The conditional mode in parametric frontier models

William C. Horrace, Hyunseok Jung, Yi Yang

Research output: Contribution to journalArticlepeer-review

1 Scopus citations


We survey formulations of the conditional mode estimator for technical inefficiency in parametric stochastic frontier models with Normal errors and introduce new formulations for models with Laplace errors. We prove that the conditional mode estimator in the Normal-Exponential model achieves near-minimax optimality by estimating small inefficiencies as exactly zero. We also consider a rule for selecting a subset of maximally efficient firms based on zero conditional mode estimates and show that the subset has reasonably high probability of containing the most efficient firm, particularly when inefficiency is exponentially distributed. We include an empirical example demonstrating the merits of the conditional mode estimator.

Original languageEnglish (US)
Pages (from-to)333-343
Number of pages11
JournalJournal of Productivity Analysis
Issue number3
StatePublished - Dec 2023


  • Conditional mode
  • Firm-level inefficiency
  • Minimax optimality
  • Ranking and selection
  • Stochastic frontier model

ASJC Scopus subject areas

  • Business and International Management
  • Social Sciences (miscellaneous)
  • Economics and Econometrics


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