Unobserved heterogeneity and endogeneity in nonparametric frontier estimation
(2016) Journal of Econometrics — Vol. 190, p. 360-373 (2016)
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- Abstract
- In production theory and eciency analysis, rm eciencies are measured by their distances to a production frontier, which is the geometrical locus of optimal combinations of inputs and outputs. It is today recognized that in the presence of heterogenous conditions (like environmental factors) that influence the shape and the position of the frontier, traditional measures of efficiency obtained in the space of inputs/outputs have no sensible economic meaning. This is because the benchmark frontier may not be attainable for a firm facing different heterogenous conditions. Using a nonparametric approach, this can be corrected by using conditional frontiers and conditional efficiency scores developed in the literature. In this paper we extend these concepts in the case where the heterogeneity is not observed. We propose and analyze a model where the heterogeneity variable is linked to a particular input (or output). It is defined as the part of the input (or the output), independent from some instrumental variable through a nonseparable nonparametric model. We discuss endogeneity issues involved in this model. Under certain regularity assumptions, we show that the model is identified, we propose nonparametric estimators of the conditional frontier and the conditional efficiency score, and analyze their asymptotic properties. When using FDH estimators we prove the asymptotic convergence to a Weibull distribution, whereas when using the robust order-m estimators we obtain the asymptotic normality of the estimators. The method is illustrated with some simulated and real data examples. A Monte-Carlo experiment shows how the procedure works for finite samples.
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Simar, L., Vanhems, A., & Van Keilegom, I. (2016). Unobserved heterogeneity and endogeneity in nonparametric frontier estimation. Journal of Econometrics, 190, 360-373. https://doi.org/10.1016/j.jeconom.2015.06.015 (Original work published 2016)