ON GMM INFERENCE: PARTIAL IDENTIFICATION, IDENTIFICATION STRENGTH, AND NONSTANDARD ASYMPTOTICS
研究了在标准正则条件可能失效时，广义矩方法（GMM）推断的渐近性质，推导了估计量和检验统计量的解析分布，适用于弱识别、部分识别等非标准情形。
This paper analyses aspects of generalized method of moments (GMM) inference in moment equality models in settings where standard regularity conditions may break down. Explicit analytic formulations for the asymptotic distributions of estimable functions of the GMM estimator and statistics based on the GMM criterion function are derived under relatively mild assumptions. The moment Jacobian is allowed to be rank deficient, so first order identification may fail, the values of the Jacobian singular values are not constrained, thereby allowing for varying levels of identification strength, the long-run variance of the moment conditions can be singular, and the GMM criterion function weighting matrix may also be chosen sub-optimally. The large-sample properties are derived without imposing a specific structure on the functional form of the moment conditions. Closed-form expressions for the distributions are presented that can be evaluated using standard software without recourse to bootstrap or simulation methods. The practical operation of the results is illustrated via examples involving instrumental variables estimation of a structural equation with endogenous regressors and a common CH features model.