Asymptotic distribution of JIVE in a heteroskedastic IV regression with many instruments

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

Research output: Contribution to journalArticle

29 Scopus citations

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 √K n/r n → 0 as n → ∞, where K n and r 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 n/r 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 n and K n.

Original languageEnglish (US)
Pages (from-to)42-86
Number of pages45
JournalEconometric Theory
Volume28
Issue number1
DOIs
StatePublished - Feb 1 2012
Externally publishedYes

ASJC Scopus subject areas

  • Social Sciences (miscellaneous)
  • Economics and Econometrics

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