This article was originally written in Greek and it has been published as part of a three-volume ... more This article was originally written in Greek and it has been published as part of a three-volume symposium on the concept of freedom in various scientific disciplines, in THEOLOGIA 93, 3 (2022), pp. 261-308, the scholarly journal of the Holy Synod of the Church of Greece. The present translation of the full text in English was done by the author. In the process, a few references were changed from Greek to English ones.
The distributional specifications for the composite regression error term most often used in Stoc... more The distributional specifications for the composite regression error term most often used in Stochastic Frontier Analysis (SFA) are inherently bounded as regards their skewness and excess kurtosis coefficients. These bounds provide simple diagnostic tools and model selection/rejection criteria for empirical studies which appear to have been overlooked by practitioners. We derive general expressions for the skewness and excess kurtosis of the composed error term in the stochastic frontier model based on the ratio of standard deviations of the two separate error components as well as theoretical ranges for the most popular empirical specifications. Simulation results are presented to detail the small-sample effects as well as to speak towards the practical relevance of these diagnostic tools and the consequences of misspecification. These insights lead us to examine quasi-maximum likelihood estimation (QMLE) of the ubiquitous Normal-Half Normal stochastic frontier model and the properties of the Skew-Normal QMLE, more generally.
European Journal of Operational Research, Sep 1, 2021
Abstract The distributional specifications for the composite regression error term most often use... more Abstract The distributional specifications for the composite regression error term most often used in stochastic frontier analysis are inherently bounded as regards their skewness and excess kurtosis coefficients. We derive general expressions for the skewness and excess kurtosis of the composed error term in the stochastic frontier model based on the ratio of standard deviations of the two separate error components as well as theoretical ranges for the most popular empirical specifications. While these simple expressions can be used directly to assess the credibility of an assumed distributional pair, they are likely to over reject. Therefore, we develop a formal test based on the implied ratio of standard deviations for the skewness and the kurtosis. This test is shown to have impressive power compared with other tests of the specification of the composed error term. We deploy this test on a range of well-known datasets that have been used across the efficiency community. For many of them we find that the classic distribution assumptions cannot be rejected.
We provide a detailed presentation and guide for the use of Copulas in order to account for endog... more We provide a detailed presentation and guide for the use of Copulas in order to account for endogeneity in linear regression models without the need for instrumental variables. We start by developing the model from first principles of likelihood inference, and then focus on the Gaussian Copula. We discuss its merits and propose diagnostics to assess its validity. We analyze in detail and provide solutions to the various issues that may arise in empirical applications for applying the method. We treat the cases of both continuous and discrete endogenous regressors. We present simulation evidence for the performance of the proposed model in finite samples, and we illustrate its application by a short empirical study. A Supplementary File contains additional simulations and another empirical illustration.
This article was originally written in Greek and it has been published as part of a three-volume ... more This article was originally written in Greek and it has been published as part of a three-volume symposium on the concept of freedom in various scientific disciplines, in THEOLOGIA 93, 3 (2022), pp. 261-308, the scholarly journal of the Holy Synod of the Church of Greece. The present translation of the full text in English was done by the author. In the process, a few references were changed from Greek to English ones.
The distributional specifications for the composite regression error term most often used in Stoc... more The distributional specifications for the composite regression error term most often used in Stochastic Frontier Analysis (SFA) are inherently bounded as regards their skewness and excess kurtosis coefficients. These bounds provide simple diagnostic tools and model selection/rejection criteria for empirical studies which appear to have been overlooked by practitioners. We derive general expressions for the skewness and excess kurtosis of the composed error term in the stochastic frontier model based on the ratio of standard deviations of the two separate error components as well as theoretical ranges for the most popular empirical specifications. Simulation results are presented to detail the small-sample effects as well as to speak towards the practical relevance of these diagnostic tools and the consequences of misspecification. These insights lead us to examine quasi-maximum likelihood estimation (QMLE) of the ubiquitous Normal-Half Normal stochastic frontier model and the properties of the Skew-Normal QMLE, more generally.
European Journal of Operational Research, Sep 1, 2021
Abstract The distributional specifications for the composite regression error term most often use... more Abstract The distributional specifications for the composite regression error term most often used in stochastic frontier analysis are inherently bounded as regards their skewness and excess kurtosis coefficients. We derive general expressions for the skewness and excess kurtosis of the composed error term in the stochastic frontier model based on the ratio of standard deviations of the two separate error components as well as theoretical ranges for the most popular empirical specifications. While these simple expressions can be used directly to assess the credibility of an assumed distributional pair, they are likely to over reject. Therefore, we develop a formal test based on the implied ratio of standard deviations for the skewness and the kurtosis. This test is shown to have impressive power compared with other tests of the specification of the composed error term. We deploy this test on a range of well-known datasets that have been used across the efficiency community. For many of them we find that the classic distribution assumptions cannot be rejected.
We provide a detailed presentation and guide for the use of Copulas in order to account for endog... more We provide a detailed presentation and guide for the use of Copulas in order to account for endogeneity in linear regression models without the need for instrumental variables. We start by developing the model from first principles of likelihood inference, and then focus on the Gaussian Copula. We discuss its merits and propose diagnostics to assess its validity. We analyze in detail and provide solutions to the various issues that may arise in empirical applications for applying the method. We treat the cases of both continuous and discrete endogenous regressors. We present simulation evidence for the performance of the proposed model in finite samples, and we illustrate its application by a short empirical study. A Supplementary File contains additional simulations and another empirical illustration.
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