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INSTRUMENTAL VARIABLE ESTIMATION IN A DATA RICH 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 regression model with endogenous regressors. The endogenous regressors along with a large number of other endogenous variables are driven by a small number of unobservable exogenous common factors. We show that the estimated common factors can be used as instrumental variables and they are more efficient than the observed variables in our framework. Whereas standard optimal generalized method of moments estimator using a large number of instruments is biased and can be inconsistent, the factor instrumental variable estimator (FIV) is shown to be consistent and asymptotically normal, even if the number of instruments exceeds the sample size. Furthermore, FIV remains consistent even if the observed variables are invalid instruments as long as the unobserved common components are valid instruments. We also consider estimating panel data models in which all regressors are endogenous but share exogenous common factors. We show that valid instruments can be constructed from the endogenous regressors. Although single equation FIV requires no bias correction, the faster convergence rate of the panel estimator is such that a bias correction is necessary to obtain a zero-centered normal distribution.

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 at Universite Catholique de Louvain, and SETA in Hong Kong. We thank seminar participants, Guido Kuersteiner (the co-editor), and two anonymous referees for many helpful comments and suggestions. We also acknowledge financial support from the NSF (grants SES-0551275 and SES-0549978).

References

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