Intertemporal Production Frontiers: With Dynamic DEA

The main goal of this monograph is to generalize our earlier work on production frontiers and performance measurement to the intertemporal case. Analysis of multi period data using activity analysis models is already widespread, of course. One obvious example is our own work on measurement of productivity using activity analysis models to construct Malmquist type productivity indexes. Although many periods are analyzed, and the change in technology over time is measured, these represent a fairly limited type of intertemporal models — one is essentially comparing a series of static models. There is no interdependence or connection over time among inputs, outputs or technology. This type of analysis is the analog of comparative statics.

In this chapter we introduce the basic building blocks which we will be using to develop our dynamic models of production. As in our previous work on production and performance measurement, we follow Shephard and begin by specifying axioms which technology should satisfy. These are chosen to provide the minimum structure and regularity necessary to allow us to employ duality results, for example. A brief overview of these axioms, including alternative specifications of returns to scale and disposability of inputs and outputs opens this chapter.

The goal of this chapter is to move toward the analysis of performance over time. One of the most basic notions used by economists in this regard is productivity and productivity growth. We deal with this topic in this chapter and in Chapter 4. Here we focus on the construction of productivity indexes. In Chapter 4 we focus on one of the components of productivity, namely technical change.

In this chapter we focus on the technical change component of productivity growth. This is the component typically associated with innovation or shifts in the frontier of technology.

This chapter focuses on indirect production. Like the more familiar idea of indirect utility, the idea is to introduce a budget constraint into the model. Instead of thinking of inputs as given, we instead think of the decision-maker as being confronted with a fixed budget which they may use to purchase inputs, at given input prices, i.e., inputs become choice variables rather than being treated as given. This type of model is useful in a variety of contexts. Perhaps the most obvious would be a government unit that receives an annual budget which they allocate and use to provide services.

Dynamic production models are the topic of this section. These models allow a decision in one period to influence the outcomes in other periods. This time interdependence, which we also recognized in Chapter 5, is the essence of a dynamic model.