Asymptotic JIVE

Asymptotic JIVE - Asymptotic Distribution of JIVE in a...

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Asymptotic Distribution of JIVE in a Heteroskedastic IV Regres- sion with Many Instruments John C. Chao, Department of Economics, University of Maryland, chao@econ.umd.edu. Norman R. Swanson, Department of Economics, Rutgers University, nswanson@econ.rutgers.edu. Jerry A. Hausman, Department of Economics, MIT, jhausman@mit.edu. Whitney K. Newey, Department of Economics, MIT, wnewey@mit.edu. Tiemen Woutersen, Department of Economics, Johns Hopkins University, woutersen@jhu.edu. August, 2007 Revised August, 2009 JEL classi f cation: C13, C31. Keywords : heteroskedasticity, instrumental variables, jackknife estimation, many instruments, weak instruments. * 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, M.Moriera, G.D.A. Phillips, P.C.B. Phillips, and J. Stock for helpful discussions .
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Proposed Running Head: JIVE With Heteroskedasticity Corresponding Author: Whitney K. Newey Department of Economics MIT, E52-262D Cambridge, MA 02142-1347 Abstract 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 estimators are asymptotically normal; and that standard errors are consistent provided that K n r n 0 , as n →∞ ,where K n and r n 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 , B 2 SLS ,and2 , all of which are inconsistent in the presence of heteroskedasticity, unless K n r n 0. We also show that the rate of convergence and the form of the asymptotic covariance matrix of the estimators will in general depend on strength of the instruments as measured by the relative orders of magnitude of r n and K n . 1
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1I n t r o d u c t i o n It has long been known that the two-stage least squares (2 SLS ) estimator is biased with many instruments (see e.g. Sawa (1969), Phillips (1983), and the references cited therein). Due in large part to this problem, various approaches have been proposed in the literature for reducing the bias of the 2 estimator. In recent years there has been interest in developing procedures based on using “delete-one” f tted values in lieu of the usual f rst-stage OLS f tted values, as the instruments employed in second stage estimation. A number of di f erent versions of these estimators, referred to as jackknife instrumental variables ( JIV ) estimators, have been proposed and analyzed by Phillips
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This note was uploaded on 12/26/2011 for the course ECON 245a taught by Professor Staff during the Fall '08 term at UCSB.

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Asymptotic JIVE - Asymptotic Distribution of JIVE in a...

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