What This Book Is About

This is a book on stochastic frontier (SF) analysis, which uses econometric models to estimate production (or cost or profit) frontiers and efficiency relative to those frontiers. Production efficiency relates actual output to the maximum possible, and is defined as the ratio of the actual output to the maximum potential output. More generally, SF analysis can be applied to any problem where the observed outcome deviates from the potential outcome in one direction, that is, the observed outcome is either less or more than the potential outcome. In the context of production efficiency, the potential output, given inputs and technology, is the maximum possible output that defines the frontier and the actual output falls below the frontier due to technical inefficiency. For cost efficiency, the frontier is defined by the potential minimum cost, and the actual cost lies above the minimum frontier owing to inefficiency. Similarly, the profit frontier is defined in terms of the maximum possible profit and profit efficiency is defined as the ratio of actual to maximum possible profit (assuming that they are both positive or negative). Other examples include the observed wage offer being less than the potential maximum; the reported crime rate being less than the true crime because of underreporting; actual investment being less than the potential optimal because of borrowing constraints; and so on. The common denominator in all of these problems is that there is something called the potential maximum or minimum or optimal level, which defines the frontier. This frontier is unobserved. So the question is how to estimate the frontier function so that efficiency can be estimated. Another complicating factor is that the frontier is often viewed as stochastic and the problem is how to estimate efficiency relative to the stochastic frontier when we can estimate only the “deterministic” part of the frontier. This book deals with the issues related to estimating the stochastic frontier econometrically first, and then estimating efficiency relative to the stochastic frontier for each observation.