Estimation of inefficiency in stochastic frontier models: a Bayesian kernel approach

  • Guohua FengEmail author
  • Chuan WangEmail author
  • Xibin ZhangEmail author


We propose a kernel-based Bayesian framework for the analysis of stochastic frontiers and efficiency measurement. The primary feature of this framework is that the unknown distribution of inefficiency is approximated by a transformed Rosenblatt-Parzen kernel density estimator. To justify the kernel-based model, we conduct a Monte Carlo study and also apply the model to a panel of U.S. large banks. Simulation results show that the kernel-based model is capable of providing more precise estimation and prediction results than the commonly-used exponential stochastic frontier model. The Bayes factor also favors the kernel-based model over the exponential model in the empirical application.


Kernel density estimation Efficiency measurement Stochastic distance frontier Markov Chain Monte Carlo 

JEL Classification

C11 D24 G21 



We would like to thank Professor Cheng Hsiao at the University of Southern California for helpful discussion. We would also like to thank the reviewers for their constructive comments that have led to substantial improvement of the paper.

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.


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© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of EconomicsUniversity of North TexasDentonUSA
  2. 2.Wenlan School of BusinessZhongnan University of Economics and LawWuhanChina
  3. 3.Department of Econometrics and Business StatisticsMonash UniversityCaulfield EastAustralia

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