Closed-skew normality in stochastic frontiers with individual effects and long/short-run efficiency |
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Authors: | Roberto Colombi Subal C Kumbhakar Gianmaria Martini Giorgio Vittadini |
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Institution: | 1. Department of Information Technology and Mathematical Methods, Università di Bergamo, Dalmine, Italy 2. Department of Economics, State University of New York at Binghamton, New York, NY, USA 3. Department of Economics and Technology Management, Università di Bergamo, 24044, Dalmine, BG, Italy 4. Department of Quantitative Methods, CRISP, Università di Milano-Bicocca, Milan, Italy
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Abstract: | This paper considers the estimation of Kumbhakar et al. (J Prod Anal. doi:10.1007/s11123-012-0303-1, 2012) (KLH) four random components stochastic frontier (SF) model using MLE techniques. We derive the log-likelihood function of the model using results from the closed-skew normal distribution. Our Monte Carlo analysis shows that MLE is more efficient and less biased than the multi-step KLH estimator. Moreover, we obtain closed-form expressions for the posterior expected values of the random effects, used to estimate short-run and long-run (in)efficiency as well as random-firm effects. The model is general enough to nest most of the currently used panel SF models; hence, its appropriateness can be tested. This is exemplified by analyzing empirical results from three different applications. |
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