Government Investment and the Stock Market

Transcription

1 Government Investment and the Stock Market Frederico Belo Jianfeng Yu May 2012 Abstract High rates of government investment in public sector capital forecast high risk premiums both at the aggregate and firm-level. This result is in sharp contrast with the well-documented negative relationship between the private sector investment rate and risk premiums. To explain the empirical findings, we extend the neoclassical q- theory model of investment and specify public sector capital as an additional input in the firm s technology. We show that the model can quantitatively replicate the empirical facts with reasonable parameter values if public sector capital increases the marginal productivity of private inputs. We thank Santiago Bazdresch, Jules van Binsbergen, Ravi Bansal, John Campbell, Hui Chen, Sydney Ludvigson, 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 (WFA discussant) for helpful suggestions, and John Boyd and John Cochrane for detailed comments. We also thank seminar participants at the University of Minnesota, the Western Finance Association, the China International Conference in Finance, the University of Minnesota Macro-Asset Pricing Conference, and the First World Finance Conference for comments. All errors are our own. Assistant Professor, Department of Finance, University of Minnesota, Carlson School of Management. Address: th Ave. South, # 3-137, Minneapolis, MN fbelo@umn.edu Assistant Professor, Department of Finance, University of Minnesota, Carlson School of Management. Address: th Ave. South, # 3-122, Minneapolis, MN jianfeng@umn.edu 1

2 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, 1 Contributionsdocumenting and explainingthe negativelinkbetween private investmentand future stock returns 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. 1

3 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 stockmarketexcessreturnswithregression-adjustedr 2 ofupto33%atthefour-yearhorizon. 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 2

4 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 2 See also Ramey (2011) for a recent survey of the literature in macroecononomics examining the effect of government spending (not just government investment) on the economy. 3 A partial list of empirical studies includes Aschauer (1989), Lynde and Richmond (1992), Shah (1992), Evans and Karras (1994a, 1994b), and Holtz-Eakin (1994). 4 Forrecentreviewsofthe literatureonreturnpredictabilityseethe specialissueinthe ReviewofFinancial Studies (Spiegel, 2008), Koijen and Van Nieuwerburgh (2011), and Lettau and Ludvigson (2010). 3

5 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 K t and the stock of effective public sector physical capital GK t to produce output Y t according to the following technology: 5 5 In the notationusedthroughoutthe paper, we usethe letter G to denote variablesrelatedto government. 4

6 Y t = e xt GK α t K t, (1) where x t 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 I t. The stock of private capital therefore evolves as follows: K t+1 = (1 δ)k t +I t 0 < δ < 1. (2) Similarly, the stock of effective public capital evolves as follows: GK t+1 = ( 1 δ GK) GK t +GIK t, (3) wheregik t GI t / GK t isthepublicsectorinvestment rate,gi t istotalinvestment inpublic sector capital, GK t is the total stock of public sector capital, and δ GK 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

7 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(i t,k t ) = c/2 IK 2 t K t, (4) in which c > 0 is a constant, and IK t = I t /K t is the private sector investment rate. 2.2 The Firm s Maximization Problem The firm is all-equity financed, and so we define D t = e xt GK α t K t I t c/2 IK 2 t K t (5) to be the dividends distributed by the firm to the shareholders. The dividends consist of output Y t minus private sector investment I t and its adjustment costs. A negative dividend is considered as equity issuance. Define the vector of state variables as s t = (K t,gk t,gik t,x t ) and let V cum (s t ) be the cum-dividend market value of the firm in period t. The firm takes as given the marketdetermined stochastic discount factor M t,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 I t and capital stock level K t+1 in each period to maximize its cum-dividend market value by solving the problem V cum (s t ) = max I t+j,k t+j+1 { [ ]} E t M t,t+j D t+j, (6) j=0 6

8 subject to the capital accumulation equations (2) and (3) for all dates t. The operator E t [.] represents the expectation over all states of nature given all the information available at time t. Let q t 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 I t and K t+1 are given by q t = 1+c IK t (7) q t = E t [ Mt,t+1 ( e x t+1 GK α t+1 +c/2 IK2 t+1 +(1 δ)(1+c IK t+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 M t,t+1. Combining the two first-order conditions, the capital accumulation equations (2) and (3), [ and simplifying, yields the standard asset-pricing equation E t Mt,t+1 Rt+1] I = 1, in which R I t+1 is the private sector investment return defined as R I t+1 ex t+1 (( 1 δ GK ) GK t +GIK t ) α +c/2 IK 2 t+1 +(1 δ)(1+c IK t+1 ) 1+c IK t. (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 Rt+1 S, state by state. 7

9 Following Zhang (2005), the stochastic discount factor is given by logm t,t+1 = logβ +γ t (x t x t+1 ) (10) γ t = γ 0 +γ 1 (x t x). (11) The parameters {β,γ 0,γ 1 } are constants satisfying 1 > β > 0, γ 0 > 0, and γ 1 < 0. The parameter γ t is time varying and decreases in the demeaned aggregate profitability shock x t x to capture the well-documented countercyclical price of risk with γ 1 < 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 E 0 [M t+1 Rt+1 S ] = 1, and the fact that there is no private investment in the second period, the expected equilibrium excess return (risk premium) is given by: E 0 [R S 1 R f,0 ] Cov 0 ( R S 1,M 0,1 ) = (( 1 δ GK ) GK 0 +GIK 0 ) α 1+c IK 0 + { }} { Cov 0 ( e x 1, βe γ 0 (x 0 x 1 ) ). (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 8

10 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 GIK 0. 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. 6 It follows from equation (1) that the output of the firm in period one is given by e x1 ((1 δ GK) GK 0 +GIK 0 ) αk1. Thus, the risk premium in equation (12) is proportional to the covariance between the cash flow of the firm and the aggregate productivity shock. 9

11 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 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 Σ H h=1y t+h = a+bgik t +cik t +ε it, (13) in which Σ H h=1 y t+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) y t = growth rate in total factor productivity (TFP); 7 and (ii) y t = r st r ft, in which r st is the log aggregate stock market return, and r ft is the log risk-free rate. For each regression, we report the slopes (coefficients b and c in equation (13)), the 7 In the internet appendix, we also investigate the link to y t = aggregate profits; and y t = aggregate dividends, and obtain similar results to those reported here for TFP. 10

12 adjusted R 2, 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 (I t ) is the seasonally adjusted total nonresidential private domestic investment, from NIPA Table 1.1.5, line 9. Public sector investment (GI t ) 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 (K t ) and public sector capital (GK t ) 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 IK t = I t /K t follows the following process: IK t = I t IK t 1 I t 1 (1 δ +IK t 1 ). (14) We set IK t 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 11

13 at all other dates. An analogous procedure is used to construct the public sector investment rate (GIK t ). 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 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 (I t ) is given by Compustat data item CAPEX (capital expenditures) minus data item SPPE (sales of property plant and equipment). The capital stock (K t ) 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, IK t = I t /(0.5 (K t + K t 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%. 12

14 Stock returns and other financial data. At the aggregate level, the stock market return r st 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 13

15 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 14

16 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 R 2 statistic is 22.5%. The magnitude of the estimated slope coefficients is also significant in economic terms. At the one-year horizon, a one-standarddeviation 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 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 15

17 and is statistically significant at all horizons. The adjusted R 2 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 onestandard-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-standarddeviation 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 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 8 In the internet appendix we also document the predictability of the governmentinvestment rate for stock market excess returns after controlling for other risk premium proxies. 16

18 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: CF t = a+ ( b+cgik t 1 +dz t 1) TFPt +ε t. (15) 17

19 Here, CF t is the firm s aggregate cash flow, which we measure as either the real growth rate of aggregate dividends ( Div t ) or aggregate profitability (Π t /K t ). The vector Z t 1 is a set of additional macro control variables which include the lagged aggregate-level dividend-price ratio andthe aggregateconsumption 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 TFP t 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. 9 The construction of the consumption surplus variable is explained in the internet appendix. 10 In the model, aggregate productivity x t 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 this section consistent with the model, we remove the effect of public capital from measured TFP as follows. Let GK denote the productivity of public capital defined by equation (3). We remove the effect of public capital on TFP by running a regression: TFP t =a+b GK t +ε t and use TˆFP t = TFP t b GK t. 18

20 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 Y it+1 = a i +bgik t +cik t +ε it, (16) in which Y i,t+1 is either Rit+1 e, the firm-level excess stock return, or ROA it+1 (return-onassets), 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

21 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

22 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, γ 0 = 20, and γ 1 = 300. Define g log(gik). The stochastic process for the log public sector investment rate is given by g t = ḡ(1 ρ g )+ρ g g t 1 +σ g ε g,t, (17) where ε g,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, 11 We specify the process for the public sector investment rate in logs and not in levels. Because of the choice of the AR(1) specification, the log choice guarantees the positivity and stationarity of the effective stock of public capital in the model. 21

23 and autocorrelation of the public sector investment rate. The stochastic process for the aggregate profitability shock is given by x t+1 = x(1 ρ x )+ρ x x t +σ x ε x,t+1, (18) where ε x,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 longrun average of aggregate profitability of x = We assume that the innovations in the public sector investment rate and in aggregate profitability are negatively correlated ρ x,g = 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 ρ x = 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 σ x = 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 = δ GK = 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

24 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. 12 The model also matches reasonably well the properties of the risk-free rate, with a mean of 0.8%, and standard deviation of 1.9%, although the mean is slightly higher than that in the data. 23

25 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 R 2 in the model perfectly matches the R 2 in the data (22%). [Insert Table 7 here] 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 R 2 across the forecasting horizon: the magnitude (in absolute value) of the slope coefficients and R 2 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

26 the estimated magnitude of the private investment rate slope coefficient and the regression R 2 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 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 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 ρ x,g. In the model, α controls the importance of public sector capital, and ρ x,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 13 We do not report the cash flow risk analysis using dividends because dividends can be negative in the model, in which case dividend growth is not well defined. 25