Increasing the power of moment-based tests

This paper shows how to increase the power of the Hansen (1982) test for the case where only a subset of the exclusion restrictions is used. The ‘ignored’ exclusion restrictions are used to derive a new estimator for the covariance matrix, which has a different probability limit than the usual one when the model is false. If the null hypothesis is true, then the proposed test has the same distribution as the existing ones in large samples. If the hypothesis is false, then the proposed test statistic is larger with probability approaching one as the sample size increases in several important examples. Simulations show that the improvement can be substantial. As the Hansen (1982) test is very popular in empirical work, including testing the validity of Euler equations, we expect the current results to be useful as well.