TY  - JOUR
AU  - Stock,James H.
AU  - Wright,Jonathan
TI  - Asymptotics for GMM Estimators with Weak Instruments
JF  - National Bureau of Economic Research Technical Working Paper Series
VL  - No. 198
PY  - 1996
Y2  - July 1996
UR  - http://www.nber.org/papers/t0198
L1  - http://www.nber.org/papers/t0198.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

Jonathan H. Wright
Department of Economics
Johns Hopkins University
3400 N. Charles Street
Baltimore, MD 21218
Tel: 410/516-5728
Fax: 410/516-7600
E-Mail: wrightj@jhu.edu
AB  - This paper develops asymptotic distribution theory for generalized method of moments (GMM) estimators and test statistics when some of the parameters are well identified, but others are poorly identified because of weak instruments.  The asymptotic theory entails applying empirical process theory to obtain a limiting representation of the (concentrated) objective function as a stochastic process.  The general results are specialized to two leading cases, linear instrumental variables regression and GMM estimation of Euler equations obtained from the consumption-based capital asset pricing model with power utility.  Numerical results of the latter model confirm that finite sample distributions can deviate substantially from normality, and indicate that these deviations are captured by the weak instrument asymptotic approximations.
ER  -