The Effects of Irreversibility and Uncertainty on Capital Accumulation

When investment decisions cannot be reversed and returns to capital are uncertain, the firm faces a higher user cost of capital than if it could reverse its decisions. This higher user cost tends to reduce the firm's capital stock. Opposing this effect is the irreversibility constraint itself: when the constraint binds, the firm would like to sell capital but cannot. This effect tends to increase the firm's capital stock. We show that a firm with irreversible investment may have a higher or a lower expected capital stock, even in the long run, compared to an otherwise identical firm with reversible investment. Furthermore, an increase in uncertainty can either increase or decrease the expected long-run capital stock under irreversibility relative to that under reversibility. However, changes in the expected growth rate of demand, the interest rate, the capital share in output, and the price elasticity of demand all have unambiguous effects.

A Unified Model of Investment Under Uncertainty

This paper extends the theory of investment under uncertainty to incorporate fixed costs of investment, a wedge between the purchase price and sale price of capital, and potential irreversibility of investment. In this extended framework, investment is a non-decreasing function of q, the shadow price of installed capital. There are potentially three investment regimes, which depend on the value of q relative to two critical values. For values of q above the upper critical value, investment is positive and is an increasing function of q, as is standard in the theory branch of the adjustment cost literature. For intermediate values of q, between two critical values, investment is zero. Although this regime features prominently in the irreversibility literature, it is largely ignored in the adjustment cost literature. Finally, if q is below the lower critical value, gross investment is negative, a possibility that is ruled out by assumption in the irreversibility of literature. In general, however, the shadow price q is not directly observable, so we present two examples relating q to observable varieties.

Q Theory Without Adjustment Costs & Cash Flow Effects Without Financing Constraints

Tobin's Q exceeds one, even without any adjustment costs, for a firm that earns rents as a result of monopoly power or of decreasing returns to scale in production. Even when there are no adjustment costs and marginal Q is always equal to one, Tobin's Q is informative about the firm's growth prospects. We show that investment is positively related to Tobin's Q (which is observable average Q). This effect can be quantitatively small, which has been taken as evidence of very high adjustment costs in the empirical literature, but here is consistent with no adjustment costs at all. In addition, cash flow has a positive effect on investment, and this effect is larger for smaller, faster growing and more volatile firms, even though capital markets are perfect. These results provide a new theoretical foundation for Q theory and also cast doubt on evidence of financing constraints based on cash flow effects on investmentQ Theory, Cash Flow, Investment

A Unified Model of Investment Under Uncertainty

This paper extends the theory of investment under uncertainty to incorporate fixed costs of investment, a wedge between the purchase price and sale price of capital, and potential irreversibility of investment. In this extended framework, investment is a non-decreasing function of q, the shadow price of installed capital. There are potentially three investment regimes, which depend on the value of q relative to two critical values. For values of q above the upper critical value, investment is positive and is an increasing function of q, as is standard in the theory branch of the adjustment cost literature. For intermediate values of q, between two critical values, investment is zero. Although this regime features prominently in the irreversibility literature, it is largely ignored in the adjustment cost literature. Finally, if q is below the lower critical value, gross investment is negative, a possibility that is ruled out by assumption in the irreversibility of literature. In general, however, the shadow price q is not directly observable, so we present two examples relating q to observable varieties

An Exact Solution for the Investment and Market Value of Firm Facing Uncertainty, Adjustment Costs, and Irreversibility

This paper derives closed-form solutions for the investment and value of a competitive firm with a constant-returns-to-scale production function and convex costs of adjustment. Solutions are derived for the case of irreversible investment as well as for reversible investment. Optimal investment is a non-decreasing function of q, the shadow value of capital. Relative to the case of reversible investment, the introduction of irreversibility does not affect q, but it reduces the fundamental value of the firm

The Mix and Scale of Factors with Irreversibility and Fixed Costs of Investment

When factors of production can be adjusted costlessly, the mix of factors can be considered separately from their scale. We examine factor choice and utilization when investment is irreversible and subject to a fixed cost, so that the capital stock is a quasi-fixed factor that is adjusted infrequently and by discrete amounts. We derive and analyze analytic approximations for optimal investment behavior, and show how the quasi-fixity of capital eliminates the dichotomy between factor mix and scale. We show that the quasi-fixity of capital can give rise to labor hoarding, even when labor is a purely flexible factor

Optimal Investment with Costly Reversibility

Investment is characterized by costly reversibility when a firm can purchase capital at a given price and sell capital at a lower price. We derive an explicit analytic solution for optimal investment by a firm facing costly reversibility. In addition, we derive a local approximation to the solution which highlights the effects of the parameters of the problem on the triggers for investment. More generally, we extend the Jorgensonian concept of the user cost of capital to the case of uncertainty and define cU and cL as the user costs of capital associated with the purchase and sale of capital, respectively. Optimality requires the" firm to purchase and sell capital as needed to keep the marginal revenue product of capital in" the closed interval [cU,cL]. This prescription encompasses the case of irreversible investment as well as the standard" neoclassical case of costlessly reversible investment. Finally, quantitative analysis suggests" that even when the difference between the purchase and sale prices of capital is small user costs associated with purchasing and selling capital are closer to those applicable under" complete irreversibility than to those applicable under costless reversibility."

Optimal Inattention to the Stock Market with Information Costs and Transactions Costs

Recurrent intervals of inattention to the stock market are optimal if consumers incur a utility cost to observe asset values. When consumers observe the value of their wealth, they decide whether to transfer funds between a transactions account from which consumption must be financed and an investment portfolio of equity and riskless bonds. Transfers of funds are subject to a transactions cost that reduces wealth and consists of two components: one is proportional to the amount of assets transferred, and the other is a fixed resource cost. Because it is costly to transfer funds, the consumer may choose not to transfer any funds on a particular observation date. In general, the optimal adjustment rule---including the size and direction of transfers, and the time of the next observation---is state-dependent. Surprisingly, unless the fixed resource cost of transferring funds is large, the consumer's optimal behavior eventually evolves to a situation with a purely time-dependent rule with a constant interval of time between observations. This interval of time can be substantial even for tiny observation costs. When this situation is attained, the standard consumption Euler equation holds between observation dates if the consumer is sufficiently risk averse.