Blaming the exogenous environment? Conditional efficiency estimation with continuous and discrete exogenous variables

This paper proposes a fully nonparametric framework to estimate relative e¢ciency of entities while accounting for a mixed set of continuous and discrete (both ordered and unordered) exogenous variables. Using robust partial frontier techniques, the probabilistic and conditional characterization of the production process, as well as insights from the recent developments in nonparametric econometrics, we present a generalized approach for conditional e¢ciency measurement. To do so, we utilize a tailored mixed kernel function with a data-driven bandwidth selection. So far only descriptive analysis for studying the e¤ect of heterogeneity in conditional e¢ciency estimation has been suggested. We show how to use and interpret nonparametric bootstrap-based signi…cance tests in a generalized conditional e¢ciency framework. This allows us to study statistical signi…cance of continuous and discrete exogenous variables on production process. The proposed approach is illustrated using simulated examples as well as a sample of British pupils from the OECD Pisa data set. The results of the empirical application show that several exogenous discrete factors have a statistically signi…cant e¤ect on the educational process. Keywords: Nonparametric estimation, Conditional e¢ciency measures, Exogenous factors, Generalized kernel function, Education JEL-classi…cation: C14, C25, I21 We would like to thank Laurens Cherchye and the participants of the Seminar on E¢ciency and Productivity Analysis at Aston University for valuable comments. Corresponding author. Tel. +447796102570.