The Analytics of Investment , , and Cash Flow ∗

This paper analyzes the relationships among investment, , and cash flow in a tractable stochastic model in which marginal  and average  are identically equal. In the special, but widely used, case of quadratic adjustment costs, it derives an expression for  that is in closed form, up to an additive constant. After analyzing the impact of changes in the distribution of the marginal operating profit of capital, the paper extends the model to include measurement error and then analyzes the cash flow coefficient in regressions of investment on  and cash flow. The coefficient on cash flow is typically estimated to be positive and to be larger for firms, such as rapidly growing firms, that are likely to face financial frictions. These findings are typically interpreted as evidence of financial frictions facing the firm. This paper derives closed-form expressions for the cash flow coefficient in the model presented here and shows that it is positive and is larger for more rapidly growing firms, even though there are no financial frictions in the model. ∗I thank Joao Gomes, Richard Kihlstrom, and Stavros Panageas for helpful discussion, Colin Ward for excellent research assistance, and participants in seminars at University of California at Santa Barbara, University of Southern California, Columbia University, and the Penn Macro Lunch Group for helpful comments. Empirical investment equations typically find that Tobin’s  has a positive effect on capital investment by firms, and that even after taking account of the effect of Tobin’s  on investment, cash flow has a positive effect on investment. Of course, the intepretations of these results rely on some theoretical model of investment. Typically, the theoretical model that underlies the relationship between Tobin’s  and investment is based on convex capital adjustment costs.1 In this framework, marginal  is a sufficient statistic for investment. No other variables, in particular, cash flow, should have any explanatory power for investment, once account is taken of marginal . The fact that cash flow has a positive impact on investment, even after taking account of , is interpreted by many researchers as evidence of financing constraints facing firms. That interpretation is bolstered by the finding that the cash flow coefficient is larger for firms that are likely to be financially constrained, such as rapidly growing firms. In this paper, I develop and analyze a tractable stochastic model of investment, , and cash flow and use it to interpret the empirical results described above. In modeling adjustment costs, the first choice is whether to specify these costs as a function of investment only (usually either gross investment or net investment) or to specify these costs as a function of the capital stock as well as of investment. The former specification is more tractable and easier to analyze in some ways, especially in the context of perfect competition and constant returns to scale in production. In that context, the marginal contribution of capital to operating profits is a function only of exogenous factors such as the price of output, the wage rate, and the level of productivity. Marginal  equals the expected present value of the stream of marginal contributions to operating profit accruing to the undepreciated portion of a unit of capital installed today. When this stream of marginal operating profits depends only on exogenous factors, the value of marginal  is exogenous to the firm, and in particular, does not depend on current or future investment decisions of the firm. In Abel (1983), I exploit this exogeneity of the stream of marginal operating profits to derive closed-form expressions for marginal  and for the value of the firm. One unfortunate implication of specifying adjustment costs to depend only on investment, and not on the capital stock also, is that the optimal level of investment is independent of the size of the firm. Two firms with the same value of marginal  would undertake the same level of investment even if one firm’s capital stock is a thousand times the size of the other firm’s capital stock. Alternatively, as shown by Lucas (1967), if the net profit of the firm, after deducting all costs associated with investment, is linearly homogeneous in capital, labor, and investment, the growth rate of the firm is independent of its size. Later, Hayashi (1982) showed that this linear homogeneity implies that Tobin’s , often called average , is identically equal to marginal . This equality of marginal  and average  is particularly powerful, because average , which is in principle observable, can be used to measure marginal , which is the appropriate shadow value of capital that determines the optimal 1Lucas and Prescott (1971) and Mussa (1977) first demonstrated the link between securities prices, which are related to Tobin’s , and investment in an adjustment cost framework.