ریسک گریزی، جایگزینی موقتی، و رابطه سرمایه گذاری کل - عدم قطعیت

We analyze the role of risk aversion and intertemporal substitution in a simple dynamic general equilibrium model of investment and savings. Our main finding is that risk aversion cannot by itself explain a negative relationship between aggregate investment and aggregate uncertainty, as the effect of increased uncertainty on investment also depends on the intertemporal elasticity of substitution. In particular, the relationship between aggregate investment and aggregate uncertainty is positive even if agents are very risk averse, as long as the elasticity of intertemporal substitution is low. A negative investment–uncertainty relationship requires that the relative risk aversion and the elasticity of intertemporal substitution are both relatively high or both relatively low. We also show that the implications of our model are consistent with the available empirical evidence.

Economic theory has been analyzing the effect of uncertainty on investment for more than 40 years. One seminal strand of the literature starts with Oi (1961), followed by Hartman (1972) and Abel (1983). They show that, in a perfectly competitive environment, an increase in output-price uncertainty raises the investment of a risk-neutral firm with a constant returns to scale technology. Intuitively, this is because constant returns to scale imply that the marginal revenue product of capital rises more than proportionally with the output price when firms can adjust employment after uncertainty is resolved. Hence, the marginal revenue product of capital is convex in the output price and, by Jensen's inequality, greater price variability translates into a higher expected return to capital and higher investment. This theoretical conclusion has been contradicted by empirical research as no study has found a positive investment–uncertainty correlation; estimates range from negative to zero. Most of the empirical evidence is about the relationship between investment and uncertainty at the aggregate level. Many studies are based either on country data (see Ramey and Ramey, 1995, Aizenman and Marion, 1999, Pindyck and Solimano, 1993, Calcagnini and Saltari, 2000 and Alesina and Perotti, 1996) or on highly aggregated data (see Huizinga, 1993; Ferderer, 1993a and Ferderer, 1993b). Only Leahy and Whited (1996), Guiso and Parigi (1999) and Bloom et al. (2005) do empirical work at the micro level. Investment irreversibility has been one of the first elements considered by economic theory to explain the negative effect of uncertainty on investment. Bernanke (1983), McDonald and Siegel (1986), Pindyck (1988) and Bertola (1988) show that, if the firm cannot resell its capital goods, then the optimal investment policy derived under reversibility, equalization of the marginal revenue product of capital and the Jorgensonian user cost of capital (Jorgenson, 1963), does not hold anymore. In particular, if investment is irreversible, the firm invests only when the marginal revenue product of capital is higher than a threshold that exceeds the Jorgensonian user cost of capital because the firm takes into account that the irreversibility constraint may be binding in the following periods. The difference between this threshold and the Jorgensonian user cost of capital represents the value of the option of investing in the future. A higher degree of uncertainty implies a higher threshold for investing since the value of the option is always increasing in the variance of the stochastic variable. The higher threshold for investing under irreversibility does not necessarily translates into lower investment however. For this to happen, two additional conditions must be satisfied. The first condition, highlighted by Caballero (1991), Pindyck (1993) and Abel and Eberly (1997), is that the marginal revenue product of capital is a decreasing function of the capital stock, i.e. that the firm operates under imperfect competition and/or decreasing returns to scale.1 Under perfect competition and constant returns to scale the marginal revenue product of capital is independent of the capital stock so that current investment does not affect the current and future marginal profitability of capital, which implies that investment irreversibility does not change optimal investment. The second condition required for the higher threshold for investing under irreversibility to generate lower investment is that the current capital of the firm is zero, which would be the case for a firm just getting started. This condition has been noted by Abel and Eberly (1999) who analyze the effect of irreversibility and uncertainty on the long-run capital stock (so that capital must be positive). They show that irreversibility and uncertainty have two effects on investment. One is the increase in the user cost of capital described above that tends to reduce the capital stock compared to the case with reversibility. But there is also a hangover effect, which implies a higher capital stock under irreversibility than under reversibility because investment irreversibility prevents the firm from selling capital when the marginal revenue product of capital is low. Abel and Eberly demonstrate that neither of the two effects dominates globally, so that irreversibility may increase or decrease capital accumulation in the long-run. Higher uncertainty reinforces both the user cost effect and the hangover effect and, therefore, does not help in obtaining an unambiguous result. If the firm has zero capital stock, the hangover effect is inoperative and the user cost effect is the only effect at work, which implies that an increase in uncertainty with investment irreversibility always lower the level of capital stock compared to the case with reversibility. It is also worthwhile noticing that the works with adjustment costs and irreversibility use partial equilibrium models with an exogenous risk-free interest rate so that it is not clear whether the results of these papers are about sectoral investment or aggregate investment. To obtain a robust negative relationship between investment and uncertainty, economic theory has taken into consideration the role of risk aversion in general equilibrium frameworks, so incorporating the role of savings into the model. Craine (1989) uses a model with many sectors and risk averse households to show that an increase in exogenous risk in one sector may lead, under some conditions, to capital being reallocated toward less risky sectors. Zeira (1990) makes a similar point in a model where sectors differ in the intensity of capital and labor used. He shows that, in some cases, higher labor cost uncertainty may shift capital from labor intensive sectors toward less risky, capital intensive, sectors. Even though Craine and Zeira use general equilibrium models, they both concentrate on the effect of uncertainty on the reallocation of savings and investment across sectors and in their work there is no effect of uncertainty on aggregate savings/investment.2 Our goal here is instead to analyze the effect of an increase in aggregate, and hence non-diversifiable, uncertainty on aggregate equilibrium investment when agents are risk averse. Therefore, we propose a dynamic general equilibrium model where households are risk averse and firms are subject to aggregate exogenous shocks. This setting allows us to focus on the effect of aggregate uncertainty on aggregate investment instead of the effect of uncertainty on the distribution of investment across sectors as analyzed in Craine (1989) or Zeira (1990). A key feature of our model is that we use Kreps–Porteus nonexpected utility preferences (recursive preferences) in order to separate the role of risk aversion from that of intertemporal substitution. As is well-known, the conventional expected utility set up with constant relative risk aversion (CRRA) preferences makes it impossible to separate the role of these two parameters. We show that risk aversion cannot by itself explain a negative relationship between investment and uncertainty at the aggregate level as the effect of increased uncertainty on investment also depends on the intertemporal elasticity of substitution. For example, we show that if the elasticity of intertemporal substitution is low, then an increase in aggregate uncertainty has a positive effect on aggregate investment even if risk aversion is very high. If the elasticity of intertemporal substitution is high, however, then even small degrees of risk aversion imply a negative investment–uncertainty relationship. Intuitively, in a dynamic framework, a high degree of risk aversion reduces the certainty equivalent of the return to capital. This does not necessarily lower investment however. The reason is that a lower rate of return to capital generates a substitution effect and an income effect affecting aggregate savings and, therefore, aggregate investment in opposite directions. The substitution effect reduces aggregate savings and investment while the income effect increases aggregate savings/investment. The relative strength of these two effects is determined by the elasticity of intertemporal substitution. If the elasticity of substitution is lower than unity, the income effect dominates and the equilibrium investment increases as a result of increased uncertainty. The opposite happens if the elasticity of substitution is greater than unity. We characterize the aggregate investment–uncertainty relationship for all possible parameter values of the Kreps–Porteus nonexpected utility preferences as well as for the standard CRRA expected utility preferences (which are a special case of the recursive preferences). We show that the relationship is generally ambiguous and depends on the value of technological and preference parameters. A negative relationship between aggregate investment and aggregate uncertainty requires that the relative risk aversion and the elasticity of intertemporal substitution are both relatively high or both relatively low. If this is not the case, the relationship is positive. With CRRA preferences the region of the parameter values where the relationship is negative is generally small and the fact that the elasticity of intertemporal substitution is the inverse of the coefficient of relative risk aversion implies that high values of risk aversion always lead to a positive correlation between aggregate investment and aggregate uncertainty.3 We also study the investment–uncertainty relationship implied by empirically plausible values of the relative risk aversion and the elasticity of intertemporal substitution and find that the wide range of estimates available in the literature implies that our model is compatible with a negative, positive, or no relationship between aggregate investment and aggregate uncertainty. Our results therefore suggest that risk aversion, as well as irreversibility, is not enough to generate a theoretically robust negative investment–uncertainty relationship. Indeed, even though increased uncertainty in one sector may reduce investment in that sector, the same needs not to be true at the aggregate level as the effect of uncertainty on aggregate savings/investment is different than the effect of uncertainty on the allocation of savings and investment across sectors. The paper is organized as follows. Section 2 presents the model with recursive preferences and analyzes the relationship between aggregate uncertainty and aggregate investment for all possible values of the coefficients of relative risk aversion and intertemporal substitution elasticity. Section 3 relates the implications of the model to the evidence on the investment–uncertainty relationship. Section 4 concludes. Detailed proofs of the main propositions and an extension of the baseline model can be found in the Appendix.

This paper has analyzed the relationship between aggregate investment and aggregate uncertainty when agents are risk averse. We have demonstrated that risk aversion does not necessarily imply a negative aggregate investment–uncertainty relationship. This is somewhat surprising as the existing literature appears to take for granted that the effect of increased uncertainty on investment is negative if agents are risk averse. We have clarified that the difference in the results is explained by the fact that the existing literature has analyzed the role of risk aversion in the investment–uncertainty relationship at the sectoral level while our work do it at the aggregate level. Using recursive preferences, we show that understanding the effect of uncertainty on aggregate investment requires to separate the role of risk aversion from the role of intertemporal substitution. This allows us also to explain why the effect of uncertainty on aggregate investment can be positive even when agents are very risk averse. In particular, we find that a low elasticity of intertemporal substitution leads to a positive association between investment and uncertainty even if (or, better, especially if) agents are very risk averse. A negative relationship between aggregate investment and aggregate uncertainty requires that the relative risk aversion and the elasticity of intertemporal substitution are both relatively high or both relatively low. This result also clarifies why high levels of risk aversion always give rise to a positive aggregate investment–uncertainty relationship when preferences display CRRA. Solving the dynamic investment problem analytically has required making simplifying assumptions, but it is not evident (as we have shown for the case of partial capital depreciation) that these assumptions drive our results. Still it would be interesting in future research to apply numerical solution methods to a more general version of the framework proposed in this paper.