Symmetry-based inference in an instrumental variable setting

P.A. Bekker, S. Lawford

Research output: Contribution to journalArticleAcademicpeer-review

Abstract

We describe exact inference based on group-invariance assumptions that specify various forms of symmetry in the distribution of a disturbance vector in a general nonlinear model. It is shown that such mild assumptions can be equivalently formulated in terms of exact confidence sets for the parameters of the functional form. When applied to the linear model, this exact inference provides a unified approach to a variety of parametric and distribution-free tests. In particular, we consider exact instrumental variable inference, based on symmetry assumptions. The unboundedness of exact confidence sets is related to the power to reject a hypothesis of underidentification. In a multivariate instrumental variables context, generalizations of Anderson-Rubin confidence sets are considered. (C) 2007 Elsevier B.V. All rights reserved.

Original languageEnglish
Pages (from-to)28-49
Number of pages22
JournalJournal of Econometrics
Volume142
Issue number1
DOIs
Publication statusPublished - Jan-2008

Keywords

  • weak instruments
  • exact inference
  • distribution-free methods
  • nonparametric tests
  • Anderson-Rubin confidence sets
  • MEDIAN-UNBIASED ESTIMATION
  • SMALL SAMPLE PROPERTIES
  • WEAK INSTRUMENTS
  • STRUCTURAL PARAMETERS
  • CONFIDENCE-INTERVALS
  • REGRESSION
  • MODELS
  • ECONOMETRICS
  • TESTS

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