Overview

This chapter characterizes production in a dynamic decision-making environment. The classic characterization of static firm decision making is contrasted with the dynamic decision environment where not all inputs are freely adjusted. The latter characterization is motivated by the conjecture that transaction costs are associated with adjusting the capital stock at a rapid rate per unit of time and these costs increase rapidly with the absolute rate of investment. In fact, these costs increase so rapidly that the firm may never attempt to achieve a jump in its capital stock at any given moment. Such transaction (or adjustment) costs have implications for the nature of the technology. This interplay is introduced in this chapter and serves as a foundation for the dynamic structure that follows throughout the book.

Introduction

This chapter focuses on the notion of production and how economists characterize production relationships in the context of the literature, and then presents a brief historical overview of the evolution of economists’ approaches to addressing the concept of time in production decision making. The major directions of production decisions having the potential to drive a dynamic decision process are presented. Being able to measure efficiency allows one to engage in benchmarking a firm against its peers to assess relative performance and obtain an objective reading to the core questions of many decision makers and planners. Productivity and economics performance are topics of high interest and have generated many studies and considerable discussion in economic policy circles across nations. Yet, theoretical and empirical studies focusing on production efficiency typically have ignored the time interdependence of production decisions and the adjustment paths of the firm over time.

Primal Analytical Foundations of Dynamic Production Analysis

This chapter develops dynamic production analysis within the context of the adjustment cost model of the firm, where adjustment costs are associated with changes in the level of the quasi-fixed factors, also known as internal adjustment costs. The chapter characterizes axiomatically several primal representations of the adjustment cost production technology. The axiomatic approach is a cornerstone to model production technology both in theoretical and empirical work. The existence of several representations of the adjustment cost production technology is essential in the analysis of the firm’s decisions and its adjustment path that are conditioned by the technology. Three set representations of the adjustment cost production technology are discussed and characterized axiomatically. Two functional representations of the technology are also addressed using an axiomatic approach.

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.

Econometric Approaches

Econometric approaches provide another avenue to implementing the frameworks and concepts of dynamic efficiency and productivity measurement. This chapter addresses both structural and reduced-form econometric approaches to estimating the dynamic directional distance function directly as well as to estimating the cost function that accommodates technical inefficiency. An application to a farm-level panel data set is presented that estimates the decomposition of dynamic cost inefficiency into technical and allocative inefficiency measures presented in Chapter 4 and then determines the components of primal and dual Luenberger total factor productivity change based on the elaboration of these concepts in Chapter 5. In addition to the discussion of empirical issues, this chapter provides an empirical illustration using micro-level data.

Nonparametric Approaches

This chapter focuses on the nonparametric data envelopment analysis (DEA) framework of structural linear programming models underlying the estimation of efficiency. The nonparametric approach to measuring technical and cost inefficiency has been adopted in the examples in earlier chapters. Chapter 3 introduced the notions of inner- and outer-bound technologies. The inner-bound technology representation has dominated the nonparametric empirical applications in the literature on measuring efficiency and productivity. However, as this chapter shows, the outer-bound representation of the technology presents a viable alternative to measuring technical and cost efficiency as well. The chapter also develops an application to farm-level panel data.

Dynamic Economic Decision Making

This chapter presents dynamic optimization for economic decision making in the context of both dynamic cost minimization and dynamic profit maximization given different primal representations of the dynamic technology. The Bellman equation of dynamic programming serves as the analytical foundation for the duality between the production technology and the economic value function. The dynamic duality relationships in the form of intertemporal versions of Hotelling’s and Shephard’s lemmas are presented. The chapter concludes with the data envelopment perspective of the dynamic decision-making framework. Allowing the data to reveal the nature of the production technology, both the input and output quantities can be used to reveal the inner bound of the technology. Alternatively, the technological information can be recovered by exploiting the dynamic cost minimization behavior using input prices and input and output quantities, to reveal the outer bound of the input requirement set.

Dynamic Structure of Production and Productivity Change

The concept of efficiency involves measuring the current practice against the maximum potential for a given technology. This chapter addresses the intertemporal measurement of economic growth and performance at the firm level, the dynamic generalizations of the economies of scale and scope, and capacity utilization in the context of the directional distance technology dynamic adjustment. These concepts serve as the foundation to characterizing the Luenberger total productivity indicator and its change at the firm level. The decomposition of the Luenberger total productivity change indicator is developed into the contribution of technical inefficiency change, scale inefficiency change, and technical change. Each of these components is impacted by different policy remedies.