A New Random Normalizing Approach to the M Test without Recursive Estimations

The traditional M test requires a consistent estimation of the asymptotic variancecovariance matrix of the estimated moments (the AVC matrix). By extending the approach of Kiefer, Vogelsang, and Bunzel (KVB; 2000, Econometrica), Kuan and Lee (KL; 2006, Journal of the American Statistical Association) contributed a new type of M test without the AVC matrix estimation but with recursive model estimations. By focusing on testing model correctness, we propose another new type of M test without the AVC matrix estimation and without recursive model estimations. The proposed approach is based on a “discretized” random normalizing matrix. It has computational and theoretical advantages over the KVB-KL approach in testing model correctness. In particular, the proposed M test statistic is simpler to compute, and has a F distribution in large samples. Our M test can also be designed to be asymptotically equivalent to the traditional M test and asymptotically more powerful than the KVB-KL M test under local alternatives. JEL classification: C12, C15