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: fbelo@umn.edu

‡Assistant Professor, Department of Finance, University of Minnesota, Carlson School of Management.Address: 321 19th Ave. South, # 3-122, Minneapolis, MN 55455. e-mail: jianfeng@umn.edu

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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.

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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

34

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

35

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

36

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