Endogenous Capital Utilization and Productivity Measurement in Dynamic Factor Demand Models : Theory and an Application to the U.S. Electrical

Studies of the firm's demand for factor inputs often assume a constant rate of utilization of the inputs and ignore the fact that the firm can simultaneously choose the level and the rate of utilization of its inputs. In particular, the literature on dynamic factor demand models has, until recently, largely overlooked the issue of capital utilization and/or did not distinguish carefully between the distinct concepts of capital and capacity utilization. In this paper we allow for variations in the rate of capital utilization within the context of a dynamic factor demand model by adopting a modeling framework within which the firm combines its beginning-of-period stocks with other inputs to produce its outputs as well as its end-of-period stocks. We also derive measures of productivity and capacity utilization for the adopted modeling framework. Given the depreciation rate is endogenous a consistent capital stock series must be generated during estimation from the investment data. This yields, as a byproduct, a consistent decon1position of gross investment into replacement and expansion investment. As an illustration, the model is applied to U.S. Electrical Machinery data