A Conditional Likelihood Ratio Test for Structural Models
Econometrica · 2003 · Volume 71 · Issue 4
Abstract
This paper develops a general method for constructing exactly similar tests based on the conditional distribution of nonpivotal statistics in a simultaneous equations model with normal errors and known reduced-form covariance matrix. These tests are shown to be similar under weak-instrument asymptotics when the reduced-form covariance matrix is estimated and the errors are non-normal. The conditional test based on the likelihood ratio statistic is particularly simple and has good power properties. Like the score test, it is optimal under the usual local-to-null asymptotics, but it has better power when identification is weak.
Keywords
Instruments, similar tests, Wald test, score test, likelihood ratio test, confidence regions, 2SLS estimator, LIML estimator
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