Introduction

The models introduced in the previous chapters are for cross-sectional data, that is, data in which every individual firm/unit is observed only once. Estimation of inefficiency in these models require distributional assumptions (unless one uses COLS and makes the assumption that there is no noise). Schmidt and Sickles (1984) mentioned three problems with the cross-sectional models that are used to measure inefficiency. First, the ML method used to estimate parameters and the inefficiency estimates using the JLMS formula depend on distributional assumptions for the noise and the inefficiency components. Second, the technical inefficiency component has to be independent of the regressor(s) (at least in the single equation models) – an assumption that is unlikely to be true if firms maximize profit and inefficiency is known to the firm (see Mundlak [1961]). Third, the JLMS estimator is not consistent, in the sense that the conditional mean or mode of u(v − u) never approaches u as the number of firms (cross-sectional units) approaches infinity.

If panel data are available, that is, each unit is observed at several different points of time, some of these rigidities/limitations can be removed. However, to overcome some of these limitations, the panel models make some other assumptions, some of which may or may not be realistic. In this chapter, we review the panel models that are used in the efficiency literature.

A key advantage of panel data is that it enables the modeler to take into account some heterogeneity that may exist beyond what is possible to control using a cross-sectional approach. This can be achieved by introducing an “individual (unobservable) effect,” say, αi, that is time-invariant and individual-specific, and not interacted with other variables.

Having information on units over time also enables one to examine whether inefficiency has been persistent over time or whether the inefficiency of units is time-varying.