government investment and the stock market
TRANSCRIPT
Electronic copy available at: http://ssrn.com/abstract=1508120
Government Investment
and the Stock Market∗
Frederico Belo† Jianfeng Yu‡
May 2012
Abstract
High rates of government investment in public sector capital forecast high riskpremiums both at the aggregate and firm-level. This result is in sharp contrast withthe well-documented negative relationship between the private sector investment rateand risk premiums. To explain the empirical findings, we extend the neoclassical q-theory model of investment and specify public sector capital as an additional inputin the firm’s technology. We show that the model can quantitatively replicate theempirical facts with reasonable parameter values if public sector capital increases themarginal productivity of private inputs.
∗We thank Santiago Bazdresch, Jules van Binsbergen, Ravi Bansal, John Campbell, Hui Chen, SydneyLudvigson, Ellen McGrattan, Po-Hsuan Hsu, Felix Meschke, Vito Gala, Bob Goldstein, Amir Yaron,Motohiro Yogo (Minnesota Macro-Asset Pricing discussant), Stavros Panageas, and Lu Zhang (WFAdiscussant) for helpful suggestions, and John Boyd and John Cochrane for detailed comments. We alsothank seminar participants at the University of Minnesota, the Western Finance Association, the ChinaInternational Conference in Finance, the University of Minnesota Macro-Asset Pricing Conference, and theFirst World Finance Conference for comments. All errors are our own.
†Assistant Professor, Department of Finance, University of Minnesota, Carlson School of Management.Address: 321 19th Ave. South, # 3-137, Minneapolis, MN 55455. e-mail: [email protected]
‡Assistant Professor, Department of Finance, University of Minnesota, Carlson School of Management.Address: 321 19th Ave. South, # 3-122, Minneapolis, MN 55455. e-mail: [email protected]
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Electronic copy available at: http://ssrn.com/abstract=1508120
1 Introduction
Understanding the impact of public sector physical capital (e.g., highways) on the economy
is a question of fundamental importance in macroeconomics and finance. Government
investment in public sector (nondefense) capital is on average about 3.7% of gross domestic
product in the U.S. postwar economy. This value may be either too large or too small,
depending on the overall effect of public sector capital on the economy. In this paper, we
study the impact of public sector capital on the productivity of private inputs at both the
aggregate and firm-level, and we investigate the implications of this link for time-varying
risk premiums in the economy.
To establish the theoretical link between public sector capital and the stock market, we
use the neoclassical model of investment (q-theory) and study its implications for asset prices
(Cochrane, 1991). In the model, firms make private investment decisions to maximize the
firms’ market value. Public sector capital is specified as an input in the firms’ production
technology, and thus it may affect the productivity of the private inputs. This feature of the
model represents the only deviation from standard q-theory. The public sector capital stock
is supplied by the government sector, and its choice is exogenous to the firm.
We obtain the main empirical prediction from the model directly from the producer’s
first-order conditions. If public sector capital increases the marginal productivity of private
inputs, the model predicts a positive relationship between the public sector investment rate
and the firm’s risk premium, controlling for the private sector investment rate. Similarly,
controlling for the public sector investment rate, the model predicts a negative relationship
between the private sector investment rate and the firm’s risk premium, consistent with the
analysis in previous studies.1
Our empirical findings provide support for the model’s main prediction. At the aggregate
level, the public sector investment rate is positively correlated with the firm’s risk premium,
1Contributions documenting and explaining the negative link between private investment and future stockreturns include Cochrane (1991), Jermann (1998), Berk, Green, and Naik (1999), Kogan (2001), Gomes,Kogan, and Zhang (2003) , Gala (2009), Bazdresch, Belo, and Lin (2009), among others.
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and the private sector investment rate is negatively correlated with the firm’s risk premium.
The public and private sector investment rates are jointly significant predictors of aggregate
stock market excess returns with regression-adjusted R2 of up to 33% at the four-year horizon.
The economic significance of these empirical links is large. A one-standard-deviation increase
in the public sector investment rate is associated with an increase of 0.6 percentage points in
the aggregate risk premium at the quarterly frequency. Similarly, a one-standard-deviation
increase in the private sector investment rate is associated with a decrease of 1.4 percentage
points in the aggregate risk premium.
The theoretical model makes two additional predictions which we confirm empirically.
First, the positive link between government investment and the firm’s risk premium operates,
at least partially, through the effect of government investment on cash flow risk (systematic
risk). We show that the conditional covariance between alternative aggregate cash flow
measures and shocks to aggregate productivity (a proxy for the stochastic discount factor
in the economy) is increasing in the public sector investment rate. Thus, an increase in the
public sector capital stock is associated with an increase in the firm’s cash flow sensitivity
to aggregate shocks, that is, higher cash flow risk.
Second, the model has implications for the cross section which allows us to further test
the model’s economic mechanism with firm-level data. In the model, the magnitude of
the positive link between government investment and the firm’s risk premium depends on
the sensitivity of the firm’s profits to changes in the stock of public capital. Because this
sensitivity varies across industries (Holtz-Eakin, 1994), the model predicts that the positive
link between the public sector investment rate and risk premiums is stronger in industries in
which public sector capital is a more important input in the firm’s production technology.
Our empirical results provide strong support for this prediction.
In addition to testing the qualitative predictions of the extended q-theory model proposed
here, we also investigate the extent to which the model can quantitatively match the data.
We show that the model, reasonably calibrated, replicates the empirical findings well. For
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this result to hold, the impact of public sector capital on firms’ marginal productivity of
private inputs must be sufficiently positive. In this case, investment in public sector capital
is associated with both an increase in future firms’ productivity as well as with an increase
in the sensitivity of firms’ cash flows to aggregate shocks (higher systematic risk). We also
show that this result does not depend on whether the government follows a countercyclical or
procyclical investment policy. Taken together, our analysis suggests that the stock of public
sector physical capital has a nontrivial effect on the risk properties of firms’ cash flows and
risk premiums of private capital.
This paper is related to several strands of literature. Building on the seminal work
by Aschauer (1989), a large empirical literature in macroeconomics studies the impact of
public sector capital on the economy using a production-function approach.2 The empirical
evidence from this approach has produced mixed results.3 We propose an alternative, yet
complementary, approach by studying the link between public sector capital and the stock
market. Asset prices are forward looking in nature, which allows us to potentially identify
the effect of public sector capital on firms’ productivity even when the effect occurs far in
the future. In addition, this approach allows us to link public capital to time-varying risk
premiums, which are an important component for understanding business cycle fluctuations.
The work in this paper is also related to a large empirical literature on the time series
predictability of stock market returns.4 This literature has largely ignored public sector
physical capital and its impact on firms’ profitability and the stock market. The financial
side of the public sector is considered explicitly in Plosser (1982 and 1987) and more recently
in Croce, Kung, and Schmid (2012), and Croce, Nguyen, Kung, and Schmid (2012). Our
work differs in that we focus on government investment and on its link to risk premiums and
firms’ profitability. Finally, this paper is also related to a macro-finance literature that links
2See also Ramey (2011) for a recent survey of the literature in macroecononomics examining the effect ofgovernment spending (not just government investment) on the economy.
3A partial list of empirical studies includes Aschauer (1989), Lynde and Richmond (1992), Shah (1992),Evans and Karras (1994a, 1994b), and Holtz-Eakin (1994).
4For recent reviews of the literature on return predictability see the special issue in the Review of FinancialStudies (Spiegel, 2008), Koijen and Van Nieuwerburgh (2011), and Lettau and Ludvigson (2010).
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firms’ productivity to asset prices. Examples include Lin (2011), Garleanu, Panageas and
Yu (2012), and Hsu (2009). Our work differs in that we link firms’ productivity directly to
public sector physical capital.
The paper proceeds as follows. Section 2 introduces a simple q-theory model with public
sector physical capital. Section 3 presents the data and empirical specifications. Section
4 presents the empirical results. Section 5 presents the results from the simulated model.
Finally, Section 6 concludes. Supplementary online appendixes provide robustness checks
and additional results.
2 The Model
To guide the empirical analysis, we introduce public sector physical capital into the
neoclassical q-theory model of investment. We use the model to derive an endogenous link
between the risk premium and the public and private physical capital investment rates
directly from producers’ first-order conditions.
2.1 The Setup
We model the stock of public sector physical capital as an additional inputs in the firms’
production technology. Public sector capital is potentially productive because it may increase
the marginal productivity of private inputs (Aschauer, 1989, and Baxter and King, 1993).
For example, a developed public highway system may increase the productivity of United
Parcel Service (UPS). Investment in the public sector capital stock is determined by the
government, and this choice is exogenous to the firm.
We consider the optimal production decision problem of a firm in the economy. The firm
uses private capital inputs Kt and the stock of effective public sector physical capital GKt
to produce output Yt according to the following technology:5
5In the notation used throughout the paper, we use the letter G to denote variables related to government.
4
Yt = extGKαt Kt, (1)
where xt is a profitability shock. The profitability shock is a composition of both demand
and productivity shocks, and this specification does not distinguish between the two shocks.
The curvature parameter α is the crucial parameter in this analysis, because it controls the
effect of public sector physical capital on private firms’ profitability. The effect increases
with α, and when α = 0, public sector capital has no effect on private firms’ profitability. By
including the stock of public capital as a determinant of the firm’s total factor productivity
(TFP), the production function in equation (1) represents the only deviation from a standard
q-theory model.
In every period t, the private capital stock depreciates at rate δ and is increased (or
decreased) by gross investment It. The stock of private capital therefore evolves as follows:
Kt+1 = (1− δ)Kt + It 0 < δ < 1. (2)
Similarly, the stock of effective public capital evolves as follows:
GKt+1 =(1− δGK
)GKt +GIKt, (3)
where GIKt ≡ GIt/GKt is the public sector investment rate, GIt is total investment in public
sector capital, GKt is the total stock of public sector capital, and δGK is the depreciation
rate. In this specification, the stock of effective public capital in each period increases by
the public sector investment rate, not by the absolute amount of public sector investment.
This specification is made for technical reasons. It guarantees that the stock of effective
public sector capital is stationary, which is a necessary condition to derive the empirical
predictions that we report below. Equivalently, the effective stock of public sector capital
can be interpreted as the detrended stock of total public sector capital.
5
Gross private capital investment incurs adjustment costs. These costs include planning
and installation costs, the costs involved in learning the use of new equipment, or the costs
incurred if production is temporarily interrupted. For tractability, we specify the standard
quadratic adjustment cost function as follows:
g(It, Kt) = c/2 · IK2t ·Kt, (4)
in which c > 0 is a constant, and IKt = It/Kt is the private sector investment rate.
2.2 The Firm’s Maximization Problem
The firm is all-equity financed, and so we define
Dt = extGKαt Kt − It − c/2 · IK2
t ·Kt (5)
to be the dividends distributed by the firm to the shareholders. The dividends consist of
output Yt minus private sector investment It and its adjustment costs. A negative dividend
is considered as equity issuance.
Define the vector of state variables as st = (Kt, GKt, GIKt, xt) and let V cum(st) be the
cum-dividend market value of the firm in period t. The firm takes as given the market-
determined stochastic discount factor Mt,t+1, which is used to value the cash flows arriving
in period t+1. The existence of a strictly positive stochastic discount factor is guaranteed by
a well-known existence theorem if there are no arbitrage opportunities in the market (see, for
example, Cochrane, 2002, chapter 4.2). The firm chooses the investment level It and capital
stock level Kt+1 in each period to maximize its cum-dividend market value by solving the
problem
V cum(st) = maxIt+j,Kt+j+1
{Et
[∞∑
j=0
Mt,t+jDt+j
]}, (6)
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subject to the capital accumulation equations (2) and (3) for all dates t. The operator Et[.]
represents the expectation over all states of nature given all the information available at
time t. Let qt denote the Lagrangian multiplier associated with the constraint in equation
(2), which, at the optimum, measures the marginal benefit of an additional unit of private
capital.
The first-order conditions with respect to It and Kt+1 are given by
qt = 1 + c · IKt (7)
qt = Et
[Mt,t+1
(ext+1GKα
t+1 + c/2 · IK2t+1 + (1− δ) (1 + c · IKt+1)
)]. (8)
Equation (7) says that the marginal benefit of investment equals the marginal cost of
investment. Equation (8) says that the marginal benefit of investment equals the next period
marginal product of capital plus the savings of investment costs due to economy of scale and
the continuation value of the private capital stock net of depreciation, discounted to time t
using the stochastic discount factor Mt,t+1.
Combining the two first-order conditions, the capital accumulation equations (2) and (3),
and simplifying, yields the standard asset-pricing equation Et
[Mt,t+1R
It+1
]= 1 , in which
RIt+1 is the private sector investment return defined as
RIt+1 ≡
ext+1
((1− δGK
)GKt +GIKt
)α+ c/2 · IK2
t+1 + (1− δ) (1 + c · IKt+1)
1 + c · IKt
. (9)
This equation says that the private sector investment return is the ratio of the marginal
benefit of investment at period t + 1 divided by the marginal cost of investment in period
t. Cochrane (1991) shows that, with constant returns to scale of both the production and
the adjustment cost functions, this ratio equals the firms’ stock market return RSt+1, state
by state.
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Following Zhang (2005), the stochastic discount factor is given by
logMt,t+1 = log β + γt(xt − xt+1) (10)
γt = γ0 + γ1(xt − x). (11)
The parameters {β, γ0, γ1} are constants satisfying 1 > β > 0, γ0 > 0, and γ1 < 0. The
parameter γt is time varying and decreases in the demeaned aggregate profitability shock
xt − x to capture the well-documented countercyclical price of risk with γ1 < 0.
2.3 Empirical Implications
To understand the main mechanism of the model and obtain testable predictions in a simple
manner, in this section we focus on a two-period (t = 0, 1) version of the model. Using
the standard asset pricing equation E0[Mt+1RSt+1] = 1, and the fact that there is no private
investment in the second period, the expected equilibrium excess return (risk premium) is
given by:
E0[RS1 −Rf,0] ≈ −Cov0
(RS
1 ,M0,1
)
=
((1− δGK
)GK0 +GIK0
)α
1 + c · IK0×
+︷ ︸︸ ︷Cov0
(ex1 ,−βeγ0(x0−x1)
). (12)
The above equation links the expected excess stock return to the public and private sector
investment rates. This equation provides the theoretical foundation for our empirical
analysis. We note that, by focusing on a two-period version, the analysis here ignores any
dynamic effect through the response of future private investment (IK 1) to the shocks, which
is typically a first-order determinant of investment returns. Thus, the analysis discussed here
illustrates only one possible mechanism through which government investment can affect risk
premiums. We consider the endogenous response of private investment in Section 5, and we
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conclude that the basic intuition from the simple two-period model that we discuss here
carries through to the more complicated dynamic model.
First, notice that the private sector investment rate IK 0 is typically positive, and thus
the first term in equation (12) is usually positive. Thus, controlling for the private sector
investment rate IK 0, the equation implies that the expected excess return is increasing in
the public sector investment rate GIK0. This is the main prediction from the model that
we test in the empirical section. In addition, the equation implies that the expected excess
return is decreasing in the private sector investment rate IK 0, consistent with the empirical
evidence (see references in the introduction).
Second, equation (12) helps us understand the mechanism through which the model links
the public sector investment rate to changes in risk premiums. In the model, all else equal,
higher rates of public sector investment lead to a higher covariance between cash flows and
the aggregate profitability shock.6 In turn, equation (12) shows that this higher covariance
leads to a high risk premium. We label this as the cash flow risk channel. In the empirical
section, we test this channel by investigating if the firm’s conditional covariance of cash flows
with the aggregate profitability shock increases with the public sector investment rate.
Finally, according to equation (12), the positive link between public sector investment
and risk premiums depends crucially on the importance of public sector capital in the firm’s
technology, as measured by the curvature parameter α. Because the importance of public
capital in the firm’s technology varies across industries (Holtz-Eakin, 1994), we can use cross
sectional data to further test the model’s economic mechanism: in industries in which profits
are more sensitive to the public sector investment rate, the positive link between the public
sector investment rate and the industry-level risk premium should be stronger.
6It follows from equation (1) that the output of the firm in period one is given by
ex1
((1− δGK
)GK0 +GIK0
)α
K1. Thus, the risk premium in equation (12) is proportional to the
covariance between the cash flow of the firm and the aggregate productivity shock.
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3 Data and Empirical Specifications
We present the empirical specifications in Section 3.1, the description of the data in Section
3.2, and the summary statistics of the public and private sector investment rates in Section
3.3.
3.1 Empirical Specifications
We study the link between the public sector and private sector investment rates with both real
economic activity (productivity and profitability) and excess stock returns (risk premium)
at the aggregate and firm level.
At the aggregate level, we perform the analysis using standard short- and long-horizon
predictive regressions. We use both short- and long-horizon regressions because, in practice,
it may take some time for the private sector to adjust its stock of private capital in response
to changes in the stock of public sector capital. As such, despite the fact that we do not
explicitly incorporate time-to-build in the model, the long-horizon predictability regressions
may provide additional information about the effects we try to identify in the data.
Following Fama and French (1989) and Lettau and Ludvigson (2002), we run
predictability regressions of the form
ΣHh=1yt+h = a+ bGIKt + cIKt + εit, (13)
in which ΣHh=1yt+h is the H -period cumulated value of the predicted variable, and H is the
forecast horizon ranging from one quarter to sixteen quarters. We consider the following
variables: (i) yt = growth rate in total factor productivity (TFP);7 and (ii) yt = rst − rft, in
which rst is the log aggregate stock market return, and rft is the log risk-free rate.
For each regression, we report the slopes (coefficients b and c in equation (13)), the
7In the internet appendix, we also investigate the link to yt = aggregate profits; and yt = aggregatedividends, and obtain similar results to those reported here for TFP.
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adjusted R2, and the corresponding t-statistics calculated from standard errors corrected for
autocorrelations and heteroskedasticity per Newey and West (1987), with lag equal to three
years plus the overlapping period. The firm-level analysis is similar to the aggregate level
analysis, but we focus on short-horizon (one-period) regressions for tractability.
3.2 Data
Public and private sector investment rates. Data are from the National Income Product
Accounts (NIPA), available through the Bureau of Economic Analysis (BEA) website.
Private investment (It) is the seasonally adjusted total nonresidential private domestic
investment, from NIPA Table 1.1.5, line 9. Public sector investment (GIt) is measured
as the seasonally adjusted nondefense total government gross investment, from NIPA Table
3.9.5, line 3, minus line 13 (federal defense spending). To help interpret this variable, note
that public sector investment expenditures include investment in highways, mass transit,
airports, electrical and gas facilities, water sewers, office buildings, police and fire stations,
courthouses, and hospitals, among other expenditures. The two investment series are
transformed into real terms by deflating each series by the corresponding investment price
index. The sample is quarterly from 1947:1 to 2010:4.
The stock of private capital (Kt) and public sector capital (GKt) necessary to construct
the private and public sector investment rates is not available at a quarterly frequency.
Following Cochrane (1991), the private and public investment rates are constructed as
follows. The law of motion of private capital (2) implies that the private investment rate
IKt = It/Kt follows the following process:
IKt =ItIt−1
IKt−1
(1− δ + IKt−1). (14)
We set IKt−1 to its “steady state”value IK∗ in 1947:1, where IK∗ is defined by the fixed
point of equation (14) . This equation is then iterated to compute the private investment rate
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at all other dates. An analogous procedure is used to construct the public sector investment
rate (GIKt). For both private and public sector capital, the depreciation rate is set at
δ = 2.6% (quarterly), which corresponds to an annual depreciation rate of 10%. These are
the close to the values used in Cochrane (1991) for private capital and in Hulten and Schwab
(1994) for aggregate public capital.
Measures of economic activity. The variable ∆GDP is the growth rate in real gross domestic
product, from NIPA Table 1.1.5, line 1, deflated by the consumer price index (CPI), NIPA
Table 2.3.4, line 1. Total factor productivity (TFP) is from John Fernald’s (Federal Reserve
Bank of San Francisco) webpage. This measure is obtained in the usual manner, as a Solow
residual. Aggregate profitability (return on assets, ROA) is computed as the ratio of real
corporate profits, from NIPA Tables 6.16B, 6.16C, and 6.16D, to the stock of private sector
physical capital, constructed using equation (14). These data are only available since 1948.
Aggregate dividends (Div) are from Robert Shiller’s (Yale University) webpage, deflated by
the CPI.
At the firm-level, the accounting information is from the Center for Research in Security
Prices CRSP/Compustat Merged Annual Industrial Files. These data is only available at
the annual frequency. Capital investment (It) is given by Compustat data item CAPEX
(capital expenditures) minus data item SPPE (sales of property plant and equipment). The
capital stock (Kt) is given by the data item NPPE (net property, plant, and equipment).
Following Bloom (2009), the firm-level private capital investment rate is then given by the
ratio of private capital investment to the average of the beginning of the period and end of
the period capital stock, IKt = It/(0.5 × (Kt + Kt−1). Firm’s profitability (ROA) is given
by the ratio of Compustat data item NI (net income) to Compustat data item AT (book
value of assets). To reduce the influence of micro caps in the firm-level regressions, we focus
on the largest 1,000 firms in Compustat. In addition, to reduce the influence of outliers, we
winsorize the private investment rate and profitability at the top and bottom 1%, and we
exclude firm-level observations in which annual excess stock returns exceed 200%.
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Stock returns and other financial data. At the aggregate level, the stock market return rst is
the return on all the stocks in NYSE/AMEX/NASDAQ obtained from CRSP. The risk-free
rate is given by the one-month Treasury bill. At the firm-level, stock returns are from CRSP.
Following Goyal and Santa-Clara (2003), we measure the aggregate dividend-to-price (DP)
ratio as the difference between the log of the last 12-month dividends and the log of the
current level of the NYSE/AMEX value-weighted index.
The use of the previous variables follows naturally from the theoretical model. In
addition, we consider the following variables which we motivate in the empirical section
below.
Other fiscal policy variables. Gov Cons. is the share of government consumption expenditures
on total GDP, from NIPA Table 3.1, line 16. Gov Deficit is measured as the net government
savings, from NIPA Table 3.1, line 27, and is given by the difference between government
current receipts and current expenditures.
3.3 Properties of the Public and Private Sector Investment Rates
Table 1 reports the summary statistics of the macroeconomic and financial variables used in
the empirical analysis.
[Insert Table 1 here]
Average (nondefense) public sector investment represents about 3.7% of GDP, whereas
average private (nonresidential) sector investment is about 10.7% of GDP (values not
tabulated). The larger weight of private investment on GDP, in comparison with public
sector investment, certainly explains why private investment has received the lion’s share of
attention in the asset-pricing literature.
The properties of the public and private sector investment rates are markedly different.
The correlation between the two series is negative, −23%. The unconditional volatility of
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the public sector investment rate is larger than the volatility of the private sector investment
rate (0.62% versus 0.38% per quarter). The mean investment rate of the two series is very
similar (3.6% per quarter), and both series have a high autocorrelation: 0.98 for the public
sector investment rate and 0.97 for the private sector investment rate.
The correlations of the private and public sector investment rates with aggregate GDP
growth are low (3% and 15%, respectively), which seems to suggest that these variables
do not move strongly with the business cycle. The real growth rate of private and public
investment however, shows that private investment is strongly procyclical (correlation with
GDP growth is 62%), whereas public investment is only weakly procyclical (correlation with
GDP growth is 14%) (values not tabulated).
Figure 1 plots the time series of the public and private sector investment rates. The
shaded bars are NBER recession quarters, as classified by the National Bureau of Economic
Research (NBER). A quarter is defined as a recession quarter if at least one month in the
quarter is classified as a recession month by the NBER. The public sector investment rate
is dominated by low frequency movements (it follows a relatively smooth and time-varying
trend over the entire sample period), whereas the private sector investment rate has relatively
more high frequency movements.
[Insert Figure 1 here]
4 Empirical Findings
This section documents the link between the public and private sector investment rates with
future economic activity, and risk premiums in the U.S. economy.
4.1 Public Sector Investment and Aggregate Productivity
According to the theoretical model in Section 2, public sector capital and stock returns are
related through the effect of public sector capital on the marginal profitability of private
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sector capital. In this section, we investigate the strength of this effect in aggregate level
data.
[Insert Table 2 here]
Panel A in Table 2 reports the results of long-horizon forecasts of aggregate TFP growth
(∆TFP) (Table 1 reports the summary statistics of this variable). The public sector
investment rate strongly positively forecasts TFP growth across all horizons. For example,
at the four-year horizon, the R2 statistic is 22.5%. The magnitude of the estimated slope
coefficients is also significant in economic terms. At the one-year horizon, a one-standard-
deviation increase in the public sector investment rate is associated with an increase of 0.7
percentage points in TFP growth. This result extends the findings in Aschauer (1989), who
first documents a strong contemporaneous correlation between TFP and the stock of public
sector capital.
4.2 Public Sector Investment and the Aggregate Risk Premium
This section reports our main empirical findings.
4.2.1 Main Result
Consistent with the theoretical model, Panel B in Table 2 reports the predictability results
of aggregate stock market excess returns (risk premium) in multivariate regressions in
which both the public and private sector investment rates are included as regressors. The
public sector investment rate forecasts excess stock returns with a positive sign, and the
magnitude of the slope coefficient increases with the forecast horizon. The slope coefficients
are statistically significant at the 2% level up to the one-year horizon, and at the 6% level
up to the three-year horizon. The table also shows that the private sector investment rate
forecasts excess stock returns with a negative sign, consistent with previous studies. The
magnitude (absolute value) of the slope coefficient also increases with the forecast horizon
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and is statistically significant at all horizons. The adjusted R2 statistic increases with the
horizon, from 3.44% at the one-quarter horizon to 32.59% at the four-year horizon.
The magnitude of the estimated investment rate slope coefficients reported in Panel
B in Table 2 is significant in economic terms. At the one-quarter horizon, a one-
standard-deviation increase in the public sector investment rate is associated with an
increase of 0.6 percentage points in the aggregate risk premium. Similarly, a one-standard-
deviation increase in the private sector investment rate is associated with a decrease of
1.4 percentage points in the aggregate risk premium. The smaller impact of the public,
relative to the private, sector investment rate on the aggregate risk premium is expected
because government nondefense investment is on average about one-third of total private
nonresidential investment.
4.2.2 Relationship with Other Fiscal Policy Variables
Naturally, total government expenditures (investment and consumption) are constrained by
the intertemporal government budget constraint. Thus, changes in government investment
need to be balanced against changes in taxes, government debt, or other expenditures and
revenues. Even though we do not formally model these other fiscal policy variables in the
theoretical analysis, it is interesting from an empirical point of view to examine whether
the empirical links between government investment and the aggregate risk premium that we
investigate here are subsumed by other fiscal policy variables.8
Because the government budget constraint provides an intertemporal link between tax
receipts, government spending, and government debt, these variables cannot be included
simultaneously in a multivariate regression. We thus control for the following measures that
are correlated with total noninvestment government spending and total government debt:
government consumption and the aggregate deficit.
Panel C in Table 2 shows that the positive slope of the public sector investment rate
8In the internet appendix we also document the predictability of the government investment rate for stockmarket excess returns after controlling for other risk premium proxies.
16
remains after controlling for the two additional fiscal policy variables considered here. In
general, the size, magnitude, and statistical significance of the public sector investment rate
slope coefficients increases relative to those reported in Panel B. The t-statistic shows that
the public sector investment rate slope coefficients are significant at all horizons up to the
three-year horizon. The magnitude and significance of the private sector investment rate
slope coefficients are very similar to those reported in Panel B.
Turning to the analysis of the slope coefficients of the other fiscal policy variables, the
results in Panel C of Table 2 show that government consumption is negatively correlated
with the aggregate risk premium, but this link is only statistically significant at long
horizons (the t-statistics are significant at the four-year horizon). This result thus shows the
importance of distinguishing between the type of government expenditures (consumption
versus investment) when evaluating the impact of government expenditures on the economy.
Finally, current deficit is negatively correlated with the risk premium as well, especially at
the one- and two-year horizons.
4.3 Public Sector Investment and Cash Flow Risk
The theoretical analysis in Section 2.3 emphasizes one channel through which investment
in public sector capital is positively correlated with risk premiums, in particular, the effect
of public sector investment on the conditional covariance of cash flows with the stochastic
discount factor. In this section, we test the importance of this cash flow risk channel.
We specify the stochastic discount factor to be a linear function of aggregate productivity
growth (∆TFP), consistent with the specification of the stochastic discount factor in the
theoretical model (equation (10)). Following the approach in Ferson and Harvey (1999),
we estimate the firm’s conditional covariance between the firm’s cash flows and aggregate
productivity (which we label as the conditional productivity beta) by running a regression
of the form:
CFt = a+(b+ cGIKt−1 + dZ ′
t−1
)×∆TFPt + εt. (15)
17
Here, CFt is the firm’s aggregate cash flow, which we measure as either the real growth rate
of aggregate dividends (∆Divt) or aggregate profitability (Πt/Kt). The vector Zt−1 is a set
of additional macro control variables which include the lagged aggregate-level dividend-price
ratio and the aggregate consumption surplus.9 We include these variables to capture possible
time variation in economic conditions that is not captured by the public sector investment
rate (we report results both with and without these controls).10
[Insert Table 3 here]
If the public sector capital increases the cash flow conditional productivity beta, the
estimated slope coefficient c in equation (15) should be positive. The results reported in
the first four columns (Data) of Table 3 support this prediction of the model. The slope
coefficient associated with the interaction term between the lagged public investment rate
and current ∆TFPt is positive for both cash flow measures. When dividend growth is used,
the interaction term is significant at the 9% significance level. The results are even stronger
when aggregate profitability is used. In this case, the interaction term is positive and strongly
significant at any reasonable significance level.
The evidence in this section helps mitigate the possible concern that the positive link
between government investment and risk premiums in the data is mechanical due to a
countercyclical investment (fiscal) policy. According to this alternative but not necessarily
mutually exclusive hypothesis, government investment is high in bad economic times when
risk premiums are also high, thus explaining the empirical pattern. The result in this section
suggests that this is not the case, and that positive link between public sector investment
and the aggregate risk premium operates, at least partially, through the positive effect of
public investment on cash flow risk.
9The construction of the consumption surplus variable is explained in the internet appendix.10In the model, aggregate productivity xt does not depend on the public capital investment rate. In the
data, however, measured productivity includes the effect of public capital. To make the analysis in thissection consistent with the model, we remove the effect of public capital from measured TFP as follows. LetGK denote the productivity of public capital defined by equation (3). We remove the effect of public capitalon TFP by running a regression: ∆TFPt =a+b∆GKt + εt and use ∆TFPt = ∆TFPt−b∆GKt.
18
4.4 Public Sector Investment, Risk Premiums and Profitability in
the Cross Section
According to the theoretical analysis in Section 2.3, the link between public sector investment
and risk premiums should be stronger in industries in which profits are more sensitive to the
public sector investment rate. In this section, we test this model’s prediction using firm-level
data. This analysis also provides additional empirical evidence for the importance of the
effect of public sector investment on cash flow risk, because only cash flow risk varies in the
cross section (the market price of risk is the same across firms).
We run regressions of the form
Yit+1 = ai + bGIKt + cIKt + εit, (16)
in which Yi,t+1 is either Reit+1, the firm-level excess stock return, or ROAit+1 (return-on-
assets), the firm-level profitability. The regressors are the one-year lagged values of the public
sector investment rate and the firm-level private sector investment rate. We focus on the
predictability at the one-year horizon. To estimate the industry-specific sensitivity (profits
and risk premium) to the public sector investment rate, we estimate equation (16) separately
across industries, using the 17- industry classification proposed by Fama-French (see Kenneth
French’s webpage for details about the construction of the industry classification). If the
economic mechanism proposed in the model is empirically relevant, the sensitivity of profits
and risk premiums to the public sector investment rate (i.e., parameter b in equation (16) in
both the risk premium and profitability regressions) should be positively correlated across
industries.
[Insert Table 4 here]
Panel A in Table 4 reports the sensitivity of the firm’s risk premium to the public and
private sector investment rates in each industry. Consistent with the aggregate level results,
19
the public sector investment rate is positively correlated with the firm-level risk premium
across all industries, and the slope coefficient is always statistically significant. Similarly,
the private sector investment rate is negatively correlated with the firm-level risk premium,
and the slope coefficient is in general statistically significant.
Panel B in Table 4 reports the sensitivity of the firm’s profitability to the public and
private sector investment rates in each industry. The public sector investment rate is
positively correlated with future firm-level profitability across most industries. The public
sector investment rate slope coefficient is negative in only four industries, but only in one
industry this negative slope is statistically significant.
More importantly, the results show that the public sector investment rate slope
coefficients in the risk premium and in the profitability regressions are highly positively
correlated across industries. The rank of the industries based on the public sector investment
rate slope coefficient in the risk premium regression (Panel A - Rank by GIK) is similar to
the rank based on the slope coefficient in the corresponding profitability regression (Panel B
- Rank by GIK). The correlation between the rank in the two regressions is 76.5% (p-value of
0.01%) across industries. Similarly, the correlation of the estimated public sector investment
slope coefficient in the two regressions is 66.4% (p-value of 0.3%) across industries.
Figure 2 provides a visual description of the strong positive link between the public sector
investment rate slope coefficients in the two regressions. This figure is a scatter plot of the
public sector investment rate slope coefficient in the risk premium regression (x-axis) against
the public sector investment rate slope coefficient in the profitability regression (y-axis), for
each of the 17 industries. The positive correlation between the two slopes across industries
is clear.
[Insert Figure 2 here]
20
5 Is the Model Consistent with the Empirical
Evidence?
In this section we evaluate whether the model, reasonably calibrated, can quantitatively
replicate the empirical findings.
5.1 Calibration
The model is calibrated at a quarterly frequency using the parameter values reported in
Table 5. The first set of parameters specifies the technology of the representative firm. The
second set of parameters describes the exogenous stochastic processes of the public sector
investment rate, the stochastic discount factor, and the aggregate profitability shock. In
this section, we describe the choice of the parameters used in the benchmark calibration
of the model. To understand the economic mechanism that drive the results, alternative
calibrations are considered in Section 5.4.
[Insert Table 5 here]
Stochastic processes. The stochastic discount factor is specified in equations (10) and (11).
Consistent with Zhang (2005), we calibrate the parameters in the stochastic discount factor
by matching the first two moments of the real interest rates and the equity premium. This
procedure leads us to choose β = 0.985, γ0 = 20, and γ1 = −300.
Define g ≡ log(GIK). The stochastic process for the log public sector investment rate is
given by
gt = g(1− ρg) + ρggt−1 + σgεg,t, (17)
where εg,t is an independently and identically distributed (i.i.d.) standard normal shock.11
The parameters in equation (17) are chosen to match the empirical mean, standard deviation,
11We specify the process for the public sector investment rate in logs and not in levels. Because of thechoice of the AR(1) specification, the log choice guarantees the positivity and stationarity of the effectivestock of public capital in the model.
21
and autocorrelation of the public sector investment rate.
The stochastic process for the aggregate profitability shock is given by
xt+1 = x(1− ρx) + ρxxt + σxεx,t+1, (18)
where εx,t+1 is an i.i.d standard normal shock. The long-run average level of aggregate
profitability, x, is a scaling variable. It determines the average private investment rate.
We simply set the average long-run private investment rate at 0.03, which implies a long-
run average of aggregate profitability of x = −2.673. We assume that the innovations in
the public sector investment rate and in aggregate profitability are negatively correlated
ρx,g = −0.40. We choose this parameter to match the observed correlation between the
public sector investment rate and the endogenous private investment rate. This correlation
is −23% in the data, as reported in Table 1. Following Zhang (2005), we set ρx = 0.95.
This value is also consistent with Cooley and Prescott (1995), and it allows us to match the
autocorrelation of the TPF growth. Finally, we choose σx = 0.0085 to match the volatility
of TFP growth in the data.
Firm’s technology. We set the depreciation rate of private and public sector capital to be
δ = δGK = 0.026, consistent with the procedure used to construct the private and public
sector investment rates in the data (see Section 3.2). The adjustment cost parameter c in
equation (4) controls the volatility of the investment return as well as the predictive power
of the private investment rate IK for stock returns. The curvature parameter α controls
the predictive power of the public sector investment rate for stock returns. We set c = 50
and α = 0.8. The choice of these parameters is reasonable. With a quadratic adjustment
cost function, the fraction of investment lost due to adjustment costs is c/2 · (IK)2. Since
the mean private investment rate is around the depreciation rate of 2.6%, the fraction of
investment lost to adjustment costs is about 1.7%. Thus, the puzzle of implausibly high
adjustment costs from standard q-theory is not present in these parameters. The curvature
22
parameter α = 0.8 is more difficult to interpret. We choose this parameter to match as
closely as possible the public sector investment rate slope coefficient in the long-horizon
predictability regressions of measured TFP (see panel A in Table 2).
5.2 Evaluating the Calibration
Table 6 reports key moments of aggregate asset prices and quantities in the artificial
data generated by the benchmark calibration of the theoretical model. We simulate the
representative firm for 26,000 quarters to calculate the population values. We discard the
first 2,000 quarters to eliminate the influence of the initial values.
[Insert Table 6 here]
The benchmark calibration does a reasonable job matching the key moments in Table
6. By construction, the model matches the aggregate risk premium and the properties
of the public sector investment rate (mean, standard deviation, and autocorrelation). In
addition, the model produces reasonable autocorrelation and volatility for the measured
TFP growth.12 The model endogenously matches the correlation between the private and
public sector investment rates, and the correlation between the aggregate dividend yield and
the public sector investment rate. The correlation between the public sector investment rate
and private sector investment rate is negative (−23% in the data and −8% in the simulation),
and the correlation between the public sector investment rate and dividend yield is positive
and reasonably close to the data (27% in the data and 22% in the simulation). The private
sector investment rate produced by the model is slightly more volatile than in the data
(0.38% in the data and 1.52% in the simulation).
5.3 Quantitative Results
In this section, we replicate the empirical analysis using simulated data.
12The model also matches reasonably well the properties of the risk-free rate, with a mean of 0.8%, andstandard deviation of 1.9%, although the mean is slightly higher than that in the data.
23
5.3.1 Public Sector Investment and Productivity in Simulated Data
Panel A of Table 7 shows that the model replicates well the predictability pattern of measured
TFP observed in the data (reported in panel A of Table 2). In the model, we compute
measured TFP as a Solow residual. As such, this TFP measure includes the exogenous
aggregate profitability as well as the productivity from the public sector capital stock. This
is consistent with how TFP is measured in the data.
In the model, the public sector investment rate positively forecasts TFP growth. The
estimated magnitude of the slope coefficients is similar to those obtained in the real data,
albeit they are slightly smaller in the model at short horizons. At long-horizons the model
matches the data very well. At the four-year horizon, the slope coefficient is 3.5 in the model
versus 3 in the real data, and the R2 in the model perfectly matches the R2 in the data
(22%).
[Insert Table 7 here]
5.3.2 Public Sector Investment and the Aggregate Risk Premium in Simulated
Data
Panel B of Table 7 shows that the model also replicates reasonably well the predictability
pattern of aggregate stock market excess return observed in the data (reported in Panel B of
Table 2). The public sector investment rate positively forecasts stock market excess returns,
whereas the private sector investment rate negatively forecasts stock market excess returns.
The model also matches the pattern of the slope coefficients and R2 across the forecasting
horizon: the magnitude (in absolute value) of the slope coefficients and R2 increases with
the investment horizon.
The model matches reasonably well the size of the public sector investment rate slope
coefficient at long horizons. At the four-year horizon, the public sector investment rate
slope coefficient is 8.8 in the model versus 7 in the data. At short horizons, the public
sector investment rate slope coefficient in the model is smaller than in the data. Similarly,
24
the estimated magnitude of the private investment rate slope coefficient and the regression
R2 are also smaller than in the data. It is likely that more complex specifications of
the adjustment cost function (i.e., allowing for nonquadratic adjustment costs) or of the
operating profit function (i.e., including multiple capital and labor inputs, and specifying a
more general constant elasticity of substitution technology) may help to further improve the
fit of the model on the predictability regressions. Given the already good fit of the simple
model proposed here, we do not pursue these extensions to keep the analysis as simple and
transparent as possible.
5.3.3 Public Sector Investment and Cash Flow Risk in Simulated Data
Finally, the model also replicates the pattern of the conditional cash flow productivity betas
observed in the data. According to the last column in Table 3 (Model), using aggregate
profitability as the cash flow measure, the coefficient associated with the interaction term
between the lagged public sector investment rate and current profitability shock is positive.
Thus, as in the real data (column Data), higher levels of government investment are
associated with an higher covariance between firms’ cash flows and the aggregate shock.13
5.4 Inspecting the Mechanism
In this section, we consider alternative calibrations of the model to understand the role of
some of the key parameters and to understand the economic mechanism in the model. We
focus our analysis on the parameters α and ρx,g. In the model, α controls the importance of
public sector capital, and ρx,g controls the cyclicality of the fiscal policy.
Panel C of Table 7 replicates the risk premium predictability regressions reported in
Panel B (benchmark calibration), but using artificial data from a specification of the model
in which the public capital curvature parameter is set at α = 0 (the other parameters are the
same as in the benchmark calibration). In this specification, the public sector investment
13We do not report the cash flow risk analysis using dividends because dividends can be negative in themodel, in which case dividend growth is not well defined.
25
rate slope coefficient is estimated to be small and statistically insignificant. Thus, even
though in this specification the fiscal policy is countercyclical (i.e., ρx,g = −0.4), this is
not sufficient to generate a positive correlation between the public sector investment rate
and the aggregate risk premium in a multivariate regression that includes the private sector
investment rate. We conclude that allowing for a positive effect of public sector capital on
private firms’ productivity is important for the model to replicate the empirical evidence.
To further understand the importance of countercyclical fiscal policy, Panel D of Table
7 replicates the risk premium predictability regressions reported in Panel B (benchmark
calibration), but using artificial data from a specification of the model in which the correlation
between the public sector investment rate shock and the aggregate profitability shock is set
to zero, ρx,g = 0 (acyclical fiscal policy). The results show that the public sector investment
rate slope coefficient remains positive and its magnitude is similar to that reported in Panel
B of Table 7. This result shows that this parameter does not drive the positive link between
the risk premium and the public sector investment rate. In the model, this link arises
endogenously due to the cash flow channel, consistent with the empirical evidence in Sections
4.3 and 4.4. We conclude that countercyclical fiscal policy is neither necessary nor sufficient
to produce predictive power for the public sector investment rate. In the internet appendix,
we provide additional sensitivity analysis on the importance of parameters α and ρx,g in the
model.
6 Concluding Remarks
The public sector investment rate is a significant predictor of risk premiums at the aggregate
and firm-level. In sharp contrast with the well-documented negative link between the
private sector investment rate and risk premiums, the relationship between the public sector
investment rate and risk premiums is positive. To understand the empirical findings, we
extend the neoclassical q-theory model of investment and introduce public sector physical
26
capital as an additional input in the firm’s production process. We show that the model,
reasonably calibrated, can replicate the empirical findings well. For this result to hold, the
impact of public sector capital on firms’ marginal productivity of private inputs must be
sufficiently positive.
Our results have implications for both asset-pricing and macroeconomics literature. The
novel empirical link between government investment and asset prices reported here suggests
that incorporating a government sector into general equilibrium asset-pricing models may be
helpful in improving the fit of these models along the asset-pricing dimension. In addition,
the effect of government investment on risk premiums documented here can potentially
amplify the effect of government spending shocks on the economy. As such, incorporating
this effect in current macroeconomic models with a government sector may be important for
this class of models to accurately assess and predict the response of macroeconomic variables
to government spending shocks.
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29
Table 1 : Summary Statistics
This table reports the summary statistics -mean, standard deviation (S.D.), first-order autocorrelation
(AC(1)), and selected correlations- of the variables used in the empirical work. The variables are the
private sector investment rate (IK), the public sector investment rate (GIK), the real growth rate in GDP
(∆GDP), the real growth rate in measured total factor productivity (∆TFP), real corporate profits scaled
by the physical capital stock (Profits, Πt/Kt), the real growth rate in aggregate dividends (∆Div), the share
of government consumption expenditures in aggregate GDP (Gov Cons.), the share of the government deficit
in aggregate GDP (Gov Deficit), the aggregate dividend-price ratio (DP), and the aggregate stock market
excess return (Rs − Rf ). All values are in percentages, except for AC(1) and correlations. The sample is
quarterly from 1947:2 to 2010:4.
Selected CorrelationsVariables Mean S.D AC(1) IK GIK ∆GDP ∆TFPPrivate and Public Investment RatesIK 3.67 0.38 0.97 1 −0.23 0.03 −0.16GIK 3.66 0.62 0.98 −0.23 1 0.15 0.18
Economic Activity and Aggregate Cash Flow Variables∆GDP 0.79 1.01 0.38 0.03 0.15 1 0.83∆TFP 0.33 0.95 0.10 −0.16 0.18 0.83 1Profits (Πt/Kt) 5.03 1.68 0.98 −0.07 0.68 0.30 0.19∆Div 0.45 2.22 0.46 −0.01 0.26 0.11 0.01
Other Fiscal Policy Variables (Share of GDP)Gov Cons. 16.27 1.31 0.97 −0.13 −0.35 −0.17 −0.10Gov Deficit −1.07 2.77 0.96 0.33 0.57 0.18 0.03
Financial VariablesDP 3.37 1.33 0.97 −0.32 0.27 −0.05 −0.04Rs−Rf 1.50 8.31 0.09 −0.19 0.13 0.13 0.15
30
Table 2 : Government Investment, Productivity, and the Aggregate Risk Premium
This table reports results from long-horizon predictability regressions of ΣHh yit+h, in which yi is either the
growth rate of total factor productivity (TFP) on the aggregate economy, or rt+h − rft+h, the log excess
returns on the aggregate stock market index. H is the forecast horizon in quarters. Each panel reports a
different combination of the H-period lagged value of the following regressors: the public sector investment
rate (GIK), the private sector investment rate (IK), the share of government consumption expenditures in
aggregate GDP (Gov Cons.), the government deficit as a fraction of aggregate GDP (Gov Deficit). For each
regression, we report the OLS estimate of the relevant slope coefficients, Slope, the Newey-West corrected
t-statistic, [t], and the adjusted R2. The sample is quarterly from 1947:2 to 2010:4.
Forecast horizon in quartersPanel Regressors 1 2 4 8 12 16
TFPA GIK Slope 0.26 0.52 1.01 1.77 2.38 3.00
[t] 2.57 2.69 2.96 3.29 3.72 4.14R2 2.43 4.77 8.20 15.02 17.59 22.46
Risk PremiumB GIK Slope 1.02 1.81 4.04 6.53 6.98 7.03
[t] 2.11 2.01 2.42 1.90 1.46 1.16IK Slope −3.80 −7.24 −12.19 −20.51 −31.25 −40.55
[t] −2.73 −2.73 −2.51 −2.69 −4.07 −5.38R2 3.44 6.04 10.42 16.32 24.67 32.59
Controls: Other Fiscal Policy VariablesC GIK Slope 2.11 3.93 8.49 11.31 9.33 4.40
[t] 3.00 2.73 3.61 2.80 2.02 0.92IK Slope −2.50 −4.76 −7.16 −15.62 −28.59 −42.48
[t] −1.72 −1.62 −1.49 −2.19 −3.28 −4.30Gov Cons. Slope −0.16 −0.28 −0.69 −2.28 −4.18 −6.79
[t] −0.54 −0.51 −0.68 −1.18 −1.64 −2.69Deficit Slope −0.41 −0.80 −1.75 −2.50 −2.26 −1.25
[t] −1.85 −1.73 −2.65 −2.63 −1.61 −0.67R2 3.52 6.73 13.14 20.08 29.14 40.35
31
Table 3 : Public Sector Investment and the Conditional Cash Flow Productivity Beta
This table examines the link between the public investment rate and the conditional cashflow productivity beta. The table reports the results from the following regression:
CFt = a+(b+ cGIKt−1 + dZ ′
t−1
)×∆TFPt + εt,
in which CFt is aggregate cash flows, which we measure as either the real growth rate ofaggregate dividends (∆Divt) or aggregate profitability (Πt/Kt). The vector Zt−1 is a set ofadditional macro control variables (Macro Controls), which include the lagged aggregate-leveldividend price ratio and the aggregate consumption surplus (the table reports the resultswith and without these controls). All variables are normalized to have mean zero and unitstandard deviation. The table reports the OLS estimate of the relevant slope coefficient, thecorresponding Newey-West corrected t-statistic, and the adjusted R2. In Panel A (Data)the sample is annual from 1947 to 2010. In Panel B (Model) the sample is artificial datagenerated from the simulation of the model using the benchmark calibration.
Panel A: Data Panel B: Model
∆Divt Πt/Kt Πt/Kt
Regressors∆TFPt Slope −0.05 −0.06 0.13 0.10 −0.02
[t] −0.66 −0.74 1.75 1.04 −0.49GIKt−1 ×∆TFPt Slope 0.10 0.10 0.23 0.19 0.59
[t] 1.73 1.69 2.82 2.48 13.14R2 0.69 2.60 7.44 9.95 1.25Macro Controls? No Yes No Yes No
32
Table 4 : Government Investment, Profitability, and Risk Premiums across Industries
This table reports the estimation results from regressions of the form
Yit+1 = ai + bGIKt + cIKt + εit, (19)
in which Yit+1 is either Reit+1, the firm-level one-year-ahead excess stock return (risk premium), or ROAit+1, the firm-level one-year-ahead profitability
(return-on-assets). The regressors are lagged values of the public sector investment rate (GIK) and the firm-level investment rate (IK). Estimation
is made using firm-level data and by pooling the firms in a given industry, using the 17 Fama-French industry classification. For the regression in
each industry, we report the OLS estimate of the GIK and IK slope coefficients, the corresponding t-statistic, and the adjusted regression R2. A firm
fixed-effect is included in the regression, the standard errors are clustered by firm, and all variables are standardized with mean zero and unit standard
deviation. Rank GIK is the rank of the industry GIK slope across all the industry-level GIK slopes. The sample is annual from 1950 to 2009.
Pane A - Dependent Variable: Ret+1 Panel B - Dependent Variable: ROAt+1
Regressors RegressorsIK GIK Rank IK GIK Rank
Industry Slope [t] Slope [t] R2 by GIK Slope [t] Slope [t] R2 by GIK
1-Food −0.01 −0.26 0.06 3.19 0.24 17 0.11 3.14 −0.03 −0.76 1.16 162-Mines 0.00 −0.14 0.09 3.89 0.68 8 0.01 0.19 0.15 2.92 2.13 43-Oil −0.08 −3.09 0.08 6.43 1.20 12 0.17 4.73 0.01 0.20 2.83 114-Clothes 0.04 1.05 0.06 2.02 0.34 16 0.30 4.02 −0.01 −0.25 8.51 145-Durables −0.07 −2.38 0.18 7.39 3.24 1 0.09 1.57 0.12 2.02 2.20 56-Chemicals −0.05 −2.10 0.06 3.69 0.46 15 0.13 4.04 0.04 1.01 1.67 87-Consumers −0.04 −1.54 0.15 6.84 2.13 4 0.06 1.63 0.07 2.38 0.79 68-Construction −0.08 −3.01 0.15 7.19 2.43 3 0.06 1.72 0.17 3.49 3.16 39-Steel −0.03 −1.15 0.15 7.93 1.89 2 0.00 −0.07 0.25 5.79 5.93 110-Fab Paper −0.11 −3.21 0.14 5.34 2.82 5 0.07 1.10 0.03 0.37 0.25 911-Machinery −0.02 −1.21 0.10 9.68 0.92 7 0.15 5.53 0.02 1.26 2.39 1012-Cars −0.03 −1.07 0.12 4.00 1.29 6 0.00 −0.08 0.17 3.47 2.63 213-Trans −0.07 −3.42 0.09 5.23 1.02 9 0.10 3.23 0.04 1.22 1.22 714-Utils 0.01 0.48 0.09 5.44 0.64 10 0.02 0.53 −0.07 −3.31 0.65 1715-Retail −0.01 −0.48 0.07 4.73 0.46 14 0.13 2.56 0.00 −0.08 1.59 1316-Finance −0.06 −3.44 0.08 6.84 1.00 11 0.03 0.82 0.00 0.09 0.05 1217-Other −0.06 −3.85 0.08 7.93 0.84 13 0.05 2.02 −0.02 −1.17 0.21 15
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Table 5 : Parameter Values
This table presents the parameter values of the benchmark calibration of the model.
Parameter Value Description
Technologyδ 0.026 Depreciation rate for private capitalδGK 0.026 Depreciation rate for effective public capitalα 0.8 Curvature parameter for public capitalc 50 Adjustment cost for private investment
Exogenous Stochastic Processesρx 0.95 Persistence of aggregate profitability, xt
σx 0.0085 Conditional S.D. of aggregate profitabilityx −2.673 Mean of aggregate profitabilityg −3.3139 Mean of log public investment rate gt, gt ≡ log(GIKt)σg −0.0412 Conditional S.D. of gρg 0.97 Persistence of gρx,g −0.40 Correlation between shocks in xt and gtβ 0.985 Subjective discount factorγ0 20 Constant price of riskγ1 −300 Time-varying price of risk
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Table 6 : Summary Statistics in Simulated Data
This table reports the summary statistics -mean, standard deviation (S.D.), first-order autocorrelation
(AC(1)), and selected correlations- of selected variables using data generated by the simulation of the
model (benchmark calibration).The variables are the public sector investment rate (GIK), the private sector
investment rate (IK), the real growth rate in (measured) total factor productivity (∆TFP), the real corporate
profits scaled by the physical capital stock (Profits, Πt/Kt), the aggregate dividend-price ratio (DP), and
the aggregate stock market excess return (Rs − Rf ). All values are in percentages, except AC(1) and
correlations.
Selected CorrelationsVariables Mean S.D AC(1) IK GIK ∆TFPPrivate and Public Investment RatesIK 2.78 1.52 0.95 1 −0.08 0.08GIK 3.68 0.62 0.97 −0.08 1 0.17
Economic Activity and Aggregate Cash Flow Variables∆TFP 0.00 0.91 0.06 0.08 0.17 1.00Profits (Πt/Kt) 9.12 0.83 0.99 0.46 0.55 0.05
Financial VariablesDP 2.36 2.48 0.94 −0.94 0.22 −0.07Rs−Rf 1.59 11.28 −0.03 0.21 −0.02 0.85
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Table 7 : Government Investment, Productivity, and the Aggregate Risk Premium
in Simulated Data
This table reports results from long-horizon predictability regressions of measured total factor productivity
growth ΣHh ∆TFPt+h (Panel A), and log excess returns, ΣH
h rt+h−rft+h (Panels B, C and D), using artificial
data generated by the simulation of the model. H is the return forecast horizon in quarters. The regressors
are a combination of the H-period lagged values of the public sector investment rate (GIK) and the private
sector investment rate (IK). We use 24,000 quarters of data to perform each regression, and report the
relevant slope coefficient, the Newey-West corrected t-statistic, [t], and the adjusted R2. The results in
Panels A and B use artificial data from a simulation of the model using the benchmark calibration. Panel
C uses artificial data from a simulation of the model in which the public capital curvature parameter is set
to α = 0 (instead of α = 0.8 in the benchmark calibration). In contrast, Panel D uses artificial data from a
simulation of the model in which the shocks of public capital investment and aggregate productivity are set
to ρ(x, g) = 0 (instead of ρ(x, g) = −0.4 in the benchmark calibration).
Forecast horizon in quartersPanel Regressors 1 2 4 8 12 16
TFPA GIK Slope 0.40 0.76 1.41 2.40 3.07 3.46
[t] 41.04 40.56 38.84 34.72 30.30 26.11R2 7.09 13.89 20.31 26.17 25.90 22.01
Risk Premium: Benchmark CalibrationB GIK Slope 0.70 1.38 2.67 5.00 7.13 8.84
[t] 6.07 6.22 6.32 6.45 6.59 6.48IK Slope −0.72 −1.39 −2.61 −4.51 −5.99 −7.26
[t] −16.37 −16.26 −15.98 −15.18 −14.49 −14.10R2 1.02 2.05 4.67 7.14 9.11 11.91
Risk Premium: Calibration with α = 0C GIK Slope −0.09 −0.15 −0.23 −0.17 0.02 0.05
[t] −0.84 −0.73 −0.59 −0.24 0.02 0.04IK Slope −1.48 −2.86 −5.32 −9.23 −12.27 −14.81
[t] −19.81 −19.71 −19.38 −18.51 −17.75 −17.29R2 2.22 3.15 6.23 10.20 13.71 15.89
Risk Premium: Calibration with ρ(x, g) = 0D GIK Slope 0.78 1.54 2.95 5.39 7.75 9.73
[t] 6.52 6.68 6.77 6.81 7.04 7.03IK Slope −0.71 −1.36 −2.56 −4.46 −6.02 −7.35
[t] −16.95 −16.81 −16.45 −15.57 −14.95 −14.50R2 1.11 2.14 4.75 6.64 8.91 10.10
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Figure 1 : Public Sector and Private Sector Investment Rates
This figure is a time series plot of the public sector (nondefense) investment rate, GIK, and the private sector
(nonresidential) investment rate, IK. Shaded bars are NBER recession quarters. The sample is quarterly
from 1947:2 to 2010:4.
Inve
stm
ent R
ate
(%)
Date
1950 1960 1970 1980 1990 2000 20102.5
3
3.5
4
4.5
5
5.5
6GIKIK
37
Figure 2 : Public Sector Investment Rate Slope Coefficient in the Risk Premium and
Profitability Regressions across Industries
This figure is a scatter plot of the public sector investment rate slope coefficient obtained from within-
industry predictability regressions of the firm’s profitability (Profitability slope) or the firm’s stock excess
return (Return slope), using the one-year lagged values of the public sector investment rate and the private
sector investment rate (not reported) as the regressors. An industry is classified according to the Fama-French
17 industry classification. The sample is annual from 1950 to 2009.
0.04 0.06 0.08 0.10 0.12 0.14 0.16 0.18−0.10
−0.05
0
0.05
0.10
0.15
0.20
0.25
Return Slope
Pro
fitab
ility
Slo
pe
1−Food
2−Mines
3−Oil 4−Clths
5−Drbl
6−Chems
7−Cnsum
8−Cnstr
9−Steel
10−FabP11−Mchn
12−Cars
13−Trans
14−Utils
15−Rtail16−Finan17−Other
Correl = 66.4%
38