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The wrong skewness problem in stochastic frontier analysis: a review

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Abstract

We provide a review of the literature related to the “wrong skewness problem” in stochastic frontier analysis. We identify two distinct approaches, one treating the phenomenon as a signal from the data that the underlying structure has some special characteristics that allow inefficiency to co-exist with “wrong” skewness, the other treating it as a sample-failure problem. Each leads to different treatments, while siding with either raises certain methodological issues, and we explore them. We offer simulation evidence that the wrong skewness as a sample problem likely comes from how the noise component of the composite error term has been realized in the sample, which points towards a new way to handle the problem. We also investigate the issues that arise when attempting to use the unconstrained Normal-Half Normal (Skew Normal) likelihood.

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Notes

  1. In light of these remarks, it is not clear why the authors considered the wrong skewness problem as “not serious”, seeing that it makes the COLS estimator inapplicable and the MLE a bad estimator.

  2. The question whether what we want to study actually exists in the real world, i.e. whether economic processes are indeed characterized by a degree of inefficiency, is constantly answered in the affirmative in the everyday world of economic activity.

  3. Griffin and Steel (2008) constructed a model to handle possible heterogeneity in the sample vis-à-vis inefficiency. They used for the purpose a two-component generalized Gamma mixture distribution, and here the skewness of the inefficiency component could be either positive or negative.

  4. A recent contribution to this line of inquiry is Haschka and Wied (2022) where they consider the healthcare sector in Germany in a panel-data setting, providing structural reasons for, and finding “wrong” skewness in parts of, their data set.

  5. The scaling is so that the Binomial and Weibull inefficiencies have essentially the same support.

  6. See also Pal (2004).

  7. Papadopoulos (2023) explores in some depth the idiosyncratic twists and turns that the seemingly innocent “noise component” may take.

  8. This is also the position taken in Simar and Wilson (2009, p. 72).

  9. The authors also consider the same setup but for the Normal-Exponential framework.

  10. But see Canale (2011) for the practical weak identification issues that arise with the Extended Skew Normal.

  11. See Papadopoulos (2023) on these matters.

  12. See Rotnitzky et al. (2000).

  13. See Marchenko and Genton (2010) for related software routines, but also Pewsey (2000) for a comparison of method-of-moments and maximum likelihood estimation of the centred specification.

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Authors and Affiliations

  1. Athens University of Economics and Business, Athens, Greece

    Alecos Papadopoulos

  2. Department of Economics, University of Miami, Coral Gables, FL, USA

    Christopher F. Parmeter

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  1. Alecos Papadopoulos
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Correspondence to Alecos Papadopoulos or Christopher F. Parmeter.

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Papadopoulos, A., Parmeter, C.F. The wrong skewness problem in stochastic frontier analysis: a review. J Prod Anal 61, 121–134 (2024). https://doi.org/10.1007/s11123-023-00708-w

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