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Choosing the number of moments in conditional moment restriction models
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gmmsel pub.pdf
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398.84 KB
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Adobe PDF
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eca1aff559b605daf425c5f4d4610969
Author(s)
Imbens, Guido W.
Donald, Stephen G.
Newey, Whitney K.
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
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.
Subjects
mean squared error
generalized empirical likelihood
generalized method of moments
conditional moment restrictions
MIT Department
Massachusetts Institute of Technology. Department of Economics
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