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Under the real options approach to investment under uncertainty, agents formulate optimal policies under the assumption that firms’ growth prospects do not vary over time. This paper proposes and solves a model of investment decisions in which the growth rate and volatility of the decision variable shift between different states at random times. A value-maximizing investment policy is derived such that in each regime the firm's investment policy is optimal and recognizes the possibility of a regime shift. Under this policy, investment is intermittent and increases with marginal q. Moreover, investment typically is very small but, in some states, the capital stock jumps. Implications for marginal q and the user cost of capital are also examined.

The notion that regime shifts are important in explaining the cyclical features of real macroeconomic variables as proposed by Hamilton [15] is noww idely accepted. Motivated by anecdotal evidence, a pervasive manifestation of this viewis that regime shifts, by changing firms growth prospects, affect capital accumulation and investment decisions. On economic grounds, there are indeed reasons to believe that regime shifts contain the possibility of significant impact on firms policy choices. For example, business cycle expansion and contraction ‘‘regimes’’ potentially have sizable effects on the profitability or riskiness of investment and, hence, on firms’ willingness to invest in physical or human capital. Yet, despite these potential effects, we still know very little about the relation between regime shifts and investment decisions. The idea that shifts in a firm’s environment can have first-order effects on its investment policy can be related to the burgeoning literature on investment decisions under uncertainty (see the survey by Dixit and Pindyck [9]). In this literature, investment opportunities are analyzed as options written on real assets and the optimal investment policy is derived by maximizing the value of the option to invest. Because option values depend on the riskiness of the underlying asset, volatility is an important determinant of the optimal investment policy. Despite this observation, models of investment decisions typically presume that this very parameter is fixed. It is not difficult to imagine however that as volatility changes over the business cycle, so does the value-maximizing investment policy. This paper develops a framework to study the behavior of investment when the dynamics of the decision variable are subject to discrete regime shifts at random times. Following Hamilton, we define shifts in regime for a process as ‘‘episodes across which the behavior of the series is markedly different’’. To emphasize the impact of regime shifts on investment decisions and capital accumulation, we construct a simple model of capacity choice that builds on earlier work by Pindyck [26] and Abel and Eberly [3]. Specifically, we consider an infinitely lived firm that produces output with its capital stock and variable factors of production. The price of the firm’s output fluctuates randomly, yielding a stochastic continuous stream of cash flows. At any time t; the firm can (irreversibly) increase capacity by purchasing capital. Investment arises when the marginal valuation of capital equals the purchase price of capital. Models of investment decisions under uncertainty generally presume that the firm’s operating profits are subject to a multiplicative shock that evolves according to a geometric Brownian motion.1 Implicit in this modeling is the assumption that the firm’s growth prospects do not vary over time. This paper solves for the valuemaximizing investment policy when the growth rate and volatility of the marginal revenue product of capital are subject to discrete regime shifts. The analysis demonstrates that, in contrast with standard models of investment, the optimal decision rule is not described by a simple threshold for the marginal revenue product of capital. Instead, the optimal investment policy is characterized by a different threshold for each regime. Moreover, because of the possibility of a regime shift, the value-maximizing threshold in each regime reflects the possibility for the firm to invest in the other regimes. That is, a value-maximizing policy is derived such that in each regime the firm’s investment policy is optimal, conditional on the optimal investment policy in the other regimes. An important question is whether regime shifts actually affect growth and capital accumulation. To answer this question, we examine the implications of the model for the optimal rate of investment. These implications are generally consistent with recent evidence on firms’ investment behavior (see [1] or [7]). In particular, the model predicts that investment is intermittent and increasing with marginal q: Moreover, the state space of the dynamic investment problem can be partitioned into various domains including an inaction region where no investment occurs. Outside of this region, the optimal rate of investment can be in one of two regimes: infinitesimal or lumpy. Investment is infinitesimal at the investment threshold. Investment is lumpy in the transient region and at the initial date if the state of the system is in the action region. Also, while it is always optimal to invest in the action region, the optimality of investment is regime dependent in the transient region. That is, regime shifts generate some time-series variation in the present value of future cash flows to current cash flows that may induce the firm to invest following a regime shift. The analysis in the present paper relates to two different strands of literature. First, from an economic point of view, it relates to the investment literature that combines real options features—irreversibility and a continuous stochastic process— with neoclassical features—no indivisibilities. In these models, investment is intermittent and, in the absence of fixed adjustment costs, involves marginal adjustments in the stock of capital (see [26,2,6,13]). When fixed adjustment costs are introduced, investment is intermittent and lumpy, and the optimal policy involves impulse control techniques (see [4] or [7]). In the present paper, there are no fixed adjustment costs. Yet, the optimal investment policy involves both marginal adjustments and jumps in the stock of capital. From a technical viewpoint, the present paper relates to a series of recent papers on option pricing with regime shifts (see [15,16,10]). One of our main contributions is the extension of techniques in these papers to the case of stochastic control problems where control policies change the underlying diffusion process. In particular, we use the solution to the optimal stopping problem derived by Guo [15] to analyze the recurrent investment decision of a firm with divisible capital. Because the firm’s problem is homogeneous, the recurrent model displays a structure that is similar to the stopping problem except that the firm obtains a newinvest ment option whenever it stops.The paper that is most closely related to the present analysis is Driffill and Sola [11]. These authors also analyze investment decisions when the dynamics of the state variable can shift between several regimes. One essential difference between the two papers is that we examine capacity choice and the valuation of interrelated options whereas they focus on the valuation of a single investment opportunity (in the spirit of McDonald and Siegel [24]). Another important point of departure is that we solve our model analytically whereas they solve their model numerically. Finally, we derive implications for capital accumulation, marginal q; and the user cost of capital, which are not examined in their paper. The remainder of the paper is organized as follows. Section 2 presents the basic model of investment decisions with regime shifts. Section 3 derives the firm’s objective function and optimality conditions. Section 4 determines the valuemaximizing investment policy. Section 5 presents simulation results. Section 6 investigates the implications of the optimal investment policy for capital accumulation and growth. Section 7 analyses marginal q and the user cost of capital. Section 8 concludes.

This paper has analyzed investment decisions under uncertainty when the dynamics of the decision variable—growth rate and diffusion coefficient—shift between different states at random times. The main analytical result of the paper is that the value-maximizing investment policy is such that in each regime the firm’s investment policy is optimal, conditional on the optimal investment policy in the other regimes. This optimal investment policy is characterized by a different investment curve for each regime. Moreover, because of the possibility of a regime shift, the investment curve in each regime reflects the possibility for the firm to invest in the other regime. To determine the implications of the model for investment decisions and capital accumulation, we showed that the state space of the dynamic investment problem can be partitioned into various domains including an inaction region where no investment occurs. Outside of this region, the optimal rate of investment can be in one of two regimes: infinitesimal or lumpy. Investment is infinitesimal following an increase of the firm cash flows in a given regime. Investment is lumpy following a shift from the regime with the highest investment curve to the regime with the lowest one. That is, the model predicts that with irreversibility and regime shifts investment is intermittent and increases with marginal q: Moreover, the optimal rate of investment typically is very small but occasionally exhibits some spurts of capacity expansion. These predictions are generally consistent with the available empirical evidence on firms’ investment behavior (see [7] or [1]). The paper also provided an analysis of the determinants of marginal q and the user cost of capital in such an environment.