Model averaging estimators for the stochastic frontier model

  • Christopher F. ParmeterEmail author
  • Alan T. K. Wan
  • Xinyu Zhang


Model uncertainty is a prominent feature in many applied settings. This is certainty true in the efficiency analysis realm where concerns over the proper distributional specification of the error components of a stochastic frontier model is, generally, still open along with which variables influence inefficiency. Given the concern over the impact that model uncertainty is likely to have on the stochastic frontier model in practice, the present research proposes two distinct model averaging estimators, one which averages over nested classes of inefficiency distributions and another that has the ability to average over distinct distributions of inefficiency. Both of these estimators are shown to produce optimal weights when the aim is to uncover conditional inefficiency at the firm level. We study the finite-sample performance of the model average estimator via Monte Carlo experiments and compare with traditional model averaging estimators based on weights constructed from model selection criteria and present a short empirical application.


Optimality J-fold cross-validation Efficiency Model selection 



We thank participants at the New York Camp Econometrics X, the 14th European Workshop on Efficiency and Productivity Analysis, LECCEWEPA 2015, the CEPA Workshop on Economic Measurement and the 2016 North American Productivity Workshop for valuable insight. Xinyu Zhang acknowledges the support from National Natural Science Foundation of China (Grant numbers 71522004, 11471324 and 71631008). The usual disclaimer applies.

Author contributions

All three authors contributed equally to this work and the order of authorship has nothing other than alphabetical significance.

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.


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Authors and Affiliations

  1. 1.Department of EconomicsUniversity of MiamiMiamiUSA
  2. 2.Department of Management SciencesCity University of Hong KongKowloonHong Kong
  3. 3.Academy of Mathematics and Systems ScienceChinese Academy of SciencesBeijingChina

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