ON STANDARD INFERENCE FOR GMM WITH LOCAL IDENTIFICATION FAILURE OF KNOWN FORMS
研究了当矩条件的雅可比矩阵在真实参数处秩不足时，如何利用其已知形式信息使GMM估计量和过度识别检验恢复标准性质，并应用于资产收益的条件异方差特征推断。
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).