Two-tiered stochastic frontier models: a Bayesian perspective

Shirong Zhao, Jeremy Losak

Research output: Contribution to journalArticlepeer-review


Bayesian methods have been well-studied in single-tiered stochastic frontier literature, but as of yet have not been proposed in a two-tiered stochastic frontier (2TSF) setting. Recently, 2TSF models have drawn much attention, observed by increased theoretical extensions and empirical applications. This paper fills the gap in the literature by presenting a Bayesian approach to estimating 2TSF models, with and without independence, as well as with and without efficiency (or bargaining power) determinants. Posterior distributions for the parameters and efficiencies for two bargaining parties are derived. To test our methods, we use both maximum likelihood estimation and Bayesian methods to analyze bargaining power in Major League Baseball salary arbitration negotiations. We find that players who generate their value by hitting for power have more bargaining power, while players who generate their value by having high on-base abilities have less bargaining power. This result is consistent with pre-Moneyball free agent market valuations for these skills.

Original languageEnglish (US)
Pages (from-to)85-106
Number of pages22
JournalJournal of Productivity Analysis
Issue number2
StatePublished - 2023


  • Bayesian econometrics
  • C1
  • C3
  • Final offer arbitration
  • Gibbs sampling
  • Moneyball
  • Two-tiered stochastic frontier
  • Z22

ASJC Scopus subject areas

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


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