Inference in Dynamic, Nonparametric Models of Production: Central Limit Theorems for Malmquist Indices

Kneip, Alois;Simar, LĂ©opold;Wilson, Paul
(2018) , 57 pages

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Abstract
The Malmquist index gives a measure of productivity in dynamic settings and has been widely applied in empirical work. The index is typically estimated using envelopment estimators, particularly data envelopment analysis (DEA) estimators. Until now, inference about productivity change measured by Malmquist indices has been problematic, including both inference regarding productivity change experienced by particular firms as well as mean productivity change. This paper establishes properties of a DEAtype estimator of distance to the conical hull of a variable-returns-to-scale production frontier. In addition, properties of DEA estimators of Malmquist indices for individual producers are derived as well properties of geometric means of these estimators. The latter requires new CLT results, extending the work of Kneip et al. (2015, Econometric Theory). Simulation results are provided to give applied researchers an idea of how well inference may work in practice in finite samples.
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Kneip, A., Simar, L., & Wilson, P. (2018). Inference in Dynamic, Nonparametric Models of Production: Central Limit Theorems for Malmquist Indices (ISBA Discussion Paper 2018/10). https://hdl.handle.net/2078.5/171764