Hausman, Jerry: A New Specification Test for the Validity of Instrumental Variables
World Conference Econometric Society, 2000, Seattle

Jinyong Hahn, University of Pennsylvania
Jerry Hausman, Massachusetts Institute of Technology
A New Specification Test for the Validity of Instrumental Variables
Session: C-2-19  Saturday 12 August 2000  by Hausman, Jerry
We develop a new specification test for the IV estimators adopting a particular second order approximation of Bekker (1994). 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 provides a reliable guide, 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 (1959). If the forward and reverse Nagar-type estimators are not significantly different we recommend estimation by LIML, which we demonstrate is the otpimal 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 (1994) and the Edgeworth expansion approach of Rothenberg (1983). Empirical examples and Monte Carlo evidence are provided.

File created by Jurgen Doornik with eswc2000.ox on 2-01-2001