英文文献：Testing the "Separability" Condition in Two-Stage Nonparametric Models of Production-生产的两阶段非参数模型的“可分性”条件检验
英文文献作者：Cinzia Daraio,Leopold Simar,Paul W. Wilson
英文文献摘要：
Simar and Wilson (J. Econometrics, 2007) provided a statistical model that can rationalize two-stage estimation of technical efficiency in nonparametric settings. Two-stage estimation has been widely used, but requires a strong assumption: the second-stage environmental variables cannot affect the support of the input and output variables in the first stage. In this paper, we provide a fully nonparametric test of this assumption. The test relies on new central limit theorem (CLT) results for unconditional efficiency estimators developed by Kneip et al. (Econometric Theory, 2015a) and new CLTs for conditional efficiency estimators developed in this paper. The test can be implemented relying on either asymptotic normality of the test statistics or using bootstrap methods to obtain critical values. Our simulation results indicate that our tests perform well both in terms of size and power. We present a real-world empirical example by updating the analysis performed by Aly et al. (R. E. Stat., 1990) on U.S. commercial banks; our tests easily reject the assumption required for two-stage estimation, calling into question results that appear in hundreds of papers that have been published in recent years.

Simar和Wilson (J. Econometrics, 2007)提供了一个统计模型，可以使非参数环境下技术效率的两阶段估计合理化。两阶段估计已经被广泛使用，但需要一个较强的假设:第二阶段的环境变量不能影响第一阶段输入和输出变量的支持度。本文给出了该假设的一个完全非参数检验。该检验依赖于Kneip等人(econom计量理论，2015a)开发的无条件效率估计量的新中心极限定理(CLT)结果和本文开发的条件效率估计量的新中心极限定理(CLT)结果。该检验可以依靠检验统计量的渐近正态性或使用bootstrap方法来获得临界值来实现。我们的仿真结果表明，我们的测试在尺寸和功率方面都表现良好。通过更新Aly等人(r.e. Stat, 1990)对美国商业银行的分析，我们提出了一个现实世界的实证例子;我们的测试很容易就否定了两阶段估算所需要的假设，并对近年来发表的数百篇论文中的结果提出了质疑。