Estimation of allocative inefficiency and productivity growth with dynamic adjustment costs

A substantial literature has been generated on the estimation of allocative and technical inefficiency using static production, cost, profit, and distance functions. We develop a dynamic shadow distance system that integrates dynamic adjustment costs into a long-run shadow cost-minimization problem, which allows us to distinguish static allocative distortions from short-run inefficiencies that arise due to period-to-period adjustment costs. The set of estimating equations is comprised of the first-order conditions from the short-run shadow cost-minimization problem for the variable shadow input quantities, a set of Euler equations derived from subsequent shadow cost minimization with respect to the quasi-fixed inputs, and the input distance function, expressed in terms of shadow quantities. This system nests within it the static model with zero adjustment costs. Using panel data on U.S. electric utilities, we contrast the results of static and dynamic shadow distance systems. First, the zero-adjustment-cost restriction is strongly rejected. Second, we find that adjustment costs represent about 0.42% of total cost, and about 1.26% of capital costs. Third, while both models reveal that labor is not utilized efficiently, the dynamic model indicates a longer period of over-use and less variance over time in the degree of inefficiency. With the dynamic model, productivity growth is larger but more stable.