Published online by Cambridge University Press: 06 June 2017
This paper studies the GMM estimation and inference problem that occurs when the Jacobian of the moment conditions is rank deficient of known forms at the true parameter values. Dovonon and Renault (2013) recently raised a local identification issue stemming from this type of degenerate Jacobian. The local identification issue leads to a slow rate of convergence of the GMM estimator and a nonstandard asymptotic distribution of the over-identification test statistics. We show that the known form of rank-deficient Jacobian matrix contains nontrivial information about the economic model. By exploiting such information in estimation, we provide GMM estimator and over-identification tests with standard properties. The main theory developed in this paper is applied to the estimation of and inference about the common conditionally heteroskedastic (CH) features in asset returns. The performances of the newly proposed GMM estimators and over-identification tests are investigated under the similar simulation designs used in Dovonon and Renault (2013).
We acknowledge useful comments from Don Andrews, Anil Bera, Xu Cheng, Denis Chetverikov, Yanqin Fan, Jonathan Gu, Jinyong Hahn, Guofang Huang, Roger Koenker, Ivana Komunjer, Rosa Matzkin, Peter Phillips, Shuyang Sheng, Ruoyao Shi, Yixiao Sun, and participants in Econometrics seminar at UC Davis, UCLA, UCSD, UIUC, Yale and 2014 Seattle-Vancouver Econometrics Conference. We also thank the Co-Editor, Anna Mikusheva, and two anonymous referees for constructive suggestions which improved this paper through the revision processes. The vast amount of outstanding editorial input by the Editor, Professor Phillips, on our last version of the manuscript is extremely appreciated. Any errors are the responsibility of the authors.