TY  - JOUR
AU  - Stock,James H.
AU  - Yogo,Motohiro
TI  - Testing for Weak Instruments in Linear IV Regression
JF  - National Bureau of Economic Research Technical Working Paper Series
VL  - No. 284
PY  - 2002
Y2  - November 2002
UR  - http://www.nber.org/papers/t0284
L1  - http://www.nber.org/papers/t0284.pdf
N1  - Author contact info:
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

Motohiro Yogo
Federal Reserve Bank of Minneapolis
Research Department
90 Hennepin Avenue
Minneapolis, MN 55401-1804
Tel: 612/204-6476
E-Mail: yogo@minneapolisfed.org
AB  - Weak instruments can produce biased IV estimators and hypothesis tests with large size distortions. But what, precisely, are weak instruments, and how does one detect them in practice? This paper proposes quantitative definitions of weak instruments based on the maximum IV estimator bias, or the maximum Wald test size distortion, when there are multiple endogenous regressors. We tabulate critical values that enable using the first-stage F-statistic (or, when there are multiple endogenous regressors, the Cragg-Donald (1993) statistic) to test whether given instruments are weak. A technical contribution is to justify sequential asymptotic approximations for IV statistics with many weak instruments.
ER  -