Dynamic Decision Making, Distance Functions, and Productive Efficiency

This chapter discusses three concepts of the directional distance function in the presence of internal adjustment costs, designated as adjustment cost directional distance functions. These functions are the building blocks of technical inefficiency measures. Duality between an adjustment cost directional distance function and an indirect optimal value function allows the construction of economic measures of inefficiency. Duality is established between the adjustment cost directional input function and the optimal current value function of the intertemporal cost minimization problem. From this dual relation, a dynamic cost inefficiency measure is derived and decomposed into technical inefficiency and allocative inefficiency. Similarly, dynamic input-output measures of inefficiency are derived from the adjustment cost directional technology distance function and duality between this function and the current profit function.