Maximum simulated likelihood estimation of the seemingly unrelated stochastic frontier regressions
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Maximum simulated likelihood estimation of the seemingly unrelated stochastic frontier regressions Hung-pin Lai1 Received: 27 February 2020 / Accepted: 13 October 2020 © Springer-Verlag GmbH Germany, part of Springer Nature 2020
Abstract In this paper, we use the maximum simulated likelihood (MSL) approach to estimate multiple stochastic frontier (SF) models with random effects and correlated composite errors. We show that the separate estimation of the single equation ignores the correlation between the composite errors and causes significant efficiency loss in estimation. In addition to using Monte Carlo simulation to investigate the finite sample performance of the simulated estimator, we demonstrate the usefulness of our approach in estimating the technical efficiency of Taiwan’s international hotels based on their accommodation and restaurant divisions. Keywords Maximum likelihood estimation · Copula · Seemingly unrelated stochastic frontier regressions · Random effects JEL Classification C3 · C5 · R3
1 Introduction Since the pioneering work of Aigner et al. (1977), stochastic frontier (SF) analysis has been widely used in productivity and efficiency studies to describe and estimate models of the production frontier. The empirical model typically assumes that a decision-making unit (DMU) employs a single production process or technology in the production of an output using multi-inputs. However, if an organization (a DMU) operates multiple production divisions (sub-DMUs), with each division supported by its own set of resource inputs, these sub-DMUs may be subject to the same random
I thank Wen-Jen Tsay for his helpful comments and suggestions. I also thank two anonymous referees for many constructive comments. The usual disclaimer applies.
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Hung-pin Lai [email protected] Department of Economics, National Chung Cheng University, Chiayi, Taiwan
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H. Lai
shocks as the parent DMU. Given that these divisions would share some commonly observed or unobserved characteristics of the parent DMU, the divisions’ technical efficiencies may well be correlated. A system of multiple stochastic frontier regressions on the sub-DMUs will be a more appropriate model to investigate a DMU’s operation and performance. Since the system estimation takes into account the mutual dependency among the composite errors, the estimator is more efficient than that from the regression-by-regression estimation. Previously, Lai and Huang (2013) discussed the estimation of a system of stochastic frontier models for cross-section data. When sub-DMUs are observed over time, some unobserved heterogeneity may exist and a model that can capture the panel characteristics will be able to provide more effective estimation and also a better prediction of the inefficiency. The unobserved heterogeneity for the firm level panel data can be incorporated into the model in several ways. For instance, one can introduce the heterogeneity through fixed effects, random effects or heterogeneous variance in the symmetric/one-sided random component. In
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