Is Investment in Public Capital Good News for the Stock Market?

Transcription

1 Is Investment in Public Capital Good News for the Stock Market? Frederico Belo Jianfeng Yu November 2009 Abstract Yes, but only for public investment in the non-defense sector. We introduce public sector physical capital (e.g. highways) into the q-theory model of stock returns and test its implications for stock market return predictability in the US economy. If public capital increases the productivity of private inputs, high rates of investment in public capital forecast high future stock returns. We find empirical support for this prediction in both aggregate level and industry level data using long-horizon predictability regressions that control for the aggregate private investment rate and for other stock return predictors. We also find that the effect of public capital on stock returns varies substantially across types of public capital, industries and over time. The empirical findings are consistent with the hypothesis that public capital in the non-defense sector has a positive impact on firms productivity. JEL Classification: G12, G28, E62, H41 Keywords: q-theory, public capital, return predictability First draft: November 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 We introduce public sector physical capital (e.g. highways) into the q-theory model of stock returns (e.g., Cochrane, 1991) and test its implications for stock return predictability in the US economy. We specify public capital as an exogenous input in the firms production technology. Under constant returns to scale, the firm s stock return equals the private capital investment return, which can be measured in the data through a production function from public and private physical capital investment data. If public capital is productive, we show that the expected investment return is increasing in the rate of public investment, thus establishing a positive relationship between the public investment rate and future stock returns. In addition, controlling for the public investment rate, the expected investment return is decreasing in the rate of private investment, a result previously established in the literature. 1 We find empirical support for the main implications of the model for short-horizon and long-horizon stock return predictability regressions. At the aggregate level, we find that both the private investment rate and the public investment rate are jointly significant predictors of aggregate stock market returns with opposite signs and with regression R 2 of up to 35% at the 16 quarters horizon. We also find that the predictability of the public investment rate is associated with positive future returns across most industries, but the strength of the link is not homogenous. We show that this finding is consistent with the hypothesis that the importance of public capital as an input in the production process varies across industries, as suggested in Holtz-Eakin (1994). Finally, we also find that the correlation between the 1 Contributions for this finding include Cochrane (1991), Cochrane (1996), Berk, Green and Naik (1999), Kogan (2001, 2004), Gomes, Kogan and Zhang (2003), Carlson, Fisher and Giammarino (2004), Zhang (2005), Cooper, Gulen and Schill (2008), Gomes, Yaron and Zhang (2006), Li, Livdan and Zhang (2008), Liu, Whited and Zhang (2009), Gomes, Kogan and Yogo (2009), among others.

3 public investment rate and future stock returns is considerably stronger in the earlier sample period from 1947 to 1977, a period characterized by relatively high and volatile rates of public investment, than in the later sample period from 1978 to 2008, a period characterized by low and smooth public investment rates, and thus with relatively low rates of new public capital formation. We also examine the relationship between stock returns and the different components of public investment in order to potentially identify the components of public investment that have a larger effect of firms productivity and hence on stock returns. The results indicate that public capital investment in the non-defense sector and public capital investment in structures are the strongest predictors of stock returns. In particular, we find no predictability from investment in public capital in the defense sector nor from investment in public capital in equipment and software. Overall, these results are consistent with the hypothesis that structures public capital in the non-defense sector have a positive effect on private firms productivity, consistent with the findings in Aschauer (1989). In order to directly test the public capital augmented q-theory model proposed here, we construct a time series of investment returns implied by the model from public and private investment data and we replicate the long-horizon stock return predictability regressions by substituting the aggregate stock market return observed in the data by the model implied investment return. We then run regressions to test whether forecasts of the stock return are equal to forecasts of the investment return. We find that both forecasts are very similar and that the model is able to replicate the empirical findings reasonably well. Our motivation for examining the link between public sector physical capital and stock returns follows from a large empirical literature in macroeconomics, started with Aschauer (1989), documenting strong correlations between public capital and aggregate and state 2

4 level productivity. 2 Our work contributes to this literature by establishing a link between public capital, firm s productivity and stock returns, thus providing a new set of testable implications that exploit the information content in easily available stock market data. In addition, the framework in this paper provides a relatively simple method for examining the heterogeneous effect of public capital on firms productivity across industries, which, barring a few exceptions (e.g. Holtz-Eakin, 1994), has largely been overlooked in the empirical macroeconomics literature. The work in this paper is also related to a large empirical literature on asset pricing that studies the time series predictability of stock market returns (e.g. Fama and French, 1989, Cochrane, 1991 and Lettau and Ludvigson, 2001). This literature however, has also largely ignored the government sector and its impact on the stock market. To this literature, our work adds the aggregate level public capital investment rate as a theoretically motivated stock return predictor. Finally, this paper is also related to a macro-finance literature that links firm s productivity to asset prices through endogenous technological progress (e.g. Lin, 2009, Garleanu, Panageas and Yu, 2009). Our work differs because we link firm s productivity directly to public capital, which is absent in these models. The paper proceeds as follows. Section 2 introduces public capital in the standard q- theory model of stock returns and derives implications for time series predictability of stock returns. Section 3 presents the data and empirical specifications and Section 4 presents the empirical results. Finally, Section 5 concludes. 2 A partiallist ofempiricalstudies include Aschauer(1989), Evans(1994aand 1994b), Holtz-Eakin(1994), Lynde (1992) and Shah (1992). 3

5 2 The Model We introduce productive public sector physical capital into the q-theory model of stock returns (e.g. Cochrane, 1991) in order to establish a link between stock returns and public and private capital investment rates. Producers in the private sector make investment decisions in order to maximize the value of the firm given the exogenous public capital stock. We assume that public capital stock facilitates the production in the private sector and thus increase the productivity in the private sector. For example, a developed public highway system may increase the productivity of UPS. Optimal private investment determines the private sector s dividends and market value thus establishing an endogenous link between the private sector s investment rate, the public sector investment rate, and the firms expected stock market return. 2.1 The Setup The economy is composed of a representative firm in the private sector. This representative firm takes as given the market-determined 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). We assume that the government investment rate is exogenously given, hence the public capital stock is exogenous to the firm. ThefirminthiseconomyusesprivatecapitalinputsK t andpubliccapitalgk t toproduce output Y t, according to the following technology 3 3 In the notation used throughout the paper, we use the letter G to denote variables related to government 4

6 Y t = e xt (PG t ) α K t (1) where x t is a productivity shock and PG t is the productivity derived from the public capital, which is defined below. The curvature parameter α controls the effect of public capital on the private firm s output. When α = 0, public capital has no effect on productivity and as α increases, the effect of public capital on the total productivity of private capital increases as well. 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 productivity from public capital (PG t ) evolves as : PG t+1 = ( 1 δ PG) PG t +GIK t, (3) where GIK t GI t /GK t is the public investment rate and GI is total public investment in public capital. In this specification, the productivity from public capital in period t increases by the amount of public investment relative to the current level of public capital stock GIK t, not by the absolute amount of public investment. This specification is reasonable. If the current public stock of capital is high, the change in productivity from an additional unit of public investment should be relatively small due to plausible decreasing marginal returns to scale of public capital. In turn, this choice guarantees that the productivity from public capital is stationary, which is naturally appealing for technical reasons and necessary for our (G). 5

7 empirical application. Due to depreciation in the public capital stock, the productivity from public capital stock depreciates at a rate of δ PG. Thefirmmakesinvestment decisioni t beforethepublicinvestment rategik t isobserved, but after the aggregate productivity x t is observed. We assume that gross private capital investment incurs adjustment costs. These costs include planning and installation costs, learning the use of new equipment, or the fact that production is temporarily interrupted. For simplicity, we specify the standard quadratic adjustment cost function: ( It ) 2 K t, (4) g(i t,k t ) = c 2 K t where c > 0 is a constant. 2.2 Firm s Maximization Problem The firm is assumed to be all-equity financed, so we define ( It ) 2 K t (5) D t = e xt (PG t ) α K t I t c 2 K t to be the dividends distributed by the firm to the shareholders. The dividends consist of output Y t, private investment I t and adjustment costs of investment. A negative dividend is considered as equity issuance. Define the vector of state variables as s t = (K t,pg t,x t ) and let V cum (s t ) be the cumdividend market value of the firm in period t. The firm chooses an investment level I t and capital stock level K t+1 in each period in order to maximize its cum-dividend market value by solving the problem: 6

8 V cum (s t ) = max i t+j,k t+j+1 { [ ]} E t M t,t+j D t+j, (6) subject to the capital accumulation equation (2) for all dates t. The operator E t [.] represents j=0 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, respectively, q t = 1+c IK t (7) [ q t = E t M t,t+1 (e x t+1 (PK t+1 ) α + c )] 2 IK2 t+1 +(1 δ)(1+c IK t+1 ), (8) in which IK t = I t /K t is the private investment rate. 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 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 investment return and is defined as R I t+1 = ex t+1 (PG t+1 ) α + c 2 IK2 t+1 +(1 δ)(1+c IK t+1) 1+c IK t. (9) This equation says that the private 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 7

9 cost functions, this ratio equals the firms stock market return R S t+1, state by state. Thus this equation holds ex-ante as well, in expectation. Hence, the model implies [ e x t+1 E[Rt+1 S ] = E (PG t+1 ) α + c 2 IK2 t+1 +(1 δ)(1+c IK ] t+1). (10) 1+c IK t 2.3 Empirical Implications Equation (10) provides the theoretical foundation for our empirical analysis. All else equal, equation (10) shows that stock return is increasing in the public investment rate (GIK t ) if the curvature parameter α is positive (recall that according to equation (3) the productivity of public capital PG t+1 is increasing in GIK t ). In addition, the private investment rate in period t (IK t ) is negatively related to expected stock returns. Figure 1 illustrates the effect (we explain the calibration of the parameters in the empirical section below). This figure plots the expected investment return as a function of the public and private investment rate for different values of α (α = 0,1 and 2). The plot is obtained by assuming that the public capital and private capital investment rate have a log normal distribution. Not surprisingly, we verify that the slope of the relationship between investment return and public investment rate increases with α, the importance of public capital in the production technology. On the other hand, as shown in the lower panel in this Figure, the relationship between private capital and private investment rate is negative, as previously documented in the literature (see references in the introduction section). Interestingly, the relationship between the private investment rate and investment returns is largely unaffected by the curvature parameter α. Our empirical work examines these predictions in the data in both short-horizon and long-horizon predictability regressions (which accumulates the short horizon returns). In order to provide a direct test the theoretical model proposed here, in the empirical 8

10 section we use equation (9) to construct a time series of investment returns using data on the private and public investment rate and we replicate the long-horizon predictability regressions by substituting the aggregate stock market return observed in the data with the model implied investment return. We then run regressions to test whether forecasts of the investment returns are equal to the forecasts of stock return observed in the data. 3 Data and Empirical Specifications In order to examine the relationship between stock returns and the private and public investment rate, we run standard long-horizon predictive regressions (e.g., Fama and French, 1989, and Lettau and Ludvigson, 2002) of stock excess returns both at the aggregate level and at the industry level. Let r t denote the log stock return and r ft the log return on the one-month Treasury bill, a proxy for the risk-free rate. The dependent variable in the predictive regression is the H-quarter cumulated log excess return, Σ H h=1 r t+h r ft+h, in which H is the forecast horizon ranging from one quarter to 16 quarters. At the aggregate level, the aggregate stock market return r t is the return on the Standard and Poor (S&P) index of 500 stocks from the Center for Research in Security Prices (CRSP). At the industry level, we use the returns on 17 industry portfolios from Kenneth French webpage. We focus our analysis on excess returns since this naturally corrects for the effects of inflation, but the predictability results reported here are very similar to those obtained with real stock returns, since the risk free rate is very smooth and persistent. The sample is quarterly from 1947 to For each regression, we report the slopes, the adjusted R2, and two sets of t-statistics: t-statistics calculated from standard errors corrected for autocorrelations per Newey and West (1987) (tnw), and t-statistics calculated from standard errors adjusted for the use of 9

11 overlapping observations in long-horizon regressions per Hodrick (1992) (thd). Both sets of t-statistics test the null hypothesis that a given slope coefficient equals zero. Presenting both sets of t-statistics is important: Ang and Bekaert (2007) show that Newey-West t-statistics can overreject the null hypothesis of no predictability at long horizons, but that Hodrick t-statistics retain the correct size in small samples. In order to examine the marginal forecasting power of the public and private investment rate for stock returns, we report regression results that control for other known predictors of stock returns. Campbell and Shiller (1988), Fama and French (1988), and Hodrick (1992) show that the dividend-to-price ratio (denoted DO) predicts future excess returns. We measure the S&P dividend-to-price as the natural logarithm of the sum of the past four quarters of dividends per share minus the natural logarithm of the S&P 500 index level. The source for the S&P index and its dividends is CRSP. Fama and Schwert (1977) and Fama (1981) find that the relative Treasury bill rate predicts returns. We measure the relative bill rate, denoted TB, as the three-month Treasury bill rate from the Federal Reserve Board minus its four-quarter moving average. Finally, Keim and Stambaugh (1986) and Fama and French (1989) document the forecasting power of the term premium (TERM). We measure the term premium as the difference between the thirty-year Treasury bond yield and thirtyday Treasury bill yield from the Federal Reserve Board. The macroeconomic data necessary to compute the private and public capital investment rate is 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 gross private domestic investment, from NIPA Table 1.1.5, line 7. The investment data is transformed into real terms by deflating it by the corresponding investment Price Index, also from NIPA. Public investment (GI t ) is measured as the seasonally adjusted total government 10

12 gross investment, from NIPA table 3.9.5, line 3. Following Cochrane (1996), the stock of private (K t ) and public capital (GK t ) are constructed using the law of motion of private capital (2), and an analogous equation for the law of motion of public capital, and iterating this equation starting at the corresponding private or public investment steady state rates. The private investment (IK t ) and public investment (GIK t ) rate are computed as IK t =I t /K t and GIK t =GI t /GK t. The public investment rate in the defense and non-defense sectors (GIK-Def and GIK-NoDef) and in structures as well as equipment and software (GIK-Struct and GIK-Eqpmt) are constructed analogously. Table 1 reports the summary statistics of the private capital and public capital investment rates, at various levels of aggregation. It also reports the summary statistics of the aggregate dividend-to-price ratio for comparison. [Insert Table 1 here] The volatility of public investment rate is substantially higher than the volatility of private investment rate (1.14% versus 0.39% per quarter). The public investment rate is acyclical whereas the private investment rate is clearly procyclical. Interestingly, the private and public investment rates are uncorrelated (correlation of -2%). All variables are highly autocorrelated. This fact implies that, in the predictability regressions, is important to adjust for autocorrelation in the regression residuals in order to compute reliable standard errors, as discussed above. Finally, it is interesting to note that the correlation between the public investment rate and the dividend-to-price ratio is high, approximately 50% in the full sample. Looking across the different components of public capital, the investment in the nondefense sector represent about 70% of the total public investment. In terms of type of public 11

13 capital, the public investment in structures represents about 61% of total public investment, and the remaining 39% is investment in equipment and software. 4 Empirical Results This section documents the relationship between aggregate public and private investment rates and stock return predictability in the US economy, both at the aggregate level and at the industry level. In order to further examine if the empirical results are consistent with the theoretical model, this section constructs a time series of the investment return using equation (9) and investigates if the predictability results using the investment return implied by the model are similar to those observed in the data using the realized stock return. 4.1 Stock Return Predictability at the Aggregate Level Table 2 reports the results of long-horizon forecasts of excess stock returns on the S&P 500 Composite Index. The estimated slope coefficient gives the effect of a one unit increase in the regressor on the cumulative excess stock return over various horizons, H. [Insert Table 2 here] Panel A in Table 2 reports our main empirical finding. This table shows that the public investment rate forecasts stock returns with a positive sign and t-statistics that begin slightly above 2 at a one quarter horizon and increase with the horizon, and an R 2 statistic that increases from 1.5% at the one quarter horizon to 27% at the 16 quarters horizon. Panel B in Table 2 shows the well documented result (e.g. Cochrane, 1991) that the private investment rate forecasts stock returns with a negative sign. The magnitude of the slope coefficient raises with the horizon and the R 2 statistics increases from 1.2% to 9% at the 16 quarters horizon. 12

14 Panel C in Table 2 reports the stock return predictability results in a multivariate regression in which both the public and private investment rate are included. The slope coefficients associated with both regressors are very similar to those found in the univariate regressions, which is not surprising given that both regressors are essentially uncorrelated. The long-horizon R 2 raises with the horizon, reaching an impressive 35% at the 16 quarters horizon. Turning to the analysis of the individual components of public capital, the result reported in Panel D, Table 2 show that only the investment in public capital in the non-defense sector is productive. The slope coefficient associated with the investment in public capital in the defense sector is indistinguishable from zero, whereas the slope coefficient associated with investment in the non-defense capital is highly significant at horizons up to 12 quarters. The results reported in Panel E in Table 2 show that the investment in structures is considerably more productive than the investment in equipment and software. The slope coefficient associated with the investment in equipment and software is indistinguishable from zero, whereas the slope coefficient associated with investment in structures capital is highly significant at horizons up to 8 quarters. Panels F and G in Table 2 reports the predictability results after controlling for other known predictors of stock returns. The predictability of both the public and the private investment rates for stock returns remains significant after controlling for the term premium and the relative risk free rate. When the aggregate dividend-to-price ratio is included, the results in Panel G show that the public investment rate looses its forecasting power at horizons up to 12 quarters. The public investment rate is only marginally significant at long horizons (16 quarters). The negative effect of the dividend-price ratio on the predictability of the public investment rate is naturally related to the very high correlation (51%) between 13

15 these two variables, as reported in Table Stock Return Predictability Over Time Turning to the analysis of the variation in the predictability over time, Table 3 reports the results of long-horizon forecasts of excess stock returns across two sub-samples of equal size. The first sub-sample covers the earlier period from 1947 to 1977 and the second sub-sample covers the more recent period from 1978 to These two samples are interesting because the behavior of the public investment rate has changed substantially in the 1970 s and 1980 s, a fact first documented in Aschauer (1989). According to the summary statistics reported in Table 1, the mean public investment rate decreased between and by almost 1 percentage point per quarter, from 4.16% to 3.31%. In addition, the standard deviation of the public investment rate has decreased substantially from 1.47% per quarter in the period to 0.27% per quarter in the period. Panel A in Table 3 reports long-horizon forecasts of excess returns for the period. Here, the predictive power of the public investment rate is impressive. The slope coefficient is positive across all horizons and the t-statistics increases from 1.91 at the one quarter horizon to 6.03 at the 16 quarter horizons. The R 2 statistic reaches 61.2% at the 16 quarter horizon. The results for the period reported in Panel B are substantially different. Here, the slope coefficient associated with the public investment rate is negative, but not statistically significant. Thus the change in the properties of the public investment rate between the two periods has generated significant changes in the forecasting ability of the public investment rate for stock returns. The lower and much smoother public investment rate in the and the lower forecasting power of the public investment rate for returns is consistent with the hypothesis in Aschauer (1989) that the slower rate of formation of 14

16 public capital has contributed to a slowdown in the increase of aggregate productivity. In turn, the effect of public capital on stock returns during this sample period is small and thus statistically difficult to detect in the data. [Insert Table 3 here] 4.3 Stock Return Predictability Across Industries We now turn to an investigation of the predictive power of the public investment rate for long-horizon stock return predictability regressions at the industry level. This analysis is interesting because it allows us to investigate the heterogeneous impact of public capital in the productivity of different industries, which has been largely overlooked in the literature (see discussion in Holtz-Eakin, 1992). Table 4 reports the results of long-horizon forecasts of excess stock returns for each of the 17 Fama-French industries. Across all industries, the public investment rate slope coefficient is positive and increases with horizon. The slope is in general statistically significant across all industries, especially at horizons higher than 8 quarters. Only in 4 industries (food industry, textiles, apparel and footwear industry (clothes), drugs, soap, perfumes, and tobacco industry (consumers) and retail industry) the public investment rate does not seem to forecast industry stock returns. The magnitude of the public investment rate slope coefficient and the regression R 2 statistic also varies substantially across industries. They are particularly high in the consumer durables, construction, steel and cars industries, for which the R 2 statistic is above 25% at the 16 quarter horizon. [Insert Table 4 here] Overall, the results reported here confirm that the public investment rate forecasts 15

17 industry stock returns in the full sample. This predictability varies across industries, suggesting that the effect of public capital is not uniform across industries. 4.4 Is the Model Consistent with the Empirical Evidence? The regression results in the previous section do not necessarily imply that public capital has an effect on firms productivity if the public investment rate is correlated with an omitted variable (e.g. aggregate productivity) which in turn could drive the true correlations in the data. Here, we investigate directly if the theoretical model can qualitatively and quantitatively replicate the empirical findings. In order to obtain the model implications for stock return predictability at both short-horizons and long-horizons, we construct the time series of aggregate investment excess returns implied by the model, by substituting the public and private investment rates into equation (9) to obtain Rt I and then subtract the risk free rate. In constructing the investment return we follow Cochrane (1991) and assume that the aggregate productivity shock x t is constant and equal to its long-run mean x. In addition, the remaining parameter values are calibrated so that the mean and standard deviation of the investment returns roughly matches the mean and standard deviation of stock returns as close as possible. The resulting parameters are: c = 30, δ = δ PG = 0.026, x = 3.47, α = 2. Here, the adjustment cost parameter, c, controls the volatility of investment return, and the curvature parameter, α, controls the predictive power of the public investment rate. These parameters are reasonable. With the adjustment cost function in equation (4), the ( fraction of investment lost to adjustment cost is c I ) 2. The parameter c equals 30, and 2 K 16

18 the mean investment rate (I/K) is around the depreciation rate of Thus the fraction of investment lost to adjustment costs is about 1%. Thus the puzzle of implausibly high adjustment costs from standard q-theory is not present in these parameters. Table 5 shows that the moments for the constructed investment excess returns matches reasonably well the moments of aggregate stock market excess returns. The mean excess investment returns perfectly matches the mean excess stock returns. The standard deviation of the investment return is smaller than the standard deviation of aggregate stock returns (similar results are reported in Cochrane, 1991), a result that can be explained by the parsimonious specification of technology (quadratic adjustment costs) adopted here. Finally, the investment returns have slightly higher first and second order autocorrelation, but it matches reasonably well higher order autocorrelations. Turning to the analysis of the long-horizon investment return predictability results reported in Panel A in Table 6, the model replicates well the predictability pattern observed in the data (reported in Panel C in Table 2). The slope coefficient of the public investment rate is positive, increases with the investment horizon, and has a magnitude that is comparable with the empirical counterpart. Similarly, the slope coefficient of the private investment rate is negative and its absolute value also increases with the investment horizon. Similarly to the data, the R 2 statistics also increase with the horizon. Figure 2 shows the close link between the forecasting regressions of stock excess returns and investment excess returns. This Figure plots the one period ahead predicted excess stock return, implied by the predictability regression results reported in Panel C, Table 2, and the one period ahead predicted excess investment return, implied by the predictability regression results reported in Panel A, Table 6. Clearly, the time series of both forecasts are very closely related. The model also matches reasonably well the pattern of sub-sample predictability results 17

19 reported in Table 3. Panel B, Table 6 shows that the public investment rate is a stronger predictor of investment returns in the earlier sample period from 1947 to 1977 than in the later sample period from 1978 to 2008, and, as in the data, the slope coefficient changes sign across sub-samples. This result establishes a close link between the empirical results and the theoretical model. It suggests that the public investment rate indeed affects stock returns through its effect on productivity, since the changes in the properties of the public investment rate are directly reflected in the properties of realized stock returns. The theoretical analysis in Section 2.3 can also be used to understand the pattern of predictability across industries. As shown in Figure 1, the relationship between expected investment returns and the public investment and private investment rate depends on the curvature parameter α in equation (1). If public capital does not affect the production in a given industry (i.e. α = 0), Figure 1 shows that the public investment rate should not predict future stock returns in that industry. In addition, the positive relationship between stock returns and the public investment rate increases as the parameter α increases. This analysis suggests that the predictability pattern across industries can be closely linked to the effect of public capital across industries: industries in which the slope coefficient associated with the public investment rate is high are industries in which public capital represents a relatively more important input in the production process. 5 Conclusion We show that the public investment rate, in addition to the private investment rate, is a significant predictor of stock returns. This finding is consistent with a standard q-theory model of stock returns in which public physical capital is a productive input in the firm s production process. 18

20 Our empirical finding suggest that public capital has a substantial effect of firms productivity, but this effect has changed substantially over time. During the 1950 s and 1960 s the effect of public capital accumulation on stock returns was positive and strong, but the effect is considerably weaker in and after the 1980 s, a period characterized by relatively low and very smooth rates of public investment, and hence of relatively low rates of accumulation of public capital. References [1] Ang, Andrew, and Geert Bekaert, 2007, Stock return predictability: Is it there? Review of Financial Studies 20, [2] Aschauer, David Alan 1989, Is public expenditure productive?, Journal of Monetary Economics 23, [3] Bazdresch, Santiago, Frederico Belo, and Xiaoji Lin, 2009, Labor hiring, investment, and stock return predictability in the cross section, working paper, University of Minnesota. [4] Berk, Jonathan B, Richard C. Green and Vasant Naik, 1999, Optimal investment, growth options and security returns, The Journal of Finance 54, [5] Campbell, John Y., and Robert Shiller, 1988, The dividend-price ratio and expectations of future dividends and discount factors, Review of Financial Studies 1, [6] Carlson, Murray, Adlai Fisher, and Ron Giammarino, 2004, Corporate investment and asset price dynamics: Implications for the cross section of returns, The Journal of Finance, 59(6), [7] Cochrane, John H., 1991, Production-based asset pricing and the link between stock returns and economic fluctuations, The Journal of Finance 461, [8] Cochrane, John H., 1996, A cross sectional test of an investment based asset pricing model, Journal of Political Economy 1043, [9] Cochrane, John H., 2002, Asset Pricing (Princeton University Press, NJ). [10] Cooper, Michael, Huseyin Gulen and Michael J. Schill, 2008, Asset Growth and the Cross-Section of Stock Returns, The Journal of Finance, 63 (4), [11] Evans, Paul and Karras, Georgios, 1994a, Is government capital productive? Evidence from a panel of seven countries, Journal of Macroeconomics 16,

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22 [28] Li, Erica X. N., Dmitry Livdan, and Lu Zhang, 2008, Anomalies, Forthcoming, Review of Financial Studies [29] Lin, Xiaoji, 2009, Endogenous Technological Progress and the Cross Section of Stock Returns, Working paper, London School of Economics. [30] Liu, Laura X. L., Toni M. Whited, and Lu Zhang, 2009, Investment-based expected stock returns, forthcoming, Journal of Political Economy. [31] Lynde, Catherine and Richmond, James, 1992, The role of public capital in production, The Review of Economics and Statistics 74, [32] Nadiri, M. Ishaq, and Theofanis P. Mamuneas, 1994, The Effects of Public Infrastructure and R&D Capital on the Cost Structure and Performance of U.S. Manufacturing Industries, The Review of Economics and Statistics 7, [33] Newey, Whitney K., and Kenneth D. West, 1987, A simple, positive semi-definite, heteroskedasticity and autocorrelation consistent covariance matrix, Econometrica 55, [34] Shah, Anwar, 1992, Dynamics of public infrastructure, industrial productivity and profitability The Review of Economics and Statistics, [35] Zhang, Lu, The value premium, The Journal of Finance 60 (1),

23 Table 1 : Summary Statistics This table reports the summary statistics (mean, standard deviation, S.D., and first order autocorrelation, AC(1)) of the public capital total investment rate (GIK), private capital total investment rate (IK), public capital investment rate in defense sector (GIK-Def), public capital investment rate in non-defense sector (GIK-NoDef), public capital investment rate in structures in the non-defense sector (GIK-Struct), public capital investment rate in equipment and software in the non-defense sector (GIK-Eqpmt) and the aggregate dividend-price ratio. All values are in percentage, except AC(1). The sample is quarterly from 1947:2 to 2008:4. 22 NBER NBER Fraction Fraction Full Sample Expans. Recess. Variables GDP G-Invest Mean S.D. AC(1) Mean S.D. Mean S.D. Mean Mean GIK IK GIK-Def GIK-NoDef GIK-Struct GIK-Eqpmt DP Correlation GIK IK GIK-Def GIK-NoDef GIK-Struct GIK-Eqpmt DP GIK IK GIK-Def GIK-NoDef GIK-Struct GIK-Eqpmt DP

24 Table 2 : Forecasting Aggregate Stock Market Excess Returns This table reports results from long-horizon regressions of log excess returns on the aggregate stock market index, Σ H h r t+h r ft+h, in which H is the return forecast horizon in quarters. The regressors are one-period lagged values of the public capital total investment rate (GIK), private capital total investment rate (IK), public capital investment rate in defense sector (GIK-Def), public capital investment rate in non-defense sector (GIK-NoDef), public capital investment rate in structures in the non-defense sector (GIK-Struct), public capital investment rate in equipment and software in the non-defense sector(gik-eqpmt), log dividend yield (DP), the detrended short-term Treasury bill rate (TB) and the term premium, (TERM). For each regressor in a given regression model, we report the OLS estimate of the slope coefficient, slope, the Newey- West corrected t-statistic, tnw, the Hodrick (1992) corrected t-statistic, thd, and the adjusted R2. The sample is quarterly from 1947:2 to 2008:4. Forecast horizon in quarters Panel Regressors A GIK Slope tnw thd R B IK Slope tnw thd R C GIK Slope tnw thd IK Slope tnw thd R D GIK-Def Slope tnw thd GIK-NoDef Slope tnw thd IK Slope tnw thd R

25 Table 2 : Forecasting Stock Market Excess Returns (cont.) Forecast horizon in quarters Panel Regressors E GIK-Struct Slope tnw thd GIK-Eqpmt Slope tnw thd IK Slope tnw thd R F GIK Slope tnw thd IK Slope tnw thd TERM Slope tnw thd RF Slope tnw thd R G GIK Slope tnw thd IK Slope tnw thd TERM Slope tnw thd RF Slope tnw thd DP Slope tnw thd R

26 Table 3 : Sub-Sample Analysis This table reports sub-sample results from long-horizon regressions of log excess returns on the aggregate stock market index, Σ H h r t+h r ft+h, in which H is the return forecast horizon in quarters. The regressors are one-period lagged values of the public capital total investment rate (GIK) and private capital total investment rate (IK). For each regressor in a given regression model, we report the OLS estimate of the slope coefficient, slope, the Newey-West corrected t-statistic, tnw, the Hodrick (1992) corrected t-statistic, thd, and the adjusted R2. The sample is quarterly from 1947:2 to 2008:4. Forecast horizon in quarters Panel Regressors From 1947 to 1977 A GIK Slope tnw thd IK Slope tnw thd R From 1978 to 2008 B GIK Slope tnw thd IK Slope tnw thd R

27 Table 4 : Forecasting Industry Level Stock Market Excess Returns This table reports results from long-horizon regressions of log excess returns on the 17 Fama-French Industries, Σ H h r t+h r ft+h, in which H is the return forecast horizon in quarters. The regressor is the one-period lagged values of the public capital total investment rate (GIK). The 17 industries are: Food; Mining and Minerals (Mines); Oil and Petroleum Products (Oil); Textiles, Apparel and Footware (Clothes); Consumer Durables (Durables); Drugs, Soap, Perfumes and Tobacco (Chemicals), Construction and Construction Materials(Construction), Steel Works Etc (Steel), Fabricated Products (Fab Prod); Machinery and Business Equipment (Machinery); Automobiles (Cars); Transportation (Trans); Utilities (Utils); Retail Stores (Retail); Banks, Insurance Companies, and Other Financials (Finance); Other industries (Other). In each regression we report the OLS estimate of the slope coefficient, slope, the Newey-West corrected t- statistic, tnw, the Hodrick (1992) corrected t-statistic, thd, and the adjusted R2. The sample is quarterly from 1947:2 to 2008:4. Forecast horizon in quarters Industry Regressors Food GIK Slope tnw thd R Mines GIK Slope tnw thd R Oil GIK Slope tnw thd R Clothes GIK Slope tnw thd R Durables GIK Slope tnw thd R Chemicals GIK Slope tnw thd R Consumers GIK Slope tnw thd R Construction GIK Slope tnw thd R

28 Table 4 : Forecasting Industry Level Stock Market Excess Returns (cont.) Forecast horizon in quarters Industry Regressors Steel GIK Slope tnw thd R Fab Paper GIK Slope tnw thd R Machinery GIK Slope tnw thd R Cars GIK Slope tnw thd R Trans GIK Slope tnw thd R Utils GIK Slope tnw thd R Retail GIK Slope tnw thd R Finance GIK Slope tnw thd R Other GIK Slope tnw thd R