Econometrica: Jul, 2003, Volume 71, Issue 4

A Conditional Likelihood Ratio Test for Structural Models

https://doi.org/10.1111/1468-0262.00438
p. 1027-1048

Marcelo J. Moreira

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.