Template-Type: ReDIF-Paper 1.0
Series: Tinbergen Institute Discussion Papers
Creation-Date: 2002-06-28
Number: 02-064/4
Author-Name: Frank Kleibergen
Author-Email: f.r.kleibergen@uva.nl
Author-Workplace-Name: University of Amsterdam
Title: Two Independent Pivotal Statistics that test Location and Misspecification and add up to the Anderson-Rubin Statistic
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.
Classification-JEL: C12; C13; C30
Keywords: Identification statistics; rank tests; Bartlett-correction; power and size properties; confidence sets; conditioning
File-Url: https://papers.tinbergen.nl/02064.pdf
File-Format: application/pdf
File-Size: 607401 bytes
Handle: RePEc:tin:wpaper:20020064