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Maximum likelihood estimation of seemingly unrelated stochastic frontier regressions

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Abstract

In this paper, we propose the copula-based maximum likelihood (ML) approach to estimate the multiple stochastic frontier (SF) models with correlated composite errors. The motivation behind the extension to system of SF regressions is analogous to the classical generalization to system of seemingly unrelated regressions (Zellner in J Am Statist Assoc 57:348–368, 1962). A demonstration of the copula approach is provided via the analysis of a system of two SF regressions. The consequences of ignoring the correlation between the composite errors are examined by a Monte Carlo experiment. Our findings suggest that the stronger the correlation between the two SF regressions, the more estimation efficiency is lost in separate estimations. Estimation without considering the correlated composite errors may cause significantly efficiency loss in terms of mean squared errors in estimation of the SF technical efficiency. Finally, we also conduct an empirical study based on Taiwan hotel industry data, focusing on the SF regressions for the accommodation and restaurant divisions. Our results, which are consistent with the findings in simulation, show that joint estimation is significantly different from separate estimation without considering the correlated composite errors in the two divisions.

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Notes

  1. This independence assumption of the error components in a single SF regression setting has been relaxed in the studies by Pal and Sengupta (1999), Pal (2004), Bandyopadhyay and Das (2006), and Smith (2008). However, these studies are all confined to a single regression case.

  2. See section 2.2.2 of Trivedi and Zimmer (2005).

  3. See Proposition 4.1 of Cherubini et al. (2004).

  4. See Serfling (1980).

  5. We thank the associate editor for this suggestion.

  6. See Cherubini et al. (2004) for the details.

  7. Tsay et al. (2012) have shown that c 1 = −1.0950081470333 and c 2 = −0.75651138383854.

  8. Since the close form of the inverse CDF is not available, we first compute, via (10), the numerical CDF at 10,000 points, and then apply the inverse of this numerical CDF at given γ to obtain ɛ.

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Acknowledgments

Lai gratefully acknowledges the National Science Council of Taiwan (NSC-98-2410-H-194-035) for the research support. The authors thank an anonymous referee and the associate editor for helpful comments.

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Authors and Affiliations

  1. Department of Economics, National Chung Cheng University, Chia-Yi, Taiwan

    Hung-pin Lai

  2. Department of Economics, Vanderbilt University, Nashville, TN, USA

    Cliff J. Huang

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  1. Hung-pin Lai
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Correspondence to Hung-pin Lai.

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Lai, Hp., Huang, C.J. Maximum likelihood estimation of seemingly unrelated stochastic frontier regressions. J Prod Anal 40, 1–14 (2013). https://doi.org/10.1007/s11123-012-0289-8

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