New test statistics for hypothesis testing of parameters in conditional moment restriction models

Based on the difference in the objective function proposed by Dominguez and Lobato between the unconstrained and constrained estimators, a simply test is proposed for hypothesis testing of parameters in conditional moment restriction models. This test is guaranteed to be consistent. The asymptotic distribution of the proposed test statistic is proved to be a linear combination of independent χ²₁ random variables under the null hypothesis. In the simulation study, the power of the proposed test is larger than that of the GMM based test under the alternative hypothesis.