Investment, Capacity Utilization, and the Real Business Cycle

In the real business cycle models of Kydland-Prescott and Long-Plosser, cycles come from shocks to the production function; this paper instead adopts Keynes’s view that it is shocks to the marginal efficiency of investment that drive output fluctuations, and asks whether such shocks can be made to work inside a neoclassical framework. The obstacle is well known and the authors state it up front: in a standard model an investment shock raises the return to investment, which induces intertemporal substitution that persuades people to work more now but also to consume less now, so consumption moves countercyclically; and because labour expands against a fixed capital stock, labour productivity falls. Both contradict the evidence. The paper’s answer is to make the rate at which installed capital is used a choice variable. Production depends on capital services – the capital stock times a utilization index – and higher utilization causes faster depreciation, which is Keynes’s own notion of user cost. The shock is a technological change that raises the productivity of newly produced capital goods only, entering as a multiplicative factor on gross investment in the capital accumulation equation and reaching output only after a time-to-build delay taken to be about a year. The mechanism then runs as follows. A positive shock lowers the replacement cost of old capital in terms of new, so it becomes optimal to run old capital harder and depreciate it off faster. Because capital and labour services are complements under constant returns, higher utilization raises the marginal product of labour, employment rises, and average labour productivity rises with it – all without relying on intertemporal substitution in labour supply, which the paper’s preference specification (utility in consumption less a convex function of labour effort) deliberately eliminates. The higher marginal product of labour also creates an intratemporal substitution away from leisure and toward consumption, which is what makes it possible for consumption and investment to rise together. The authors are explicit that the restriction to new capital is load-bearing: if the technological shift is applied to installed capital as well, the shock drops out of the utilization and labour conditions entirely, and “the positive effects of a technological shift on h, l, y, and productivity, in addition to the procyclical effect on consumption, are all lost.” Quantitatively, the model is parameterised annually (discount factor 0.96, capital share 0.29 from the average 1950-85 U.S. figure, labour supply elasticity 1.7, depreciation elasticity 1.42 chosen to deliver a steady-state depreciation rate of 0.1), solved exactly by computing the stationary joint distribution of capital and the two-state shock over a discretised state space, and calibrated so that it reproduces the standard deviation and first-order autocorrelation of detrended U.S. output for 1948-85 – and nothing else. It then reproduces qualitatively the relative volatilities of consumption, investment and hours, though it exaggerates them, and it ranks the persistence of consumption, productivity and investment correctly. Fit is better at a risk aversion of 2 than of 1: the correlation of consumption with output rises from 0.50 to 0.79 against an actual 0.74, and the standard deviation of investment falls from 14.7 to 11.6 percent against an actual 10.5. A notable auxiliary finding is that the required exogenous persistence is far lower than in conventional Solow-residual-driven models: the fitted annual autocorrelation of the shock is 0.47 or 0.51, against Hansen’s quarterly 0.95, which implies a four-quarter figure of 0.81. On shock size the authors concede no advantage – the ratio of shock to output standard deviation, 1.47, sits inside Hansen’s range of 1.3 to 1.7 – but argue that a shock of a given size is a weaker requirement here because it applies only to new capital goods. The paper’s own conclusion is hedged throughout: variable capacity utilization “may be important” and “may allow for a smaller burden to be placed on intertemporal substitution.”

Gregory W. Huffman | Macro Paper Warehouse

Investment, Capacity Utilization, and the Real Business Cycle