Estimation of Allocative Inefficiency and Productivity Growth with Dynamic Adjustment Costs

Abstract

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 quasifixed 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 .42 percent of total cost and about 1.26 percent 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.JEL Categories: C13, C33

Pricing Inputs and Outputs: Market Prices Versus Shadow Prices, Market Power, and Welfare Analysis

“…The shadow distance system can be estimated both in the static framework and in the dynamic framework, which accounts for adjustment costs of inputs. Atkinson and Cornwell (2011) Based on the standard economic model of shadow cost minimizing behavior of firms, it seems a natural choice to use shadow input quantities while analyzing cost minimizing behavior of firms. However, this approach involves significant challenges in terms of estimation.…”

Rational inefficiency, adjustment costs and sequential technologies

“…Dynamic models of inefficiency (see e.g. Sengupta (1999), Nemoto andGoto (1999, 2003), Silva andStefanou (2003, 2007) and Atkinson and Cornwell (2011)) estimate optimal paths of dynamic efficiency accounting for adjustment costs. 2 In these models DMUs can be rationally inefficient if the adjustment costs associated with reaching the technological frontier are higher than the intertemporal cost reductions.…”