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

Arbeitspapier

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.

Object Details

• Language: Englisch

References and Relationships

• Bibliographic citation: Series: Tinbergen Institute Discussion Paper ; No. 02-064/4

Classification and Topics

• Classification: Wirtschaft ; Hypothesis Testing: General ; Estimation: General ; Multiple or Simultaneous Equation Models; Multiple Variables: General
• Subject: Identification statistics ; rank tests ; Bartlett-correction ; power and size properties ; confidence sets ; conditioning ; Statistischer Test ; Schätztheorie ; Theorie

Contributors, Places and Time

• Event: Geistige Schöpfung
• (who): Kleibergen, Frank
• Event: Veröffentlichung
• (who): Tinbergen Institute
• (where): Amsterdam and Rotterdam
• (when): 2002

Further information

• Handle: http://hdl.handle.net/10419/85918
• Last update: 10.03.2025, 11:43 AM CET