Journal of Productivity Analysis

, Volume 50, Issue 1–2, pp 1–24 | Cite as

Estimation and testing of stochastic frontier models using variational Bayes

  • Gholamreza Hajargasht
  • William E. GriffithsEmail author


We show how a wide range of stochastic frontier models can be estimated relatively easily using variational Bayes. We derive approximate posterior distributions and point estimates for parameters and inefficiency effects for (a) time invariant models with several alternative inefficiency distributions, (b) models with time varying effects, (c) models incorporating environmental effects, and (d) models with more flexible forms for the regression function and error terms. Despite the abundance of stochastic frontier models, there have been few attempts to test the various models against each other, probably due to the difficulty of performing such tests. One advantage of the variational Bayes approximation is that it facilitates the computation of marginal likelihoods that can be used to compare models. We apply this idea to test stochastic frontier models with different inefficiency distributions. Estimation and testing is illustrated using three examples.


Technical efficiency Marginal likelihood Time-varying panel Environmental effects Mixture Semiparametric model 

JEL classification

C11 C12 C23 D24 


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© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Swinburne Business SchoolSwinburne University of TechnologyMelbourneAustralia
  2. 2.Department of EconomicsUniversity of MelbourneMelbourneAustralia

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