TY  - JOUR
AU  - Staiger,Douglas
AU  - Stock,James H.
TI  - Instrumental Variables Regression with Weak Instruments
JF  - National Bureau of Economic Research Technical Working Paper Series
VL  - No. 151
PY  - 1994
Y2  - January 1994
UR  - http://www.nber.org/papers/t0151
L1  - http://www.nber.org/papers/t0151.pdf
N1  - Author contact info:
Douglas O. Staiger
Dartmouth College
Department of Economics
HB6106, 301 Rockefeller Hall
Hanover, NH 03755-3514
Tel: 603/646-2979
Fax: 603/646-2122
E-Mail: douglas.staiger@dartmouth.edu

James H. Stock
Department of Economics
Harvard University
Littauer Center M27
Cambridge, MA 02138
Tel: 617/496-0502
Fax: 617/495-7730
E-Mail: James_Stock@harvard.edu
AB  - 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%).
ER  -