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sftfe: A Stata command for fixed-effects stochastic frontier models estimation


  • Federico Belotti

    (CEIS, University of Rome Tor Vergata)

  • Giuseppe Ilardi

    (Bank of Italy)


The classical stochastic frontier panel-data models provide no mechanism to disentangle individual time-invariant unobserved heterogeneity from inefficiency. Greene (2005a,b) proposed the so-called true fixed-effects specification that distinguishes these two latent components and allows for time-varying inefficiency. However, because of the incidental parameters problem, the maximum likelihood estimator proposed by Greene leads to biased variance estimates in short panels. sftfe allows the estimation of this model via three alternative estimators (Belotti and Ilardi 2012; Chen et al. 2014), which by relying on data transformation, achieve consistency for n ! 1 with fixed T. Of special note is that sftfe allows the underlying mean and variance of the inefficiency to be expressed as functions of exogenous covariates. Furthermore, the new command allows the estimation of a "true" fixed-effects model in which the inefficiency is assumed to follow a first-order autoregressive process. These features can be considered relevant from the methodological point of view because both model parameters and inefficiency estimates may be adversely affected when inefficiency heterogeneity, heteroskedasticity, and serial correlation are neglected. They are also important empirically because they allow for testing specific hypotheses of interest and policy implications and avoid biased two-step procedures.

Suggested Citation

  • Federico Belotti & Giuseppe Ilardi, 2014. "sftfe: A Stata command for fixed-effects stochastic frontier models estimation," Italian Stata Users' Group Meetings 2014 05, Stata Users Group.
  • Handle: RePEc:boc:isug14:05

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    References listed on IDEAS

    1. Federico Belotti & Silvio Daidone & Giuseppe Ilardi & Vincenzo Atella, 2013. "Stochastic frontier analysis using Stata," Stata Journal, StataCorp LP, vol. 13(4), pages 718-758, December.
    2. Chen, Yi-Yi & Schmidt, Peter & Wang, Hung-Jen, 2014. "Consistent estimation of the fixed effects stochastic frontier model," Journal of Econometrics, Elsevier, vol. 181(2), pages 65-76.
    3. Jondrow, James & Knox Lovell, C. A. & Materov, Ivan S. & Schmidt, Peter, 1982. "On the estimation of technical inefficiency in the stochastic frontier production function model," Journal of Econometrics, Elsevier, vol. 19(2-3), pages 233-238, August.
    4. Greene, William, 2005. "Reconsidering heterogeneity in panel data estimators of the stochastic frontier model," Journal of Econometrics, Elsevier, vol. 126(2), pages 269-303, June.
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    Cited by:

    1. Sun, Huaping & Edziah, Bless Kofi & Sun, Chuanwang & Kporsu, Anthony Kwaku, 2019. "Institutional quality, green innovation and energy efficiency," Energy Policy, Elsevier, vol. 135(C).

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