Statistical Inference in Nonparametric Frontier Estimation: recent developments and dynamic extensions

Léopold Simar (Université Catholique de Louvain)

May 17, 2018, 11:00–12:15


Room MC 203

MAD-Stat. Seminar


Deterministic nonparametric frontier estimation has been popularized by the use of envelopment estimators in the family of FDH/DEA estimators. Once the efficient frontier has been estimated, the efficiency of each firm is evaluated by gauging its distance to the estimated efficient frontier. The statistical properties of the estimators, evaluated at fixed point are well established and the bootstrap is the way to handle practical inference for individual efficiency scores. When general features of the production set is the interest of the analysis, like average efficiency measures over groups, comparisons of group of firms, shape of the production set (convexity or not), returns to scale assumptions, testing separability, etc. a test statistics has to be provided which is often a function of averages of efficiency scores estimated under various assumptions. Basic results have been obtained to derive central limit theorems for means of efficiency scores, where it appears clearly that the inherent bias of the FDH/DEA estimators jeopardize the properties of simple, naive averages. Still it is possible to correct for this problem by correcting the bias term and if necessary by taking averages on subsamples. This has been used in various testing situations (equality of means of groups of firms, returns to scale assumptions, convexity, separability with respect to some environmental variables, etc.). Recent directions extend now these ideas to dynamic setups, where the Malmquist index is one of the basic tools used to analyze the evolution over time of the production sets. New theoretical developments allow indeed to extend the previous results to Malmquist indices. New version of central limit theorems are available and some Monte-Carlo experiments confirm the nice behavior of group means of these Malmquitst indices in finite samples.This is joint work with Alois Kneip and Paul Wilson. Main References: Kneip, A., Simar, L. and P.W. Wilson (2015), When bias kills the variance: Central Limit Theorems for DEA and FDH efficiency scores, Econometric Theory, 31, 394–422. Kneip, A., Simar, L. and P.W. Wilson (2016), Testing Hypothesis in Nonparametric Models of Production, Journal of Business and Economic Statistics, 34:3, 435–456. Simar, L. and V. Zelenyuk (2018), Central Limit Theorems for Aggregate Efficiency, Operations Research, 66, 1, 137--149. Daraio, C., Simar, L. and P.W. Wilson (2018), Central Limit Theorems for Conditional Efficiency Measures and Tests of the "Separability" Condition in Nonparametric, Two-Stage Models of Production, Discussion paper 2016/27, ISBA, UCL, in press The Econometrics Journal, doi: 10.1111/ectj.12103 Kneip, A. , Simar, L. and P.W. Wilson (2018), Inference in Dynamic, Nonparametric Models of Production: Central Limit Theorems for Malmquist Indices, Discussion paper 2018/10, ISBA, UCL.