Asymptotic Distributions of Instrumental Variables Statistics with Many Instruments

Stock, James H.; Yogo, Motohiro

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Asymptotic Distributions of Instrumental Variables Statistics with Many Instruments

IDENTIFICATION AND INFERENCE FOR ECONOMETRIC MODELS: ESSAYS IN HONOR OF THOMAS ROTHENBERG, Ch. 6, 2005

23 Pages Posted: 5 Jan 2011 Last revised: 31 Jul 2013

See all articles by James H. Stock

James H. Stock

Harvard University - Department of Economics; National Bureau of Economic Research (NBER); Harvard University - Harvard Kennedy School (HKS)

Motohiro Yogo

Princeton University - Department of Economics; National Bureau of Economic Research

Date Written: September 10, 2004

Abstract

This paper extends Staiger and Stock’s (1997) weak instrument asymptotic approximations to the case of many weak instruments by modeling the number of instruments as increasing slowly with the number of observations. It is shown that the resulting “many weak instrument” approximations can be calculated sequentially by letting first the sample size, and then the number of instruments, tend to infinity. The resulting distributions are given for k-class estimators and test statistics.

JEL Classification: C01

Suggested Citation: Suggested Citation

Stock, James H. and Yogo, Motohiro, Asymptotic Distributions of Instrumental Variables Statistics with Many Instruments (September 10, 2004). IDENTIFICATION AND INFERENCE FOR ECONOMETRIC MODELS: ESSAYS IN HONOR OF THOMAS ROTHENBERG, Ch. 6, 2005, Available at SSRN: https://ssrn.com/abstract=1734937