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FINITE-SAMPLE INSTRUMENTAL VARIABLES INFERENCE USING AN ASYMPTOTICALLY PIVOTAL STATISTIC

Published online by Cambridge University Press:  04 August 2003

Paul Bekker  and
Frank Kleibergen
Paul Bekker
Affiliation:
University of Groningen
Frank Kleibergen
Affiliation:
University of Amsterdam
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Abstract

We consider the K-statistic, Kleibergen's (2002, Econometrica 70, 1781–1803) adaptation of the Anderson–Rubin (AR) statistic in instrumental variables regression. Whereas Kleibergen (2002) especially analyzes the asymptotic behavior of the statistic, we focus on finite-sample properties in a Gaussian framework. The AR statistic then has an F-distribution. The finite-sample distribution of the K-statistic is, however, affected by nuisance parameters. We consider two extreme cases for the nuisance parameters, which provide tight bounds for the exact distribution. The first case amounts to perfect identification—which is similar to the asymptotic case—where the statistic has an F-distribution. In the other extreme case there is total underidentification. For the latter case we show how to compute the exact distribution. We thus provide tight bounds for exact confidence sets based on the K-statistic. Asymptotically the two bounds converge, except when there is a large number of redundant instruments.The authors' research documented in this paper has been funded by the NWO Vernieuwingsimpuls research grant “Empirical Comparison of Economic Models.”

Type
Research Article
Information
Econometric Theory , Volume 19 , Issue 5 , October 2003 , pp. 744 - 753
Copyright
© 2003 Cambridge University Press

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References

REFERENCES

Anderson, T.W. & H. Rubin (1949) Estimators on the parameters of a single equation in a complete set of stochastic equations. Annals of Mathematical Statistics 21, 570–582.Google Scholar
Bekker, P.A. (1994) Alternative approximations to the distributions of instrumental variable estimators. Econometrica 62, 657–681.Google Scholar
Hausman, J. & J. Hahn (1999) A New Specification Test for the Validity of Instrumental Variables. Working paper, Massachusetts Institute of Technology.
Kleibergen, F. (2002) Pivotal statistics for testing structural parameters in instrumental variables regression. Econometrica 70, 1781–1803.Google Scholar
Nelson, C.R. & R. Startz (1990) Some further results on the exact small sample properties of the instrumental variables estimator. Econometrica 58, 967–976.Google Scholar
Sargan, J.D. & A. Bhargava (1983) Testing residuals from least squares regression for being generated by the Gaussian random walk. Econometrica 51, 153–174.Google Scholar
Staiger, D. & J.H. Stock (1997) Instrumental variables regression with weak instruments. Econometrica 65, 557–586.Google Scholar
Zivot, E., R. Startz, & C.R. Nelson (1998) Valid confidence intervals and inference in the presence of weak instruments. International Economic Review 39, 1119–1144.Google Scholar