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

Abstract

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 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.

Keywords:

• Conditional moment restrictions
• test statistic
• hypothesis testing

Acknowledgements

We are grateful to the anonymous referee, an associate editor and the co-editor for helpful and constructive comments on earlier versions.

Additional information

Funding

Chen’s research is supported in part by National Nature Science Foundation of China (Project Nos. 11871477 and 11401593) and Hunan Provincial Natural Science Foundation of China (Project No. 2016JJ3138). Yan Zhou’s research was supported by the National Science Foundation of China (Grant No. 11701385), National Statistical Research Project (Grant No. 2017LY56) and Doctor start fund of Guangdong Province (Grant No. 2016A030310062).