اولویت های فردی و اثر عدم قطعیت بر سرمایه گذاری غیر قابل برگشت

This paper considers a relationship between investment behavior and an agent’s preferences in a stochastic one-sector growth model with irreversible investment. Further, it explores the effect of uncertainty in investment policies by using a non-expected utility function. Since uncertainty has an impact on investment policies not only through an option value but also through a risk-adjusted time preference rate in a general equilibrium framework, it is significant to distinguish the two preference parameters of the agent. While the previous partial equilibrium models with irreversible investment have exhibited a negative relationship between the desired capital stock and uncertainty, this paper implies that it is possible to generate a positive relationship for the appropriate parameters. This shows that the results of Hartman and Abel have been robust even in a general equilibrium model.

This paper considers a relationship between investment policies and an agent’s preferences in a stochastic one-sector growth model with irreversible investment. In particular, we focus on investment policies in a general equilibrium framework. The main objective of this paper is to examine the impact of uncertainty in investment behavior in a general equilibrium model with irreversible investment. Pommeret (2002) shows that uncertainty affects the optimal decision of irreversible investment through two transmission channels in a general equilibrium framework: one is an option value, and the other is agent’s preferences. However, he does not distinguish the effect of the two preference parameters of the agent because he adopts the constant relative risk aversion (CRRA) utility function. We analyze the effect of uncertainty in investment policies by using a non-expected utility function by Epstein–Zin/Kreps–Porteus, which enables us to shed light on the relationship between irreversible investment and uncertainty in a general equilibrium framework. Let us consider the previous literature regarding the relationships between uncertainty and irreversible investment. Arrow (1968) has been an early and prominent publication introducing the concept of irreversibility.1 Once investments are undertaken and capital equipment is built by a firm, it may be difficult to recover the investment costs and break down the equipment even if the firm desires to withdraw from the enterprise later. In other words, there exist sunk costs; thereby, investments contain the characteristic of irreversibility. Hartman (1972) has shown that increased output price uncertainty leads to a competitive risk-neutral firm, which faces convex adjustment costs to increase its investment in a discrete-time dynamic model without irreversibility. Abel (1983) has verified that the result of Hartman (1972) also holds by using a continuous-time setting in which price follows a geometric Brownian motion with mean zero. These Hartman–Abel paradoxical results, wherein investment increases as uncertainty increases, are interesting and probably against our common sense; however, they are robust since the profit function is convex for output price. In reality, Ferderer (1993) and Leahy and Whited (1996) have found empirical evidence for the negative relationship between investment and uncertainty, considering the partial equilibrium model with irreversibility or the industry equilibrium model with irreversibility. Recently, there have been numerous papers on a partial equilibrium model with irreversible investment. McDonald and Siegel (1986) is a seminal paper that introduces irreversibility into the partial equilibrium model of a firm, studying an optimal timing of one-time-only investment in an irreversible project by means of the optimal stopping of dynamic programming. They have shown that in the case of reasonable parameter values, it is optimal to wait until the benefits are twice the investment costs. Pindyck (1988) has applied the option pricing technique to incremental investments and capacity choices. In general, it is believed that uncertainty causes firms to decrease investments in the partial equilibrium model with irreversibility.2 In contrast, with regard to general equilibrium literature with irreversibility,3 there exist few papers. A general equilibrium approach to irreversible investment is not new [a paper by Dumas (1989) is usually credited for being the first such study; since then, other studies have adopted a similar approach]. However, the research on irreversible investment has developed mostly by using a partial or industry-level equilibrium approach. Faig (2001) has provided analytical results that explain the contrast between the consequences of investment irreversibility for individual firms and those of irreversibility on the effective wealth of consumers and the return on assets. Faig (2001) has also shown that as long as the intertemporal elasticity of substitution is realistically low (less than one), the investment irreversibility not only prevents capital destruction but also induces capital creation. However, Faig (2001) has not considered the effect of uncertainty in the capital stock in terms of long-run periods. While our paper considers a persistent macroeconomic uncertainty, Gilchrist and Williams (2000) have exhibited a general equilibrium model with a non-persistent idiosyncratic shock and irreversible investment. In such a model, uncertainty reduces the idiosyncratic investments but encourages aggregate investments. In Faig (2001) and Gilchrist and Williams (2000), although uncertainty reduces investments at the firm level, it increases investment at the entire economy level. This result is achieved by assuming that shocks are transitory. After all, even today, the situation is such that the effect of uncertainty in investments is ambiguous in a general equilibrium framework with irreversible investment. A major portion of the papers pertaining to a general equilibrium framework with irreversible investment applies to numerical analysis and simulation techniques.4 Kogan (2001) has proposed a general equilibrium model of a two-sector production economy with irreversible investment. He implies that the relationship between uncertainty and capital stock is ambiguous. Hugonnier et al. (2005) show that the general equilibrium feedback effects of lumpy investments on optimal consumption decisions can erode the option value of waiting even for moderate levels of risk aversion. This paper considers a relationship between investment behavior and an agent’s preferences in a stochastic one-sector growth model with irreversible investment. We focus on the characteristics regarding investment policies that are determined endogenously within our model. Moreover, this paper explores the effect of uncertainty in investment policies. We develop the model with irreversible investment on the basis of Pommeret (2002). Unlike Pommeret (2002), we adopt a non-expected utility function of the Epstein–Zin/Kreps–Porteus type–the utility function of a continuous-time version used by Obstfeld (1994), which can isolate relative risk aversion from an intertemporal elasticity of substitution. Uncertainty affects the optimal decision through two different transmission channels. One is irreversibility, and the other is agent’s preference. The combination of irreversibility and uncertainty generates the value of waiting to invest (McDonald and Siegel, 1986). The irreversible investment opportunity is similar to the financial call option. Since an economy is stochastic, an agent may prefer to wait for new information before committing to investment. Meanwhile, in the case of the consumption/saving trade-off, there exists a concept of precautionary saving (Kimball, 1990), which is linked to risk aversion. Considering the portfolio choice and consumption/saving model (Merton, 1971), uncertainty will favor savings as soon as the relative risk aversion coefficient is greater than unity. The effect of uncertainty in investment policy depends on the intertemporal elasticity of substitution as well as on the relative risk aversion. Since uncertainty impacts investment policy not only through an option value but also through a risk-adjusted time preference rate in a general equilibrium framework, it is significant to distinguish the two preference parameters of the agent. While the previous partial equilibrium models with irreversible investment have exhibited a negative relationship between uncertainty and the desired capital stock, this paper implies that it is possible to generate a positive relationship. In other words, we show that extending the analysis to a general equilibrium framework may reverse the relationship, which results from partial equilibrium models with irreversibility. If the effect of uncertainty through a risk-adjusted time preference dominates the effect of uncertainty through an option value, there exists a positive relationship between uncertainty and the desired capital stock. The empirical literature mention that the relative risk aversion parameters may be approximately from four to eight. This paper shows that the results of Hartman (1972) and Abel (1983) have been robust under the appropriate parameters of an intertemporal elasticity of substitution even in a general equilibrium model. The remainder of the paper is organized as follows. Section 2 is the model. Section 2.1 exhibits a model setup; in this subsection, we derive the value of the program when there is no investment. In Section 2.3, by comparing the various current and expected gains and losses in this value that are generated by the marginal investment, we can obtain the investment policy function. In other words, the investment decision should be the result of an arbitrage between increasing the expected intertemporal utility through future cash flows and decreasing the expected intertemporal utility through current consumption. Section 2.4 explains the barrier control curve and investment policies. Section 2.5 analyzes the effect of uncertainty in investment policies; Section 2.6 summarizes the results of Section 2.5. Section 2.7 summarizes the effect of uncertainty in the desired capital stock. Section 2.8 exhibits numerical examples showing that it is possible to generate a positive relationship between the desired capital stock and uncertainty. Section 3 concludes the paper.

This paper considers a relationship between investment behavior and an agent’s preferences in a stochastic one-sector model with irreversible investment. Mainly, we have focused on investment policies. First, we have analyzed the characteristics of investment policies, considering the agent’s two preference parameters: a relative risk aversion and an intertemporal elasticity of substitution. Second, we have examined the impact of uncertainty in investment policies. Pommeret (2002) has shown that uncertainty affects the optimal decision of irreversible investment through two transmission channels: One is an option value, and the other is an agent’s preferences. In the first case, the larger uncertainty increases the option value to invest, which causes the agent to have a tendency toward waiting to invest currently. In the latter case, uncertainty affects the rate at which the sum of the instantaneous utilities is discounted. Since Pommeret (2002) has used a CRRA utility function, he has not distinguished the agent’s two preference parameters. We have analyzed the effect of uncertainty in investment policies and the desired capital stock by using a non-expected utility function, which can separate the relative risk aversion from the intertemporal elasticity of substitution. The impact of uncertainty in investment behavior depends on both the relative risk aversion as well as the intertemporal elasticity of substitution. Since uncertainty impacts investment policies not only through the option value but also through the risk-adjusted time preference in a general equilibrium framework, it is crucial to distinguish the agent’s two preference parameters. The previous partial equilibrium models with irreversible investment have exhibited a negative relationship between uncertainty and the desired capital stock. However, this paper has shown that it is possible to generate a positive relationship between the two when a relative risk aversion coefficient is more than one and an intertemporal elasticity of substitution is less than a share of energy input or more than one. Therefore, we show that the results of Hartman (1972) and Abel (1983) are robust even in a general equilibrium model when the intertemporal elasticity of substitution is more than one. This paper has presented and solved a model with irreversible investment, claiming two contributions. First, the study uses a non-expected utility function to disentangle the impact of uncertainty in investment through its effects on the “option value” of investment and “time preference”. While non-expected utility functions have been used widely in the literature, one may not be aware of any research with respect to studying their interaction with investment irreversibility. In this sense, this is a kind of an innovation in this line of research. Second, the paper solves a general equilibrium model with irreversible investment, as a necessary by-product to examine the impact of non-expected utility on investment. Although a general equilibrium approach to irreversible investment is not new [for instance, Dumas (1989) is usually credited for being the first to conduct such a study], the research on irreversible investment has developed largely by using a partial or industry-level equilibrium approach. These two twists of the standard irreversible investment problem yield a prediction unlike that of a majority of (though not all) previous studies in this field, whereby increased uncertainty regarding the future impacts investment in a negative manner. In the model presented in this paper, increased uncertainty impacts investment in an ambiguous manner, as the effects of the relative strength of the “option value” and “time preference” on investment varies across parameters values. In the case of some parametric ranges, increased uncertainty strengthens an agent’s preference for future consumption to the point that the agent becomes more willing to invest immediately, despite the rising option value of investing. It may be argued that there exist sufficient studies offering reasons for the ambiguous impact of uncertainty in investment. However, readers interested in the intimate working of irreversible investment models may find it useful to know that some of the implications of simpler models are not robust to allow for non-standard utility functions. Since it is a non-expected utility function that is more general and more universalistic than the expected utility function of von Neumann–Morgenstern or the CRRA utility function, it is the prediction of our model that represents more general and universalistic results because of the following two ingredients. First, the wedge between the risk aversion and the inverse of intertemporal elasticity of substitution are broken down; second, not only the option value but also the risk-adjusted time preference has different and conflicting effects on the investment behavior in a general equilibrium framework. The solution method in our model is to solve from the viewpoint of a benevolent central planner. It would be useful to note whether such equilibrium can be decentralized by an equilibrium set of prices. Recall that the fundamental structure of our model is similar to that of the RBC model, whereby the decrease in the exogenous energy price in our model corresponds to the positive technological shock in the RBC model. A large part of the RBC model can be solved from the viewpoint of a benevolent central planner, since the fundamental theorems of welfare economics hold. However, it is necessary to strictly verify whether or not the equilibrium of the central planner can be decentralized by a competitive equilibrium set of prices in a general equilibrium model with irreversible investment by means of adopting an option value technique. Merely for the purpose of reference, Van and Vailakis (2003) prove the existence of a competitive equilibrium in a version of one-sector model in which the agents are heterogeneous and gross investment is constrained to be non-negative. This model is not exactly a real business cycle model because the labor supply is not endogenous. However, an increase in the energy price in this model corresponds to the negative real shock in an RBC model. Therefore, it is fair to say that this paper has examined almost analytically the characteristics of investment behavior in an RBC model with irreversible investment. A fairly important caveat to the analysis is that the study does not, strictly speaking, offer conditions for which the economy will operate with a higher stock of capital in equilibrium. Technically, the model studies the impact of uncertainty in the level of the state variable (the energy price) that triggers new investment. A higher trigger implies more reluctance to invest; however, it does not automatically imply an average lower equilibrium capital stock, as the agent will often be stuck with a higher-than-desired stock. The relevant concept in this case is actual (equilibrium) capital stock, not desired (shadow) capital stock–with irreversibility, the actual capital will often exceed the desired capital. In order to mitigate such a potential regret, an investor facing irreversibility will be more reluctant to invest but will not completely eliminate the risk of investing a large amount. A complete analysis of the dynamic general equilibrium model with irreversible investment by means of the option value techniques requires computing the unconditional expectation of the capital stock using its ergodic distribution, 5 which would be well-characterized in this type of one-barrier stochastic control problems. It is an issue to be discussed in the future.