Economics at your fingertips  

Asymptotic Normality of Single-Equation Estimators for the Case with a Large Number of Weak Instruments

John Chao () and Norman Swanson ()

Departmental Working Papers from Rutgers University, Department of Economics

Abstract: This paper analyzes conditions under which various single-equation estimators are asymptotically normal in a simultaneous equations framework with many weak instruments. In particular, our paper adds to the many instruments asymptotic normality literature, including papers by Morimune (1983), Bekker (1994), Angrist and Krueger (1995), Donald and Newey (2001), Hahn, Hausman, and Kuersteiner (2001), and Stock and Yogo (2003). We consider the case where instrument weakness is such that rn, the rate of growth of the concentration parameter, is slower than Kn, the growth rate of the number of instruments, but such that Kn^.5/rn --> 0 as n --> 1: In this case, the rate of convergence is shown to be rn/Kn^.5 . We also show that formulae for the asymptotic variances of various single-equation estimators are di®erent from those obtained under assumptions of stronger instruments, i.e., cases where rn is assumed to grow at the same rate or at a faster rate than Kn. An interesting finding of this paper is that, for the case we study here, both the LIML and the Fuller estimators can be shown to be asymptotically more e±cient than the B2SLS estimator not just for the case where the error distributions are assumed to be Gaussian but for all error distributions that lie within the elliptical family.

Keywords: CLT for bilinear forms; instrumental variables; k-class estimator; local-to-zero framework; pathwise asymptotics, weak instruments (search for similar items in EconPapers)
JEL-codes: C13 C31 (search for similar items in EconPapers)
Date: 2003-10-20
New Economics Papers: this item is included in nep-ecm
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (5) Track citations by RSS feed

Downloads: (external link) (application/pdf)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link:

Access Statistics for this paper

More papers in Departmental Working Papers from Rutgers University, Department of Economics Contact information at EDIRC.
Bibliographic data for series maintained by ().

Page updated 2020-01-18
Handle: RePEc:rut:rutres:200312