기술적 비효율성의 오지정이 확률변경모형의 최대가능도 추정에 미치는 영향

Abstract

The stochastic frontier model is a widely used econometric method for assessing production efficiency concerning the maximum achievable output given a specific input, where the difference between the maximum and actual production is referred to as technical inefficiency. Statistically, the stochastic frontier model adjusts a standard regression model with normally distributed errors by introducing a non-negative random variable to account for technical inefficiency. By computing the probability density of the composed error, which defined by subtracting the non-negative random variable from the normal error, the maximum likelihood estimators (MLE) for the stochastic frontier model can be obtained. In principle, the technical inefficiency cannot be directly observed so that the distributional assumption is necessary to fit the model. Consequently, it is common to encounter model misspecification problem, which involves inaccurate assumption of the distribution of technical inefficiency. This research aims to explore limiting behaviors of the MLE in the stochastic frontier model under misspecified technical inefficiency distribution. We also investigate the minimizers of the Kullback-Leibler divergence between the true and misspecified model, wherein the MLE obtained from the misspecified model converges. Subsequently, we employ Monte Carlo experiments to examine the finite sample performance and to explain the similarity of MLE for slope parameters regardless of the distributional assumption of technical inefficiency as mentioned in the previous studies.