ASYMPTOTIC DISTRIBUTION OF JIVE IN A HETEROSKEDASTIC IV REGRESSION WITH MANY INSTRUMENTS
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Hausman_Asymptotic Distribution.pdf
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Author(s)
Chao, John C.
Swanson, Norman R.
Hausman, Jerry A.
Newey, Whitney K.
Woutersen, Tiemen
Date Issued
September 2011
Journal
Econometric Theory
Publisher
Cambridge University Press
Citation
Chao, John C., Norman R. Swanson, Jerry A. Hausman, Whitney K. Newey, and Tiemen Woutersen. “ASYMPTOTIC DISTRIBUTION OF JIVE IN A HETEROSKEDASTIC IV REGRESSION WITH MANY INSTRUMENTS.” Econometric Theory 28, no. 01 (February 13, 2012): 42-86. © Cambridge University Press 2011
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Final published version
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 K[subscript n] and r[subscript n] 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 K[subscript n]/r[subscript n]→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 r[subscript n] and K[subscript n].
MIT Department
Massachusetts Institute of Technology. Department of Economics
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DOI of Published Version
https://doi.org/10.1017/s0266466611000120
