Two-stage inference using data envelopment analysis efficiency measurements in univariate production models

This article addresses the problem of modeling data envelopment analysis (DEA) inefficiencies as dependent on contextual variables. For this purpose we use a statistical model similar in appearance to inefficiency component specifications in stochastic frontier models. The underlying production response is univariate. The approach is asymptotic and is based on a two-stage statistical inference procedure. In the first stage inefficiencies are estimated using DEA. In the second stage these estimates are modeled as if they were the true inefficiencies by means of a statistical model dependent on the contextual variables. To define this data generating process one could use a flexible family of distributions like the truncated normal. Theoretical inefficiencies are assumed to be independent but not identically distributed. Some of the asymptotic results implied by the two-stage inference procedure are inspected in finite samples by means of Monte Carlo simulations. The procedure is illustrated with an example where a deterministic production model is fitted to research data generated by the major state company responsible for agricultural research in Brazil.