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8 - Weak Instruments and Empirical Likelihood: A Discussion of the Papers by D. W. K. Andrews, J. H. Stock, and Y. Kitamura

Published online by Cambridge University Press:  05 January 2013

Richard Blundell
Affiliation:
University College London
Whitney Newey
Affiliation:
Massachusetts Institute of Technology
Torsten Persson
Affiliation:
Stockholms Universitet
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Summary

INTRODUCTION

These two papers represent the fruition of important and thorough investigations undertaken by the authors of their respective fields of enquiry. I feel that they will add considerably to our understanding of these topics. Before describing the contents of my discussion I initially and briefly outline the contributions of both sets of authors.

Andrews and Stock (2005), henceforth referred to as AS, continues the program of research initiated with the papers by Moreira (2001, 2003) through Andrews, Moriera, and Stock (2004), henceforth AMS. Like those contributions, this paper is primarily concerned with the weak instrument problem for the classical two variable linear simultaneous equations model with normally distributed reduced form errors and known error variance matrix. The particular advantage of using a well-understood classical framework for analysis is that results here as elsewhere should have important implications and conclusions for estimators and statistics in more general settings enabling specific recommendations for practice. Apart from reviewing and detailing existing results, this paper provides a comprehensive treatment of the many weak instrumental variables problem for this model. Generally speaking with weak instruments standard point estimators such as 2SLS and LIML are no longer consistent and have nonstandard limiting distributions which cannot be consistently estimated. Therefore recourse is typically made to tests based on unconditionally or conditionally pivotal statistics. Acceptance regions associated with these tests may then be inverted to provide valid confidence interval estimators for the parameters of interest. I now briefly summarize their findings and conclusions.

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Advances in Economics and Econometrics
Theory and Applications, Ninth World Congress
, pp. 238 - 260
Publisher: Cambridge University Press
Print publication year: 2007

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