Expected efficiency ranks from parametric stochastic frontier models

William C. Horrace, Seth Richards-Shubik, Ian A. Wright

Research output: Contribution to journalArticlepeer-review

6 Scopus citations


In the stochastic frontier model, we extend the multivariate probability statements of Horrace (J Econom, 126:335–354, 2005) to calculate the conditional probability that a firm is any particular efficiency rank in the sample. From this, we construct the conditional expected efficiency rank for each firm. Compared to the traditional ranked efficiency point estimates, firm-level conditional expected ranks are more informative about the degree of uncertainty of the ranking. The conditional expected ranks may be useful for empiricists. A Monte Carlo study and an empirical example are provided.

Original languageEnglish (US)
Pages (from-to)829-848
Number of pages20
JournalEmpirical Economics
Issue number2
StatePublished - Mar 2015


  • Efficiency estimation
  • Multiplicity
  • Multivariate inference
  • Order statistics

ASJC Scopus subject areas

  • Statistics and Probability
  • Mathematics (miscellaneous)
  • Social Sciences (miscellaneous)
  • Economics and Econometrics


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