参见Greene(2008), pp.155, Section 2.6.2
Greene, W. 2008, The Econometric Approach to Efficiency Analysis[C], in H. O. Fried, C. Lovell,S. S. Schmidt eds, The Measurement of Productive Efficiency and Productivity Change 92-251. (http://pages.stern.nyu.edu/~wgreene/StochasticFrontierModels.pdf)
Wang(2002)
Wang, H., 2002, Heteroscedasticity and non-monotonic efficiency effects of a stochastic frontier model, Journal of Productivity Analysis, 18 (3): 241-253.
One of the most important recent developments lies in the investigation of how exogenous factors influence the one-sided inefficiency effect. This effort allows researchers to understand not only the production unit’s state of efficiency, but also the contributing factors of the efficiency. Kumbhakar and Lovell (2000, Chapter 7) discuss in detail how the literature evolves from the early two-step approach, by which inefficiency and exogenous effects are identified sequentially, to the more recent one-step approach by which the exogenous effects are estimated simultaneously with the model’s other parameters. The extensive Monte Carlo results presented by Schmidt and Wang (2002) give evidence in favor of the one-step approach.
Kumbhakar, S., C. Lovell. Stochastic Frontier Analysis[M]. Cambridge: Cambridge University Press, 2000.
Coelli et al.(1998), p207
Coelli, T., D. Prasada Rao, G. E. Battese. An Introduction to Efficiency and Productivity Analysis[M]. Boston: Kluwer Academic Publishers 1998.
使用SFA模型的一个主要目的是研究影响效率的因素,早期的文献主要使用两步法(two-stage approach),而近期的文献则主要使用一步法。
在两步法的第一步是估计SFA模型并得到TE的估计值,在第二步中再以TE为被解释变量与理论上可能影响效率的因素进行回归分析。这种处理方式主要存在如下两个方面的问题。其一,研究假设前后矛盾。在第一阶段的分析中,需要假设无效率项u是独立同分布的,即iid,唯有如此才能使用Jondrow et al.(1982)提出的方法估算效率值TE。然而,在第二步中,TE被设定为一系列公司特征变量的函数,这意味着TE并不是独立同分布的,这与第一步中的假设相矛盾(Coelli et al.(1998), pp.207)。