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ASYMPTOTIC DISTRIBUTION OF JIVE IN A HETEROSKEDASTIC IV REGRESSION WITH MANY INSTRUMENTS

Published online by Cambridge University Press:  13 September 2011

John C. Chao ,
Norman R. Swanson ,
Jerry A. Hausman ,
Whitney K. Newey  and
Tiemen Woutersen
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Abstract

This paper derives the limiting distributions of alternative jackknife instrumental variables (JIV) estimators and gives formulas for accompanying consistent standard errors in the presence of heteroskedasticity and many instruments. The asymptotic framework includes the many instrument sequence of Bekker (1994, Econometrica 62, 657–681) and the many weak instrument sequence of Chao and Swanson (2005, Econometrica 73, 1673–1691). We show that JIV estimators are asymptotically normal and that standard errors are consistent provided that as n→∞, where Kn and rn denote, respectively, the number of instruments and the concentration parameter. This is in contrast to the asymptotic behavior of such classical instrumental variables estimators as limited information maximum likelihood, bias-corrected two-stage least squares, and two-stage least squares, all of which are inconsistent in the presence of heteroskedasticity, unless Kn/rn→0. We also show that the rate of convergence and the form of the asymptotic covariance matrix of the JIV estimators will in general depend on the strength of the instruments as measured by the relative orders of magnitude of rn and Kn.

Type
Research Article
Information
Econometric Theory , Volume 28 , Issue 1 , February 2012 , pp. 42 - 86
Copyright
Copyright © Cambridge University Press 2011

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Footnotes

Earlier versions of this paper were presented at the NSF/NBER conference on weak and/or many instruments at MIT in 2003 and at the 2004 winter meetings of the Econometric Society in San Diego, where conference participants provided many useful comments and suggestions. Particular thanks are owed to D. Ackerberg, D. Andrews, J. Angrist, M. Caner, M. Carrasco, P. Guggenberger, J. Hahn, G. Imbens, R. Klein, N. Lott, M. Moriera, G.D.A. Phillips, P.C.B. Phillips, J. Stock, J. Wright, two anonymous referees, and a co-editor for helpful comments and suggestions.

References

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