A New Specification Test for the Validity of Instrumental Variables
提出一种新的设定检验，通过比较正向和反向两阶段最小二乘估计量或Nagar型估计量的差异，判断传统一阶渐近理论是否可靠，并推荐在无显著差异时使用有限信息最大似然估计。
We develop a new specification test for IV estimators adopting a particular second order approximation of Bekker. The new specification test compares the difference of the forward (conventional) 2SLS estimator of the coefficient of the right-hand side endogenous variable with the reverse 2SLS estimator of the same unknown parameter when the normalization is changed. Under the null hypothesis that conventional first order asymptotics provide a reliable guide to inference, the two estimates should be very similar. Our test sees whether the resulting difference in the two estimates satisfies the results of second order asymptotic theory. Essentially the same idea is applied to develop another new specification test using second-order unbiased estimators of the type first proposed by Nagar. If the forward and reverse Nagar-type estimators are not significantly different we recommend estimation by LIML, which we demonstrate is the optimal linear combination of the Nagar-type estimators (to second order). We also demonstrate the high degree of similarity for "k"-class estimators between the approach of Bekker and the Edgeworth expansion approach of Rothenberg. An empirical example and Monte Carlo evidence demonstrate the operation of the new specification test. Copyright The Econometric Society 2002.