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Two-tier stochastic frontier analysis using Stata


  • Yujun Lian

    (Sun Yat-sen University)

  • Chang Liu

    (Sun Yat-sen University)

  • Christopher F. Parmeter

    (University of Miami)


In this article, we introduce the sftt command, which fits two-tier stochastic frontier (2TSF) models with cross-sectional data. Like most frontier models, a 2TSF model consists of a linear frontier model and a composite error term. The error term is assumed to be a mixture of three components: two one- sided inefficiency terms—strictly nonnegative and nonpositive, respectively—and a symmetric noise term. When providing appropriate distributional assumptions, sftt can fit models with exponential and half-normal specifications. sftt also fits 2TSF models with the scaling property to mitigate concerns over distributional specifications. In addition, we provide two subcommands, sftt sigs and sftt eff, to assist in postestimation efficiency analysis. We provide an overview of the 2TSF literature, a description of the sftt command and its options, and examples using simulated and actual data.

Suggested Citation

  • Yujun Lian & Chang Liu & Christopher F. Parmeter, 2023. "Two-tier stochastic frontier analysis using Stata," Stata Journal, StataCorp LP, vol. 23(1), pages 197-220, March.
  • Handle: RePEc:tsj:stataj:v:23:y:2023:i:1:p:197-229
    DOI: 10.1177/1536867X231162033
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