Two Independent Pivotal Statistics that test Location and Misspecification and add up to the Anderson-Rubin Statistic

Frank Kleibergen

No 02-064/4, Tinbergen Institute Discussion Papers from Tinbergen Institute

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.

Keywords: Identification statistics; rank tests; Bartlett-correction; power and size properties; confidence sets; conditioning (search for similar items in EconPapers)
JEL-codes: C12 C13 C30 (search for similar items in EconPapers)
Date: 2002-06-28
References: Add references at CitEc
Citations: View citations in EconPapers (1)

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