NATIONAL BUREAU OF ECONOMIC RESEARCH
NATIONAL BUREAU OF ECONOMIC RESEARCH

Inference with Weak Instruments

Donald W.K. Andrews, James H. Stock

NBER Technical Working Paper No. 313
Issued in August 2005

This paper reviews recent developments in methods for dealing with weak instruments (IVs) in IV regression models. The focus is more on tests and confidence intervals derived from tests than on estimators. The paper also presents new testing results under "many weak IV asymptotics," which are relevant when the number of IVs is large and the coefficients on the IVs are relatively small. Asymptotic power envelopes for invariant tests are established. Power comparisons of the conditional likelihood ratio (CLR), Anderson- Rubin, and Lagrange multiplier tests are made. Numerical results show that the CLR test is on the asymptotic power envelope. This holds no matter what the relative magnitude of the IV strength to the number of IVs.

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Document Object Identifier (DOI): 10.3386/t0313

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