Please use this identifier to cite or link to this item: http://hdl.handle.net/10419/85918
Authors: 
Kleibergen, Frank
Year of Publication: 
2002
Series/Report no.: 
Tinbergen Institute Discussion Paper 02-064/4
Abstract: 
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.
Subjects: 
Identification statistics
rank tests
Bartlett-correction
power and size properties
confidence sets
conditioning
JEL: 
C12
C13
C30
Document Type: 
Working Paper

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