Semiparametric Stochastic Frontier Estimation via Profile Likelihood
提出一种基于条件剖面似然函数的半参数随机前沿模型估计方法，该估计量渐近正态且无偏，在广泛半参数估计类中有效，并通过蒙特卡洛模拟验证了有限样本性质。
We consider the estimation of a nonparametric stochastic frontier model with composite error density which is known up to a finite parameter vector. Our primary interest is on the estimation of the parameter vector, as it provides the basis for estimation of firm specific (in)efficiency. Our frontier model is similar to that of Fan et al. (1996 Fan , Y. , Li , Q. , Weersink , A. ( 1996 ). Semiparametric estimation of stochastic production frontier models . Journal of Business and Economic Statistics 14 : 460 – 468 .[Taylor & Francis Online], [Web of Science ®] , [Google Scholar]), but here we extend their work in that: a) we establish the asymptotic properties of their estimation procedure, and b) propose and establish the asymptotic properties of an alternative estimator based on the maximization of a conditional profile likelihood function. The estimator proposed in Fan et al. (1996 Fan , Y. , Li , Q. , Weersink , A. ( 1996 ). Semiparametric estimation of stochastic production frontier models . Journal of Business and Economic Statistics 14 : 460 – 468 .[Taylor & Francis Online], [Web of Science ®] , [Google Scholar]) is asymptotically normally distributed but has bias which does not vanish as the sample size n → ∞. In contrast, our proposed estimator is asymptotically normally distributed and correctly centered at the true value of the parameter vector. In addition, our estimator is shown to be efficient in a broad class of semiparametric estimators. Our estimation procedure provides a fast converging alternative to the recently proposed estimator in Kumbhakar et al. (2007 Kumbhakar , S. C. , Park , B. U. , Simar , L. , Tsionas , E. ( 2007 ). Nonparametric stochastic frontiers: A local maximum likelihood approach . Journal of Econometrics 137 : 1 – 27 .[Crossref], [Web of Science ®] , [Google Scholar]). A Monte Carlo study is performed to shed light on the finite sample properties of these competing estimators.