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Overidentification in Regular Models

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  • Xiaohong Chen
  • Andres Santos

Abstract

In the unconditional moment restriction model of Hansen (), 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/nonparametric 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.

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  • Xiaohong Chen & Andres Santos, 2018. "Overidentification in Regular Models," Econometrica, Econometric Society, vol. 86(5), pages 1771-1817, September.
  • Handle: RePEc:wly:emetrp:v:86:y:2018:i:5:p:1771-1817
    DOI: 10.3982/ECTA13559
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    5. Hidehiko Ichimura & Whitney K. Newey, 2022. "The influence function of semiparametric estimators," Quantitative Economics, Econometric Society, vol. 13(1), pages 29-61, January.
    6. Christoph Breunig, 2019. "Specification Testing in Nonparametric Instrumental Quantile Regression," Papers 1909.10129, arXiv.org.
    7. Haitian Xie, 2020. "Efficient and Robust Estimation of the Generalized LATE Model," Papers 2001.06746, arXiv.org, revised Feb 2022.
    8. Shantanu Gupta & Zachary C. Lipton & David Childers, 2020. "Estimating Treatment Effects with Observed Confounders and Mediators," Papers 2003.11991, arXiv.org, revised Jun 2021.
    9. Rahul Singh, 2021. "A Finite Sample Theorem for Longitudinal Causal Inference with Machine Learning: Long Term, Dynamic, and Mediated Effects," Papers 2112.14249, arXiv.org.
    10. Andres Santos, 2020. "A Comment on: “On the Informativeness of Descriptive Statistics for Structural Estimates” by Isaiah Andrews, Matthew Gentzkow, and Jesse M. Shapiro," Econometrica, Econometric Society, vol. 88(6), pages 2271-2276, November.

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