OVERIDENTIFICATION IN REGULAR MODELS

• 成果类型: Article
• 署名作者: Chen, Xiaohong; Santos, Andres
• 署名单位: Yale University; University of California System; University of California Los Angeles
• 刊物名称: ECONOMETRICA
• ISSN/ISSBN: 0012-9682
• DOI: 10.3982/ECTA13559
• 发表日期: 2018
• 页码: 1771-1817
• 关键词: asymptotic efficiency; nonparametric-estimation; Moment restrictions; generalized-method; identification; inference; INFORMATION; EQUATIONS; parameter; bounds

摘要

In the unconditional moment restriction model of Hansen (1982), specification tests and more efficient estimators are both available whenever the number of moment restrictions exceeds the number of parameters of interest. We show that a similar relationship between potential refutability of a model and existence of more efficient estimators is present in much broader settings. Specifically, a condition we name local overidentification is shown to be equivalent to both the existence of specification tests with nontrivial local power and the existence of more efficient estimators of some smooth parameters in general semi/nonparametric models. Under our notion of local overidentification, various locally nontrivial specification tests such as Hausman tests, incremental Sargan tests (or optimally weighted quasi likelihood ratio tests) naturally extend to general semi/nonparametric settings. We further obtain simple characterizations of local overidentification for general models of nonparametric conditional moment restrictions with possibly different conditioning sets. The results are applied to determining when semi/non-parametric models with endogeneity are locally testable, and when nonparametric plug-in and semiparametric two-step GMM estimators are semiparametrically efficient. Examples of empirically relevant semi/nonparametric structural models are presented.