Internet Appendix to: “Government Investment and the Stock Market” Frederico Belo∗

Jianfeng Yu†

May 2012

This Appendix reports the following additional analysis and robustness checks: 1. Show that the public sector investment rate positively forecasts several alternative measures of aggregate cash flows, not only aggregate total factor productivity (TFP) as reported in the main text. 2. Show that government investment predicts investment returns constructed from macroeconomic data. 3. Document the link between government investment and the aggregate risk premium controlling for other risk premium proxies, perform a sub-sample analysis, and address the spurious regression critique of Ferson, Sarkissian, and Simin (2003). 4. Provide additional empirical evidence that the link between government investment and risk premium operates, at least partially, through the positive link between government investment and cash flow risk. 5. Provide an extended discussion on the model’s economic mechanism underlying the results. ∗

Assistant Professor, Department of Finance, University of Minnesota, Carlson School of Management. Address: 321 19th Ave. South, # 3-137, Minneapolis, MN 55455. e-mail: [email protected] † Assistant Professor, Department of Finance, University of Minnesota, Carlson School of Management. Address: 321 19th Ave. South, # 3-122, Minneapolis, MN 55455. e-mail: [email protected]

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1

Additional Data

The main variables used are discussed in the main paper. Here, we define the additional variables used in this Appendix. Public and private sector real growth rate of investment. The variable ∆I is the real growth rate in total nonresidential private investment, which is computed as ∆It = log(It )−log(It−1 ). The variable ∆GIt is the real growth rate of public sector investment, which is computed as ∆GIt = log(GIt )−log(GIt−1 ). Since these growth variables do not depend on the construction of the capital stock, they can be used to check the robustness of the findings. Risk premium proxies. We consider two risk premium proxies in the additional empirical analysis reported here: the aggregate dividend-to-price ratio (denoted DP) which is discussed in the main text; and the consumption surplus (denoted CSPLS) variable. Following Wachter (2006), the consumption surplus is constructed as a smoothed average of the past 40 quarters of the consumption of nondurables and services real growth rate:

j CSPLSt = Σ40 j=1 φ ∆ct−j , with φ = 0.97.

Because quarterly consumption data are available only since 1947:1, annual consumption data before 1947 are used to compute the initial value of the consumption surplus in 1947:1 (calculated as the smoothed average of the past 10 years of the consumption growth rate). Table 1 reports the summary statistics of the main variables used in the empirical analysis. This table is a slightly extended version of Table 1 reported in the main text. We note here that the real growth rate of private and public investment (∆I and ∆GI) shows clearly that private investment is strongly procyclical (correlation of ∆I with ∆GDP is 62%), whereas public investment is only weakly procyclical (correlation of ∆GI with ∆GDP is 14%). [Insert Table 1 here]

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2

Government Investment and Aggregate Economic Activity

In the model, the link between public sector capital and stock returns depends crucially on the positive effect of public sector capital on the productivity of private inputs. In the main text we provide support for this specification by showing that public sector investment rate positively forecasts aggregate total factor productivity. Here, we show that government investment forecasts other alternative measures of aggregate cash flows: aggregate dividends growth (∆Div) and aggregate profits (Πt /Kt ). (Refer to Table 1 for the summary statistics of these three variables.). For completeness, in Panel A in Table 2 we report the results for aggregate ∆TFP as reported in the main text. [Insert Table 2 here] Panel B in Table 2 shows that the public sector investment rate also positively forecasts aggregate dividends.

The public sector investment rate slope coefficient is statistically

significant at all horizons, and the R2 statistic increases from 5.9% at the one-quarter horizon to 8.7% at the one-year horizon. After the one-year horizon, the R2 decreases. The lower R2 statistic from these regressions, in comparison with the R2 statistic from the TFP growth predictability regressions, is consistent with the well-established fact that dividends are difficult to predict, especially at the aggregate level (e.g., Cochrane, 2008, Lettau and Ludvigson, 2010, among others). Panel C in Table 2 reports the results of long-horizon forecasts of aggregate profitability. Consistent with the previous results, the public investment rate strongly positively forecasts future profitability as well. The public sector investment rate slope coefficients are positive and increasing in the forecast horizon. The R2 statistics are high and increase with the horizon from 42.8% at the one-quarter horizon to 48.6% at the four-year horizon.

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3

Government Investment and Investment Returns

In the model, investment returns and stock returns are equal state-by-state. In the main text we investigate the predictability of excess stock returns using stock return data. Here, we investigate the predictability of investment returns, constructed from macroeconomic data. This analysis thus allows us to provide an additional check of the models’ predictions. From the theoretical analysis, the investment returns are given by:

I Rt+1 ≡

2 Yt+1 /Kt+1 + c/2 · IKt+1 + (1 − δ) (1 + c · IKt+1 ) . 1 + c · IKt

(1)

where we used the fact that Yt = ext GKtα Kt to measure the marginal product of capital (Yt+1 /Kt+1 ). Since output (Yt ) can be measured in the data, we can thus measure the marginal product of capital without having to specify the parameter α, and without data on public sector capital. Our production function ignores labor. In practice, however, labor is an important component of the production process. Thus we adjust our measure for the marginal product of capital to be 40% of Yt+1 /Kt+1 , which roughly corresponds to the share of physical capital in a typical aggregate production function. Our results are very similar to those reported here if we ignore this adjustment. We construct a time series of investment returns by substituting the corresponding macroeconomic variables in equation (1). We set c = 50, consistent with the calibration of the theoretical model, and we subtract the risk-free rate to focus on excess investment returns. [Insert Table 3 here] Table 3 shows that the public sector investment rate and private investment rate forecasts investment excess returns with slope coefficients that have the same sign as those reported for the aggregate stock market excess returns. The magnitude of the slope coefficient for the public sector investment rate is overall very similar, but the slope coefficient for the private 4

sector investment rate is smaller. The R2 are also comparable across the two regressions. Taken together, the analysis reported here is consistent with the main results reported in the paper for the predictability of aggregate stock market excess returns.

4

Relationship with other Risk Premium Proxies

In this section we perform several robustness checks. First we address the concern that the government investment rate is a spurious regressor. Then we investigate the marginal forecasting ability of the public and private sector investment rates for the aggregate risk premium, after controlling for other risk premium proxies. Finally, we perform a sub-sample analysis.

4.1

Spurious Regression Critique

Because the public and private investment rates are persistent regressors, the results reported here are subject to the spurious regression critique of Ferson, Sarkissian, and Simin (2003). To address this concern, we replicate the multivariate long-horizon stock return predictability regression using the growth rate of public investment (∆GI) and private investment (∆I) as two alternative measures of investment rates. As documented in Table 1 of this Appendix, the autocorrelation of these two series is much lower (14% for the public sector investment growth rate and 45% for the private sector investment growth rate). The results reported in Panel B of Table 4 help mitigate the concern that the public and private sector investment rates are spurious regressors. Consistent with the previous analysis, the growth rate of public and private sector investment remains a significant predictor of excess stock returns, with slope coefficients that have the same sign as those reported in Panel A of Table 4. [Insert Table 4 here]

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4.2

Relationship with other Risk Premium Proxies

Here, we investigate the marginal forecasting ability of the public and private sector investment rates for the aggregate risk premium, after controlling for other risk premium proxies. By performing this analysis, we depart from the theoretical model in that, according to the model, only the private and public sector investment rates should matter for the aggregate risk premium. However, because macroeconomic variables like the public and private sector investment rates are measured with error, and because the model is naturally a simplified description of reality, other variables should matter in practice. The empirical asset-pricing literature documents a large set of return predictors. We focus on a subset of return predictors that are available for the entire sample period (starting in 1947) and which are known to investors at time t. For tractability, we only consider two additional risk premium proxies: one financial variable and one macroeconomic variable. We examine the aggregate dividend-to-price ratio (denoted DP) following Campbell and Shiller (1988), Fama and French (1988), and Hodrick (1992), who show that this variable predicts future excess returns. In addition, we consider the consumption surplus (CSPLS) of the representative agent. Campbell and Cochrane (1999) show that habit formation, captured by CSPLS, can endogenously explain variation in the price of risk over time. Li (2001) shows that the consumption surplus predicts aggregate stock returns (risk premium). This variable is particularly interesting because, similar to the public and private sector investment rates, it is a macroeconomic variable and thus not constructed from asset price data. We focus on a small set of additional risk premium proxies because our goal is not to show that government investment has predictive power for stock returns that is robust to the inclusion of all the predictors previously established in the literature. From a general equilibrium perspective, consumption-based (or other) risk premium proxies can fully explain expected excess returns, yet the production-based perspective that we investigate here can still be correct.1 1

In unreported results, we also control for the Lettau and Ludvigson’s (2001) cay variable. The results

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Panel C in Table 4 reports the predictability results after controlling for the two alternative risk premium proxies. The size, magnitude, and statistical significance of the public sector investment rate slope coefficients increases relative to the slope coefficients reported in Panel A in Table 4. The slope coefficient of the public sector investment rate is positive and statistically significant across all horizons. The slope coefficient of the private sector investment rate remains negative across all horizons. However, it is no longer statistically significant in the presence of the other return predictors. As discussed in Cochrane (1991), and as further discuss below when we further study the results from the theoretical model, this result is to be expected. In a simple q-theory model as we have here, the dividend-price ratio should be highly correlated with the private investment rate. Because the dividend-price ratio is a financial variable and hence has less measurement error, it is natural to expect that this variable, in a multivariate regression, absorbs the predictive power of the private sector investment rate for the aggregate risk premium. Finally, the slope coefficients of the two risk premium proxies, DP and CSPLS, are all statistically significant across all horizons and have the sign previously documented in the literature. The R2 statistic increases with the horizon from 5.9% at the one-quarter horizon to 57.8% at the four-year horizon.

4.3

Sub-Sample Analysis

As reported in Figure 1 in the main text, the business-cycle properties of the public investment rate seem to vary between the first and second half of the sample. It is clear that the 1950s is a period characterized by high rates of formation of public sector capital. In the 1960s until the 1980s we observe the well documented (Aschauer, 1989) decline in the public sector investment rate. Given these changes, here we perform a sub-sample analysis. [Insert Table 5 here] are consistent with those reported here. We have not used the cay variable here because this variable is not available for the full sample period (the cay variable is available only after 1952 at quarterly frequency, whereas the main sample in the paper starts in 1947).

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According to the results reported in Table 5, the public investment rate is positively correlated with risk premiums in the two sub-samples.2 Although not clear in the results reported here, we note that the predictability results across other set of control variables tend to be somewhat weaker in the second half of the sample. There are several reasons that may explain this result. As discussed before, the first half of the sample is a period characterized by high rates of formation of public sector capital. Thus this period is likely to be more informative for detecting the effect of government investment on productivity/risk that we want to estimate in the data. In addition, the change in the properties of the public sector investment rate raises the possibility of a structural break which are not properly handled in these regressions. Identifying and establishing the existence of a structural break is difficult given the persistence of the public sector investment rate and the relatively small sample size.

5

Public Sector Investment Rate and Cash Flow Risk: Additional Results

According to the theoretical analysis, investment in public sector capital is positively correlated with the aggregate risk premium through the impact of public capital on the conditional covariance between cash flows and the stochastic discount factor.

In the

main text, we provide support for this link by documenting a positive link between government investment and the conditional covariance between alternative aggregate cash flow measures and aggregate productivity. Here, we extend the analysis by examining the covariance between alternative aggregate cash flow measures and aggregate consumption (not productivity). In addition, we further extend the analysis in the paper as follows: (i) study the conditional covariance with aggregate stock market excess returns, not just dividends or 2

To save space, in Table 5 we only report the predictability results up to the 2-years horizon for each sub-sample.

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profitability; and (ii) run the regressions at both quarterly and annual frequencies, to avoid possible distortionary effects of seasonality in higher frequency (quarterly) macroeconomic data.

5.1

Government Investment and Productivity Betas

To investigate the link between government investment and systematic risk, in the paper, 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. The top panels in Table 6 in this Appendix shows the full set of results from this analysis. As discussed in the main text, the conditional productivity beta in general increases with the public sector investment rate, as predicted by the model. [Insert Table 6 here]

5.2

Government Investment and Consumption Betas

We also investigate the link between government investment and the conditional covariance with aggregate consumption growth ∆Ct (instead of using aggregate productivity ∆T F P ). This alternative specification is consistent with the standard consumption-based approach to asset pricing (e.g., Lucas, 1978, and Breeden, 1979). The empirical analysis is similar to the analysis in the previous section and is explained in the main text. Specifically, we estimate the firm’s conditional cash flow consumption beta by running a regression of the form:


′ CFt = a + b + cGIKt−1 + dZt−1 × ∆Ct + εt ,

(2)

in which CFt is the firm’s aggregate cash flow, which we measure as either the real growth rate of aggregate dividends (∆Divt ), aggregate profitability (Πt /Kt ), or aggregate stock e market excess returns (Rt+1 ). The vector Zt−1 is a set of additional macro control variables

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which include the lagged aggregate-level dividend-price ratio and the aggregate consumption surplus. The bottom panels in Table 6 reports the results from this analysis.

Overall, the

conclusion from this analysis is similar to that reported in the main text. Investment in public sector capital predicts an increase in the sensitivity of aggregate cash flows (dividends, profits and excess returns) to consumption risk. That is, government investment is associated with an increase in cash flow risk in the economy, which in turn explains the results from the risk premium regressions.

6

Quantitative Model Results: Additional Analysis

Here, we present additional results from the theoretical model. In addition, we perform a more detailed analysis of the economic mechanism underlying the results (we report the main summary of this analysis in the main text).

6.1

Dividend-Price Ratio and Private Investment

According to the summary statistics of selected variables in the model (see Table 6 in the main text), the correlation between the dividend-price ratio and the private sector investment rate is strongly negative in the simulated data. This result explains why, in the data, the predictive power of the private sector investment rate in the risk premium regressions is significantly reduced once the dividend-price ratio is included in the regression (see Panel C in Table 4 in this Appendix). According to the model, both variables have approximately the same explanatory power, but in the data, the dividend-price ratio performs better because, being a financial variable, it is likely to have less measurement error than the private sector investment rate (a macroeconomic variable).

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6.2

Government Investment and Productivity Betas in the Simulated Model

The model replicates the pattern of the conditional cash flow productivity betas observed in the data, as reported in Table 6 in this Appendix (see analysis in Section 5). According to the last column in Table 3 (Model), using aggregate profitability as 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 data, higher levels of

government investment are associated with an higher covariance between firm’s cash flows and the aggregate shock.

6.3

Inspecting the Mechanism

In the benchmark calibration of the model, we make several assumptions. 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 following two parameters. To understand the importance of public sector capital, we do a sensitivity analysis with respect to the public capital curvature parameter α. To understand the importance of countercyclical fiscal policy, we do a sensitivity analysis to the parameter ρx,g . This parameter controls the correlation between innovations in the public sector investment rate and aggregate profitability, and thus determines the procyclicality or countercylicality of the fiscal policy in the model. The analysis in this section extends the similar analysis reported in the main text (a summary of the results reported there). Importance of the curvature parameter α: Panel C of Table 7 in the main text shows that countercyclical fiscal policy is not sufficient to generate a positive correlation between the public sector investment rate and the aggregate risk premium. Allowing for a positive effect of public sector capital on private firms’ productivity is important for the model to replicate the empirical evidence. More generally, the top panel in Figure 1 in this Appendix

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plots the public sector and private sector slope coefficients in risk premium predictability regressions, across artificial data generated by economies with different values of the public capital curvature parameter α. The figure shows that the slope coefficients for both the public sector and private sector investment rates increase with the curvature parameter α. Specifically, the slope coefficient of the public sector investment rate is nonnegative and almost a linear function of α, thus showing the importance of this parameter. [Insert Figure 1 here] Importance of countercyclical fiscal policy ( ρx,g < 0): In the benchmark calibration, the correlation between the public sector investment rate shock and the aggregate profitability shock is negative, ρx,g = −0.4. This parameter has a first-order effect on the correlation of the public sector and private sector investment rates, and we chose this value to match the low but negative correlation between the public sector and the private sector investment rates observed in the data. One potential concern with this specification is that, by exogenously specifying a countercyclical public investment rate, the positive correlation between the public investment rate and the aggregate risk premium in the model follows mechanically and is independent of its effect on systematic risk. That is, the positive correlation follows from the exogenously specified positive correlation between the public sector investment rate with the (countercyclical) market price of risk in the stochastic discount factor, rather than from the cash flow channel that we highlight in the theoretical section of the main paper. However, the previous results reported in Panels C and D of Table 7 in the main text show that a countercyclical fiscal policy is neither sufficient nor necessary for the model to generate additional predictive power for the public sector investment rate, after controlling for the private sector investment rate. Even though a countercyclical fiscal policy does not seem to be important to generate the risk premium results, it has a first order effect on the dynamic correlation between private and public sector capital. To understand this effect, the last two panels in Figure 1 plot the estimated public and private capital slope coefficients from risk premium predictability 12

regressions in simulated data, as well as the endogenous correlation between the public sector and private sector investment rates, as a function of ρx,g . Consistent with the previous analysis, the public sector investment rate slope coefficient is positive even if the public investment rate is specified to be procyclical (i.e., ρx,g > 0). In fact, the public sector investment rate slope coefficient is similar for most of the values of ρx,g and then increases for large values of ρx,g . The increase in the slope coefficient can be explained as follows. When the parameter ρx,g is positive (high), high values of aggregate profitability tend to occur when the public sector investment rate is high, which leads to an even higher increase in future marginal productivity of private capital. As a result, an high public sector investment rate induces more private investment, which in turn leads to a positive correlation between the public sector and private sector investment rates (see bottom panel of Figure 1). Because the private investment rate is negatively correlated with future stock returns, controlling for the private investment rate in the stock return predictability regression increases the slope coefficient on the public investment rate. As a consequence, the public capital investment rate can positively predict future excess returns in a multivariate regression that includes the private investment rate, even for large values of the correlation parameter ρx,g (procyclical public sector investment rate). Overall, the analysis in this section shows that a positive public capital curvature parameter (α > 0) is necessary for the model to replicate the positive link between public sector investment and the risk premium, but a countercyclical fiscal policy is neither necessary nor sufficient for the model to replicate this link. Thus, when considered with the empirical evidence in Section 4 in the main text, this analysis suggests that the cash flow channel (systematic risk) should be at least partially responsible for the predictive ability of the public investment rate observed in the data.

References [1] Aschauer, David Alan, 1989, Is public expenditure productive? Journal of Monetary Economics, 23(2), 177-200. 13

[2] Breeden, Douglas T., 1979, An intertemporal capital pricing model with stochastic investment opportunities, Journal of Financial Economics, 7(3), 265-296. [3] Campbell, John, and John Cochrane, 1999, By force of habit: a consumption-based explanation of aggregate stock market behavior, Journal of Political Economy, 107(2), 205-51. [4] Campbell, John Y., and Robert J. Shiller, 1988, The dividend-price ratio and expectations of future dividends and discount factors, Review of Financial Studies, 1(3), 195–228. [5] Cochrane, John H., 1991, Production-based asset pricing and the link between stock returns and economic fluctuations, Journal of Finance, 461(1), 209-237. [6]

, 2008, The dog that did not bark: A defense of return predictability, Review of Financial Studies, 21(4), 1533-1575.

[7] Fama, Eugene F., and Kenneth R. French, 1988, Dividend yields and expected stock returns, Journal of Financial Economics, 22(1), 3–25. [8] Ferson, Wayne E., Sergei Sarkissian, and Timothy T. Simin, 2003, Spurious regressions in financial economics? Journal of Finance, 58(4), 1393-1413. [9] Hodrick, Robert J., 1992, Dividend yields and expected stock returns: Alternative procedures for inference and measurement, Review of Financial Studies, 5(3), 357–386. [10] Lettau, Martin, and Sydney Ludvigson, 2001, Consumption, aggregate wealth, and expected stock returns, Journal of Finance, 56(3), 815–849. [11]

, 2010, Measuring and modeling variation in the risk-return trade-off, Handbook of Financial Econometrics, ed. Yacine Ait-Sahalia and Lars P. Hansen vol. 1, pp. 617-690. Elsevier Science B.V., North Holland, Amsterdam.

[12] Li, Yuming, 2001, Expected returns and habit persistence, Review of Financial Studies, 14(3), 861–899. [13] Lucas, Robert. E. Jr, 1978, Asset prices in an exchange economy, Econometrica, 46(6), 1426-1446: [14] Wachter, Jessica, 2006, A consumption-based model of the term structure of interest rates, Journal of Financial Economics, 79, 365-399.

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Table 1 : Summary Statistics This table reports the summary statistics -mean, standard deviation (S.D.), first-order autocorrelation (AC(1)), and selected correlations- of the variables used in the empirical work. The variables are the private sector investment rate (IK), the public sector investment rate (GIK), the real growth rate in private investment (∆I), the real growth rate in public investment (∆GI), the real growth rate in GDP (∆GDP), the real growth rate in measured total factor productivity (∆TFP), real corporate profits scaled by the physical capital stock (Profits, Πt /Kt ), the real growth rate in aggregate dividends (∆Div), the share of government consumption expenditures in aggregate GDP (Gov Cons.), the share of the government deficit in aggregate GDP (Gov Deficit), the aggregate consumption surplus (CSPLS), the aggregate dividend-price ratio (DP), and the aggregate stock market excess return (Rs − Rf ). All values are in percentages, except for AC(1) and correlations. The sample is quarterly from 1947:2 to 2010:4.

Selected Correlations Variables Mean S.D AC(1) IK GIK ∆GDP ∆TFP Private and Public Investment Rates and Growth Rates IK 3.67 0.38 0.97 1 −0.23 0.03 −0.16 GIK 3.66 0.62 0.98 −0.23 1 0.15 0.18 ∆I 1.05 2.76 0.45 0.28 −0.01 0.62 0.35 ∆GI 1.05 3.51 0.14 −0.01 0.29 0.14 0.15 Economic Activity ∆GDP ∆TFP Profits (Πt /Kt ) ∆Div

and Aggregate Cash 0.79 1.01 0.38 0.33 0.95 0.10 5.03 1.68 0.98 0.45 2.22 0.46

Flow Variables 0.03 0.15 −0.16 0.18 −0.07 0.68 −0.01 0.26

1 0.83 0.30 0.11

0.83 1 0.19 0.01

Other Fiscal Policy Variables (Share of GDP) Gov Cons. 16.27 1.31 0.97 −0.13 −0.35 Gov Deficit −1.07 2.77 0.96 0.33 0.57

−0.17 0.18

−0.10 0.03

Risk Premium Proxies and Financial Variables CSPLS 13.14 3.14 0.99 0.19 DP 3.37 1.33 0.97 −0.32 Rs −Rf 1.50 8.31 0.09 −0.19

0.17 −0.05 0.13

0.07 −0.04 0.15

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0.37 0.27 0.13

Table 2 : Government Investment and Aggregate Cash Flows This table reports results from long-horizon predictability regressions of ΣH h yit+h , in which yi is either the growth rate of total factor productivity, aggregate real dividends, or aggregate profitability, and H is the forecast horizon in quarters. The regressor is the H-period lagged value of the public capital investment rate (GIK). For each regression, we report the OLS estimate of the slope coefficient, slope, and the Newey-West corrected t-statistic, [t], and the adjusted R2 . The sample is quarterly from 1947:2 to 2010:4.

Panel

Regressors

1

Forecast horizon in quarters 2 4 8 12

16

A

GIK

Slope [t] R2

0.26 2.57 2.43

0.52 2.69 4.77

TFP 1.01 1.77 2.96 3.29 8.20 15.02

2.38 3.72 17.59

3.00 4.14 22.46

B

GIK

Slope [t] R2

0.89 2.17 5.86

1.67 2.26 7.18

Dividends 3.12 3.90 2.48 2.77 8.71 4.76

3.51 2.24 2.46

3.72 2.10 2.48

3.62 4.91 43.70

Profitability 7.32 14.66 4.78 4.64 45.41 47.07

21.67 4.60 47.76

28.49 4.64 48.59

C

GIK

Slope [t] R2

1.80 4.98 42.82

Table 3 : Government Investment and Predictability of Investment Returns This table reports the results from long-horizon predictability regressions of the log excess investment returns , ΣH h rt+h − rf t+h , in which H is the return forecast horizon in quarters. The regressors are the following: the H-period lagged value of the public sector investment rate (GIK), and the private sector investment rate (IK). We report the OLS estimate of the relevant slope coefficients, Slope, the Newey-West corrected t-statistic, [t], and the adjusted R2 . The sample is quarterly from 1947:2 to 2010:4.

Panel A

Regressors GIK IK

Slope [t] Slope [t] R2

1 0.54 2.15 −0.59 −2.75 11.82

Forecast horizon in quarters 2 4 8 12 1.09 2.24 4.32 6.20 2.19 2.22 2.07 2.07 −1.26 −2.77 −5.43 −7.33 −3.02 −3.49 −3.05 −2.54 19.75 31.33 36.87 36.70

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16 8.31 2.28 −8.34 −2.29 36.90

Table 4 : Government Investment and the Aggregate Risk Premium This table reports the results from long-horizon predictability regressions of the log excess returns on the aggregate stock market index, ΣH h rt+h − rf t+h , in which H is the return forecast horizon in quarters. Each panel reports a different combination of the following regressors: the H-period lagged value of the public sector investment rate (GIK), the private sector investment rate (IK), the real growth rate in public investment (∆GI), the real growth rate in private investment (∆I), the log aggregate dividend-price ratio (DP), and the aggregate consumption surplus (CSPLS). For each regression, we report the OLS estimate of the relevant slope coefficients, Slope, the Newey-West corrected t-statistic, [t], and the adjusted R2 . The sample is quarterly from 1947:2 to 2010:4.

Panel A

Regressors GIK IK

B

∆GI ∆I

C

GIK IK DP CSPLS

Slope [t] Slope [t] R2 Slope [t] Slope [t] R2 Slope [t] Slope [t] Slope [t] Slope [t] R2

Forecast horizon in quarters 1 2 4 8 12 16 1.02 1.81 4.04 6.53 6.98 7.03 2.11 2.01 2.42 1.90 1.46 1.16 −3.80 −7.24 −12.19 −20.51 −31.25 −40.55 −2.73 −2.73 −2.51 −2.69 −4.07 −5.38 3.44 6.04 10.42 16.32 24.67 32.59 0.32 0.15 0.80 0.99 1.38 1.13 2.89 0.77 3.54 2.80 2.82 2.05 −0.31 −0.73 −1.28 −1.15 −1.61 −1.47 −1.56 −2.24 −2.51 −1.78 −2.63 −2.36 1.83 2.02 5.72 3.04 4.81 2.72 Controls: Other Risk Premium Proxies 1.67 2.96 6.43 9.94 10.55 11.28 2.42 2.18 2.83 3.07 2.71 2.86 −1.59 −2.71 −3.24 −6.64 −14.84 −22.01 −1.07 −0.97 −0.72 −0.85 −1.68 −2.88 1.07 2.35 4.68 8.03 9.80 11.00 2.85 3.23 3.89 4.01 4.90 6.58 −0.51 −1.01 −2.13 −3.54 −4.12 −4.77 −2.43 −2.57 −3.30 −3.29 −3.20 −3.87 5.94 11.79 23.47 37.55 47.48 57.75

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Table 5 : Government Investment and the Aggregate Risk Premium across Sub-Samples This table reports the results from long-horizon predictability regressions of the log excess returns on the aggregate stock market index, ΣH h rt+h −rf t+h , in which H is the return forecast horizon in quarters. The regressors are the following: the H-period lagged value of the public sector investment rate (GIK), the private sector investment rate (IK), the aggregate dividend-price ratio (DP), and the surplus consumption ratio (CSPLS). We report the OLS estimate of the relevant slope coefficients, Slope, the Newey-West corrected t-statistic, [t], and the adjusted R2 . The full sample is quarterly from 1947:2 to 2010:4. First half is from 1947:2 to 1980:4 and Second half is from 1981:1 to 2010:4.

18 Regressors GIK IK DP CSPLS

Slope [t] Slope [t] Slope [t] Slope [t] R2

Full Sample Forecast horizon in quarters 1 2 4 8 1.67 2.96 6.43 9.94 2.42 2.18 2.83 3.07 −1.59 −2.71 −3.24 −6.64 −1.07 −0.97 −0.72 −0.85 1.07 2.35 4.68 8.03 2.85 3.23 3.89 4.01 −0.51 −1.01 −2.13 −3.54 −2.43 −2.57 −3.30 −3.29 5.94 11.79 23.47 37.55

First Half Forecast horizon in quarters 1 2 4 8 1.17 1.83 4.80 8.24 1.68 1.38 2.54 3.15 −1.76 −3.05 −1.54 6.95 −0.98 −0.91 −0.32 0.96 0.99 2.40 4.47 10.00 2.01 2.47 3.10 4.55 −0.74 −1.32 −2.94 −4.96 −2.60 −2.74 −3.34 −3.41 9.19 17.69 35.82 56.52

Second Half Forecast horizon in quarters 1 2 4 8 6.11 13.14 26.12 31.32 1.66 1.75 2.27 2.27 −0.30 0.33 1.75 −9.39 −0.11 0.07 0.21 −0.66 2.01 4.70 9.64 12.12 1.69 1.97 2.49 2.78 −0.92 −1.97 −4.13 −7.16 −1.53 −1.80 −2.44 −2.32 1.43 7.08 18.05 29.15

Table 6 : Public Investment Rate, Productivity and Consumption Cash Flow Betas

This table examines the link between the public investment rate and the conditional cash flow productivity (Productivity risk) and consumption (Consumption risk) betas. The table reports the results from the following regressions:
′ Yt = a + b + cGIKt−1 + dZt−1 × ∆TFPt + εt
′ Yt = a + b + cGIKt−1 + dZt−1 × ∆Ct + εt ,

19

in which Yt is either the real growth rate of aggregate dividends (∆Divt ), aggregate profitability (Πt /Kt ), or the aggregate stock market excess returns. The vector Zt−1 is a set of additional macro control variables (Macro Controls), which include the lagged aggregate-level dividend price ratio and the aggregate consumption surplus (the table reports the results with and without these controls). Each regression is performed at quarterly frequency in Panel A, and at annual frequency in Panel B (to avoid possible seasonality problems). To help in the interpretation, all variables are normalized to have mean zero and unit standard deviation. The table reports the OLS estimate of the relevant slope coefficient, the corresponding Newey-West corrected t-statistic, and the adjusted R2 . The sample is from 1947 to 2010. Panel A: Quarterly Frequency ∆Divt Regressors TFPt [t] GIKt−1 ×TFPt [t] R2 Macro Controls?

∆Ct [t] GIKt−1 × ∆Ct [t] R2 Macro Controls?

−0.05 −0.06 −0.66 −0.74 0.10 0.10 1.73 1.69 0.69 2.60 No Yes

0.06 0.52 0.12 1.23 1.80 No

0.08 0.68 0.16 1.88 2.42 Yes

Πt /Kt

0.13 1.75 0.23 2.82 7.44 No

0.10 1.04 0.19 2.48 9.95 Yes

0.13 0.07 0.93 0.50 0.53 0.38 4.56 4.23 32.96 48.12 No Yes

Panel B: Annual Frequency Rte

Πt /Kt

Rte

0.20 2.18 0.25 2.36 4.02 Yes

0.32 0.29 2.80 1.99 0.37 0.32 2.69 2.23 28.26 34.60 No Yes

0.11 0.12 0.82 0.78 0.07 0.06 0.91 0.40 0.49 −1.09 No Yes

Consumption Risk 0.19 0.20 0.29 0.35 2.80 2.66 1.48 1.78 0.01 0.03 0.18 0.23 0.26 0.59 1.21 1.71 3.42 6.25 10.56 15.90 No Yes No Yes

0.39 0.36 5.29 6.40 0.69 0.53 7.19 6.49 66.46 77.59 No Yes

0.04 0.39 0.18 3.03 1.82 No

∆Divt

Productivity Risk 0.13 0.15 0.18 1.73 1.72 1.88 0.02 0.03 0.17 0.41 0.48 2.19 1.42 2.95 5.89 No Yes No

0.14 1.11 0.15 1.79 13.86 Yes

Figure 1 : Inspecting the Mechanism

Coefficient on GIK and IK

The top and middle panels plot the slope coefficients on the public sector investment rate (GIK) and the private sector investment rate (IK) from predictability regressions of one-quarter-ahead excess stock returns, as a function of the public capital curvature parameter α (top panel) and as a function of the correlation between the shocks to GIK and the shocks to xt (middle panel). The bottom panel plots the contemporaneous and cross correlation between GIK and IK as a function of the correlation between the shocks to GIK and the shocks to xt . All the other parameters are the same as in benchmark calibration reported in Table 5 in the main text. .

2

0 −1 −2

Coefficients on GIK and IK

−3

Correlation Between GIK and IK

GIK Coef IK Coef

1

0

0.2 0.4 0.6 0.8 α: Curvature Parameter for Public Capital

1

3 2

GIK coef IK coef

1 0 −1 −2 −1

−0.5 0 0.5 The Correlation Between Shocks to GIK and Shocks to x

1

1 Corr(GIK , IK ) t

0.5

t

Corr(GIK , IK t

)

t+1

0 −0.5 −1 −1

−0.5 0 0.5 The Correlation Between Shocks to GIK and Shocks to x

20

1