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 statistic tests misspecification. The chi-squared distribution of the location statistic has a degrees of freedom parameter that is equal to the number of parameters of interest while the degrees of freedom parameter of the misspecification statistic equals the degree of over- identification. We show that statistics with good power properties, like the likelihood ratio statistic, are a weighted average of these two statistics. The location statistic is also a Bartlett-corrected likelihood ratio statistic. We obtain the limit expressions of the location and misspecification statistics, when the parameter of interest converges to infinity, to obtain a set of statistics that indicate whether the parameter of interest is identified 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 statistical models for which our results are of interest, i.e. the instrument al variables regression and the observed factor model.
Download Info
To download:
If you experience problems downloading a file, check if you have the
proper application to
view it first. Information about this may be contained
in the File-Format links below. In case of further problems read
the IDEAS help
file. Note that these files are not on the IDEAS
site. Please be patient as the files may be large.
Cited by: (explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)
Did you know? All full texts are decentralized with the publishers, none reside on this server, thus making it possible to offer this service for free to all parties.