Statistical properties of data envelopment analysis estimators of production functions

This paper develops the statistical properties of nonparametric estimators of production functions obtained through the use of data envelopment analysis (DEA). For deterministic production models it is shown that DEA production functions are consistent non parametric maximum likelihood estimators and generate technical inefficiencies that converge in distribution. The asymptotic joint distribution of the estimated technical inefficiencies allows hypothesis testing in DEA. These results are due mainly to Banker (1993) and here they are refined and extended. Relaxing the assumption of equally distributed inefficiencies and allowing for an arbitrary scale of operation for the underlying technology, it is shown the strong consistency of the DEA production function and how one can model effects causing inefficiencies under the assumptions of half-normal, truncated normal or gamma distributions for the inefficiencies, not ruling out heteroscedasticity. Measures of goodness of fit are also developed for the iid case assuming an exponential or a half-normal distribution. An empirical application illustrates the theoretical results and investigates the nature of the production function of the major state company responsible for agricultural research in Brazil, namely Embrapa (Empresa Brasileira de Pesquisa Agropecuária).