Instrumental Variables Regression with Weak Instruments

71 Pages Posted: 15 Sep 2000 Last revised: 2 Jun 2023

See all articles by Douglas Staiger

Douglas Staiger

Dartmouth College - Department of Economics; National Bureau of Economic Research (NBER)

James H. Stock

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

Date Written: January 1994

Abstract

This paper develops asymptotic distribution theory for instrumental variable regression when the partial correlation between the instruments and a single included endogenous variable is weak, here modeled as local to zero. Asymptotic representations are provided for various instrumental variable statistics, including the two-stage least squares (TSLS) and limited information maximum- likelihood (LIML) estimators and their t-statistics. The asymptotic distributions are found to provide good approximations to sampling distributions with just 20 observations per instrument. Even in large samples, TSLS can be badly biased, but LIML is, in many cases, approximately median unbiased. The theory suggests concrete quantitative guidelines for applied work. These guidelines help to interpret Angrist and Krueger's (1991) estimates of the returns to education: whereas TSLS estimates with many instruments approach the OLS estimate of 6%, the more reliable LIML and TSLS estimates with fewer instruments fall between 8% and 10%, with a typical confidence interval of (6%, 14%).

Suggested Citation

Staiger, Douglas and Stock, James H., Instrumental Variables Regression with Weak Instruments (January 1994). NBER Working Paper No. t0151, Available at SSRN: https://ssrn.com/abstract=225111

Douglas Staiger (Contact Author)

Dartmouth College - Department of Economics ( email )

Hanover, NH 03755
United States
603-643-2979 (Phone)

National Bureau of Economic Research (NBER)

1050 Massachusetts Avenue
Cambridge, MA 02138
United States

James H. Stock

Harvard University - Department of Economics ( email )

Littauer Center
Cambridge, MA 02138
United States
617-496-0502 (Phone)
617-496-5960 (Fax)

National Bureau of Economic Research (NBER)

1050 Massachusetts Avenue
Cambridge, MA 02138
United States

Harvard University - Harvard Kennedy School (HKS) ( email )

79 John F. Kennedy Street
Cambridge, MA 02138
United States