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INSTRUMENTAL VARIABLE ESTIMATION IN A DATARICH ENVIRONMENT

Published online by Cambridge University Press:  17 March 2010

Jushan Bai  and
Serena Ng
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Abstract

We consider estimation of parameters in a regressionmodel with endogenous regressors. The endogenousregressors along with a large number of otherendogenous variables are driven by a small number ofunobservable exogenous common factors. We show thatthe estimated common factors can be used asinstrumental variables and they are more efficientthan the observed variables in our framework.Whereas standard optimal generalized method ofmoments estimator using a large number ofinstruments is biased and can be inconsistent, thefactor instrumental variable estimator (FIV) isshown to be consistent and asymptotically normal,even if the number of instruments exceeds the samplesize. Furthermore, FIV remains consistent even ifthe observed variables are invalid instruments aslong as the unobserved common components are validinstruments. We also consider estimating panel datamodels in which all regressors are endogenous butshare exogenous common factors. We show that validinstruments can be constructed from the endogenousregressors. Although single equation FIV requires nobias correction, the faster convergence rate of thepanel estimator is such that a bias correction isnecessary to obtain a zero-centered normaldistribution.

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Type
Research Article
Information
Econometric Theory , Volume 26 , Issue 6 , December 2010 , pp. 1577 - 1606
Copyright
Copyright © Cambridge University Press 2010

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Footnotes

This paper was presented at Columbia, Duke,Harvard/MIT, Michigan, Queen’s, Yale, UCSD, UCR,UPenn, Wisconsin, Institute of Statistics atUniversite Catholique de Louvain, and SETA in HongKong. We thank seminar participants, GuidoKuersteiner (the co-editor), and two anonymousreferees for many helpful comments andsuggestions. We also acknowledge financial supportfrom the NSF (grants SES-0551275 andSES-0549978).

References

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