Asymptotic Distribution of JIVE in a Heteroskedastic IV Regression with Many Instruments

61 Pages Posted: 31 May 2011

See all articles by John C. Chao

John C. Chao

University of Maryland

Norman R. Swanson

Rutgers University - Department of Economics; Rutgers, The State University of New Jersey - Department of Economics

Jerry A. Hausman

Massachusetts Institute of Technology (MIT) - Department of Economics; National Bureau of Economic Research (NBER)

Whitney K. Newey

Massachusetts Institute of Technology (MIT) - Department of Economics; National Bureau of Economic Research (NBER)

Tiemen Woutersen

University of Arizona

Date Written: August 1, 2009

Abstract

[enter Abstract Body]This paper derives the limiting distributions of alternative jackknife IV (JIV ) estimators and gives formulae for accompanying consistent standard errors in the presence of heteroskedasticity and many instruments. The asymptotic framework includes the many instrument sequence of Bekker (1994) and the many weak instrument sequence of Chao and Swanson (2005). We show that J IV estimators are asymptotically normal; and that standard errors are consistent provided that √Kn/rn → 0, as n → ∞, where Kn and rn denote, respectively, the number of instruments and the rate of growth of the concentration parameter. This is in contrast to the asymptotic behavior of such classical IV estimators as LIML, B2SLS, and 2SLS, 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 strength of the instruments as measured by the relative orders of magnitude of rn and Kn.

JEL Classification: C13, C31

Suggested Citation

Chao, John C. and Swanson, Norman Rasmus and Swanson, Norman Rasmus and Hausman, Jerry A. and Newey, Whitney K. and Woutersen, Tiemen, Asymptotic Distribution of JIVE in a Heteroskedastic IV Regression with Many Instruments (August 1, 2009). Available at SSRN: https://ssrn.com/abstract=1856038 or http://dx.doi.org/10.2139/ssrn.1856038

John C. Chao

University of Maryland ( email )

Department of Economics
College Park, MD 20742
United States
301-405-1579 (Phone)
301-408-3542 (Fax)

Norman Rasmus Swanson (Contact Author)

Rutgers University - Department of Economics ( email )

NJ
United States

HOME PAGE: http://econweb.rutgers.edu/nswanson/

Rutgers, The State University of New Jersey - Department of Economics ( email )

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HOME PAGE: http://econweb.rutgers.edu/nswanson/

Jerry A. Hausman

Massachusetts Institute of Technology (MIT) - Department of Economics ( email )

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National Bureau of Economic Research (NBER)

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Whitney K. Newey

Massachusetts Institute of Technology (MIT) - Department of Economics ( email )

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Cambridge, MA 02142
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National Bureau of Economic Research (NBER) ( email )

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Tiemen Woutersen

University of Arizona ( email )

Department of Economics
Tucson, AZ 85721
United States

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