Journal Of The Econometric Society

An International Society for the Advancement of Economic
Theory in its Relation to Statistics and Mathematics

Edited by: Guido W. Imbens • Print ISSN: 0012-9682 • Online ISSN: 1468-0262

Econometrica: Sep, 2002, Volume 70, Issue 5

Pivotal Statistics for Testing Structural Parameters in Instrumental Variables Regression
p. 1781-1803

Frank Kleibergen

We propose a novel statistic for conducting joint tests on all the structural parameters in instrumental variables regression. The statistic is straightforward to compute and equals a quadratic form of the score of the concentrated log–likelihood. It therefore attains its minimal value equal to zero at the maximum likelihood estimator. The statistic has a χ limiting distribution with a degrees of freedom parameter equal to the number of structural parameters. The limiting distribution does not depend on nuisance parameters. The statistic overcomes the deficiencies of the Anderson–Rubin statistic, whose limiting distribution has a degrees of freedom parameter equal to the number of instruments, and the likelihood based, Wald, likelihood ratio, and Lagrange multiplier statistics, whose limiting distributions depend on nuisance parameters. Size and power comparisons reveal that the statistic is a (asymptotic) size–corrected likelihood ratio statistic. We apply the statistic to the Angrist–Krueger (1991) data and find similar results as in Staiger and Stock (1997).

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