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Choosing the number of moments in conditional moment restriction models

Author(s)
Imbens, Guido W.; Donald, Stephen G.; Newey, Whitney K.
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Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use.
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Abstract
Properties of GMM estimators are sensitive to the choice of instruments. Using many instruments leads to high asymptotic asymptotic efficiency but can cause high bias and/or variance in small samples. In this paper we develop and implement asymptotic mean square error (MSE) based criteria for instrumental variables to use for estimation of conditional moment restriction models. The models we consider include various nonlinear simultaneous equations models with unknown heteroskedasticity. We develop moment selection criteria for the familiar two-step optimal GMM estimator (GMM), a bias corrected version, and generalized empirical likelihood estimators (GEL), that include the continuous updating estimator (CUE) as a special case. We also find that the CUE has lower higher-order variance than the bias-corrected GMM estimator, and that the higher-order efficiency of other GEL estimators depends on conditional kurtosis of the moments.
URI
http://hdl.handle.net/1721.1/53516
Department
Massachusetts Institute of Technology. Department of Economics
Journal
Forthcoming in Econometrica
Citation
Newey, Whitney K., Guido Imbens and Stephen G. Donald. "Choosing the number of moments in conditional moment restriction models." Forthcoming in Econometrica.
Version: Author's final manuscript
Keywords
mean squared error, generalized empirical likelihood, generalized method of moments, conditional moment restrictions

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