NATIONAL BUREAU OF ECONOMIC RESEARCH
NATIONAL BUREAU OF ECONOMIC RESEARCH

The Distribution of the Instrumental Variables Estimator and Its t-RatioWhen the Instrument is a Poor One

Charles R. Nelson, Richard Startz

NBER Technical Working Paper No. 69
Issued in September 1988
NBER Program(s):   ME

When the instrumental variable is a poor one, in the sense of being weakly correlated with the variable it proxies, the small sample distribution of the IV estimator is concentrated around a value that is inversely related to the feedback in the system and which is often further from the true value than is the plim of OLS. The sample variance of residuals similarly becomes concentrated around a value which reflects feedback and not the variance of the disturbance. The distribution of the t-ratio reflects both of these effects, stronger feedback producing larger t-ratios. Thus, in situations where OLS is badly biased, a poor instrument will lead to spurious inferences under IV estimation with high probability, and generally perform worse than OLS.

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Document Object Identifier (DOI): 10.3386/t0069

Published: Econometrica, April 1990.

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