Testing overidentifying restrictions with a restricted parameter space

Abstract

We show that the standard test for testing overidentifying restrictions, which compares the J-statistic (Hansen, 1982) to χ2 critical values, does not control asymptotic size when the true parameter vector is allowed to lie on the boundary of the (optimization) parameter space. We also propose a modified J-statistic that, under the null hypothesis, is asymptotically χ2 distributed, such that the resulting test does control asymptotic size.