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Kleibergen, Frank
Year of Publication: 
Series/Report no.: 
Tinbergen Institute Discussion Paper 02-064/4
We show that the Anderson-Rubin (AR) statistic is the sum of two independent piv-otal statistics. One statistic is a score statistic that tests location and the other statistictests misspecification. The chi-squared distribution of the location statistic has a degreesof freedom parameter that is equal to the number of parameters of interest while thedegrees of freedom parameter of the misspecification statistic equals the degree of over-identification. We show that statistics with good power properties, like the likelihoodratio statistic, are a weighted average of these two statistics. The location statistic isalso a Bartlett-corrected likelihood ratio statistic. We obtain the limit expressions ofthe location and misspecification statistics, when the parameter of interest converges toinfinity, to obtain a set of statistics that indicate whether the parameter of interest isidentified in a specific direction. We show that all exact distribution results straight-forwardly extend to limiting distributions, that do not depend on nuisance parameters,under mild conditions. For expository purposes, we briefly mention a few statisticalmodels for which our results are of interest, i.e. the instrument al variables regressionand the observed factor model.
Identification statistics
rank tests
power and size properties
confidence sets
Document Type: 
Working Paper

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