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Overidentification in Regular Models

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In the unconditional moment restriction model of Hansen (1982), speci"cation tests and more e"icient estimators are both available whenever the number of moment restrictions exceeds the number of parameters of interest. We show a similar relationship between potential refutability of a model and existence of more e"icient estimators is present in much broader settings. Speci"cally, a condition we name local overidenti"cation is shown to be equivalent to both the existence of speci"cation tests with nontrivial local power and the existence of more e"icient estimators of some "smooth" parameters in general semi/nonparametric models. Under our notion of local overidenti"cation, various locally nontrivial speci"cation 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 overidenti"cation for general models of nonparametric conditional moment restrictions with possibly di"erent conditioning sets. The results are applied to determining when semi/nonparametric models with endogeneity are locally testable, and when nonparametric plug-in and semiparametric two-step GMM estimators are semiparametrically e"icient. Examples of empirically relevant semi/nonparametric structural models are presented.

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  • Xiaohong Chen & Andres Santos, 2015. "Overidentification in Regular Models," Cowles Foundation Discussion Papers 1999R, Cowles Foundation for Research in Economics, Yale University, revised Jun 2018.
  • Handle: RePEc:cwl:cwldpp:1999r
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