Optimal Two-Sided Invariant Similar Tests for Instrumental Variables Regression

This paper considers tests of the parameter on an endogenous variable in an instrumental variables regression model. The focus is on determining tests that have some optimal power properties. We start by considering a model with normally distributed errors and known error covariance matrix. We consi...

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Bibliographic Details
Published in:Econometrica 2006-05, Vol.74 (3), p.715-752
Main Authors: Andrews, Donald W. K., Moreira, Marcelo J., Stock, James H.
Format: Article
Language:English
Subjects:
Applications
Asymptotic methods
Average power
Covariance matrices
Critical values
Econometrics
Error
Error rates
Estimators
Exact sciences and technology
Instrumental variables
instrumental variables regression
Insurance, economics, finance
invariant tests
Lagrange multiplier
Linear inference, regression
Mathematical independent variables
Mathematics
Matrix calculus
Methodology
Multivariate analysis
Null hypothesis
optimal tests
Power
power envelope
Power functions
Probability and statistics
Regression analysis
Sampling
Sciences and techniques of general use
Significance tests
similar tests
Statistical theories
Statistics
Studies
Tests
two-sided tests
Variance
weak instruments
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Summary:This paper considers tests of the parameter on an endogenous variable in an instrumental variables regression model. The focus is on determining tests that have some optimal power properties. We start by considering a model with normally distributed errors and known error covariance matrix. We consider tests that are similar and satisfy a natural rotational invariance condition. We determine a two-sided power envelope for invariant similar tests. This allows us to assess and compare the power properties of tests such as the conditional likelihood ratio (CLR), the Lagrange multiplier, and the Anderson-Rubin tests. We find that the CLR test is quite close to being uniformly most powerful invariant among a class of two-sided tests. The finite-sample results of the paper are extended to the case of unknown error covariance matrix and possibly nonnormal errors via weak instrument asymptotics. Strong instrument asymptotic results also are provided because we seek tests that perform well under both weak and strong instruments.
ISSN:0012-9682
1468-0262
DOI:10.1111/j.1468-0262.2006.00680.x