover the business cycle?”
Main features
I Trying to answer this question both theoretically andquantitatively
I Using a general equilibrium search and matching model withdefaultable debt and searching in two markets
I Taking into account saving and lending institutions
I Both aggregate and idiosyncratic shocks, heterogeneity inemployment outcome and credit histories and interactionbetween them
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Main Question
”How growth and fluctuations in households’ access to creditmarkets since the 1970s have affected the way employment evolvesover the business cycle?”
Main features
I Trying to answer this question both theoretically andquantitatively
I Using a general equilibrium search and matching model withdefaultable debt and searching in two markets
I Taking into account saving and lending institutions
I Both aggregate and idiosyncratic shocks, heterogeneity inemployment outcome and credit histories and interactionbetween them
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Main Contributions
I The paper develops a general equilibrium search and matchingmodel with defaultable debt
I The paper measures the mechanisms through which creditaccess impacts unemployment over the business cycle
I The paper constructs aggregate time series for unemployedhouseholds’ access to credit and use of credit from 1970onwards
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Main Results
I Credit fluctuations have contributed to moderately deeper andlong lasting recessions over the last 40 years
I As more individuals obtained credit access from 1977 to 2010,credit fluctuations became more important determinants ofemployment dynamics
I Even though business cycles are more volatile, newbornsstrictly prefer to live in the economy with growing, butfluctuating, access to credit markets
I In the absence of procyclical credit fluctuations, slow-movingtrend credit growth may actually dampen business cycledynamics
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ModelNotation
I Time is discrete
I T ≥ 2 overlapping generations of risk averse HH facing bothidiosyncratic and aggregate shocks
I Each household lives T periods deterministically
I ct : consumption, ht : indivisible labor, and η: leisure
I x(D): penalties of default (fraction of debt defaulted upon)
I χc : cost of searching in credit market
I States:I HH:
e ∈ W ,U, a ∈ C ,N,w ∈W , z = γw ∈ Z , b ∈ B, t ∈ NT
I Aggregate state: Ω = [y ,A, µ]I µ : W ,U × C ,N ×W ∪ Z ××B × NT → [0, 1]
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ModelNotation
I Time is discrete
I T ≥ 2 overlapping generations of risk averse HH facing bothidiosyncratic and aggregate shocks
I Each household lives T periods deterministically
I ct : consumption, ht : indivisible labor, and η: leisure
I x(D): penalties of default (fraction of debt defaulted upon)
I χc : cost of searching in credit market
I States:I HH:
e ∈ W ,U, a ∈ C ,N,w ∈W , z = γw ∈ Z , b ∈ B, t ∈ NT
I Aggregate state: Ω = [y ,A, µ]I µ : W ,U × C ,N ×W ∪ Z ××B × NT → [0, 1]
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Household ProblemTiming
Each period consists of three stages:
1. HH participate in asset market, search for borrowingopportunities and make accumulation and default decision
2. HH enter labor market and make job search decision
3. Expense shocks are realized
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Household Problemfirst stage
I HH choose whether or not to look for credit, cost = χc
I w.p AψU,t(z , b, ; Ω) they will match and bargain over terms ofloan (A is matching efficiency)
I They remains matched until the HH defaults, D > 0, or thematch is destroyed exogenously (with rate s)
I Breakup probability:
s(D) =
1 if D > 0
s if D = 0
I BE for employed and unemployed agent:
Ut(z , b, ; Ω) = maxAψU,t(z , b, ; Ω)UCt (z , b, ; Ω) + (1− AψU,t(z , b, ; Ω))
UNt (z , b, ; Ω)− χC ,U
Nt (z , b, ; Ω) ∀t ≤ T
Wt(z , b; Ω) = maxAψW ,t(w , b; Ω)W Ct (w , b; Ω) + (1− AψW ,t(w , b; Ω))
WNt (w , b; Ω)− χC ,W
Nt (w , b; Ω) ∀t ≤ T
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Household Problemsecond stage
I Asset market closes and aggregate state is realized
I Unemployed agents enter the labor market looking for jobspaying w ∈W
I Each submarket is indexed by a wage and age pair (w , t)
I pt(w ,Ω′): Pr. of matching with an employer paying w
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Household Problemthird stage
I Labor market closes and expense shock is realized
I This shock is designed to disconnect default from employmentstatus
I With probability px , they begin the next period with anadditional debt burden of x
I For each BE V ∈ W ,W c ,U,UC :
V (w , b′; Ω′) = pxV (w , b′ − x ; Ω′) + (1− px)V (w , b′; Ω′)
I LOM for aggregate state:
Ω′ = (µ′,A′, y ′) µ′ = Φ(ω,A′, y ′)y′ ∼ F (y ′|y) A′ ∼ G(A′|A)
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Household ProblemBellman Equation
For an unemployed with access to credit:
UCt (z, b, ; Ω) = max
b′∈B,D∈[0,1]u(c)− x(D) + η
+(1-s(D))βEΩ′
[maxw∈W
pt+1(w ; Ω′)(W Ct+1(w , b′; Ω′))+(1−pt+1(w ; Ω′))UC
t+1(z, b′, ; Ω′)
]+s(D)βEΩ′
[maxw∈W
pt+1(w ; Ω′)(Wt+1(w , b′; Ω′)) + (1− pt+1(w ; Ω′))Ut+1(z, b′, ; Ω′)
]
UCT+1(z, b; Ω) = 0
subject to the budget constraint:
c + qU,t(z, b′,D,Ω)b′ ≤ z + (1− D)b
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Household ProblemBellman Equation
For an unemployed without access to credit:
UNt (z, b; Ω) = max
b′≥0,D∈[0,1]u(c)− x(D) + η
+βE
[maxw∈W
pt+1(w ; Ω′)(Wt+1(w , b′; Ω′)) + (1−pt+1(w ; Ω′))Ut+1(z, b′, ; Ω′)
]∀t ≤ T
UNT+1(z, b; Ω) = 0
subject to the budget constraint:
c + 11+rf
b′ ≤ z + (1− D)b
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Household ProblemBellman Equation
For an employed household:
W Ct (w , b; Ω) = max
b′∈B,D∈[0,1]u(c)− x(D) + βE
[(1− δ)(Wt+1(w , b′; Ω′)) +
δmaxw∈W
pt+1(w ; Ω′)(Wt+1(w , b′; Ω′)) + (1−pt+1(w ; Ω′))Ut+1(γw , b′, ; Ω′)]∀t ≤ T
subject to:
c + qW ,t(w , b′,D; Ω)b′ ≤ w + (1− D)b
WNt (w , b; Ω) = max
b′≥0,D∈[0,1]u(c)− x(D) + βE
[(1− δ)(Wt+1(w , b′; Ω′)) +
δmaxw∈W
pt+1(w ; Ω′)(Wt+1(w , b′; Ω′)) + (1−pt+1(w ; Ω′))Ut+1(γw , b′, ; Ω′)]∀t ≤ T
subject to:
c + 11+rf
b′ ≤ w + (1− D)b
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Saving Institutions and Lending Institutions
I Unit measure of risk neutral saving institutions and a unitmeasure of risk neutral lending institutions
I Saving institutions accept deposit each period in a frictionlessmarket offering the risk free rate (rf ) on saving
I Lending institutions send out credit offers to potentialborrowers with cost κC and are guaranteed a minimumproportional service fee τ
I After being matched, households have full bargaining powerand send take-it-or-leave-it bond price offer
qe,t(w , b′,D; Ω)=
sE [1− Da′e′,t+1
(w ′, b′; Ω′)] + (1− s)E [1− DCe′,t+1
(w ′, b′; Ω′)]
1 + rf + τif b′ ∈ B−and D = 0
0 if b′ ∈ B−and D > 0
1
1 + rfif b′ ∈ B+
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Firms
I Firms post fixed wage contracts (w,t) with cost κL
I The posted wage w is fixed once an employee is found
I Vacancy filling rate: ft(w ; Ω)
I BE for a firm:
Jt(w ; Ω) = y − w + βE[(1− δ)Jt+1(w ; Ω)
]∀t ≤ T
I Free entry of firms:
κL = ft(w ; Ω)Jt(w ; Ω) iff θt(w ; Ω) > 0
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Equilibrium
I We will focus on Block Recursive Competitive Equilibria
I Under relatively weak assumptions, a block recursiveequilibrium exists
I Under more restrictive conditions, the equilibrium is unique
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Stochastic Steady Statespecifying the functions
I Preferences:u(c) + η(1− h)− x(D) = c1−σ−1
1−σ + η(1− h)− κD D1−D+εD
I Matching function in both labor and credit market:M(u, v) = u.v
(uζ+vζ)1ζ∈ [0, 1)
I Aggregate productivity deviations:ln(y ′) = ρln(y) + ε1 ε1 ∼ (0, σ2
e )
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Stochastic Steady stateCalibration
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Stochastic Steady state1977 vs. 2010
Same calibration, different matching efficiency: A1977 = 0.48 andA2010 = 0.72
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Exploring the Model’s Mechanismstwo effects
When credit access expands:I Expansion Effect
I In the short run, acts like a safety net and households feelmore secure
I HH optimally search for better-paying but harder-to-find jobsI If credit grows coming out of a recession, this may lead to
elevated unemployment in the short run and a slower recovery;
I Level EffectI With greater long-run levels of credit access, more individuals
dissave and enter recessions indebtedI With a tighter labor market in a recession, indebted agents
avoid default by cutting their reservation wagesI Tends to dampen employment volatility over the business cycle
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IR Experiment of a productivity shockcredit expansion: before vs. after recession
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IR Experiment of a productivity shockthe level matters!
Larger Fraction Borrowing Amplifies Credit Shocks
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Main Quantitative Results
I Credit growth coming out of the 1990, 2001, and 2007recessions increases the severity of each downturn
I In the 2001 and 2007 recessions, credit growth reduces thespeed of recovery
I At every point along the transition path, newborns prefer tolive in the world with fluctuating, but growing, credit access,even though the unemployment rate is more volatile, and lastly
I Credit fluctuations, as opposed to trend credit growth, areprimarily responsible for generating slower recoveries
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Main Quantitative Resultsfixed access vs. expanding and fluctuating access
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fixed access vs. expanding and fluctuating access
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fixed access vs. expanding and fluctuating access
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Main Quantitative ResultsWelfare Gains from 1977 to 2010
I During the late 2000s, individuals are willing to give up moreto live in an economy with greater credit access, even thoughbusiness cycles are more volatile
I Credit is more valuable during recessions, welfare gains arehigher for cohorts born during the 2007-2009 crisis
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Main Quantitative ResultsTrend vs. Cycle
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Trend vs. Cycle
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Trend vs. Cycle
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Conclusion
I Unemployed households’ access to credit has grownremarkably, but how it affects business cycles and welfare?
I Credit fluctuations have contributed to moderately deeper andmore protracted recessions over the last 40 years
I As more individuals obtained credit access, credit fluctuationsbecame more important determinants of employmentdynamics
I Even though business cycles are more volatile, newbornsstrictly prefer to live in the economy with growing, butfluctuating, access to credit markets
I In the absence of procyclical credit fluctuations, trend creditgrowth may actually dampen business cycle dynamics
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