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

This paper proposes a fully nonparametric framework to estimate relative efficiency 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 efficiency 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 effect of heterogeneity in conditional efficiency estimation has been suggested. We show how to use and interpret nonparametric bootstrap-based significance tests in a generalized conditional efficiency framework. This allows us to study statistical significance 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 significant effect on the educational process.