Econometrica

Journal Of The Econometric Society

An International Society for the Advancement of Economic
Theory in its Relation to Statistics and Mathematics

Edited by: Guido W. Imbens • Print ISSN: 0012-9682 • Online ISSN: 1468-0262

Econometrica: Nov, 2016, Volume 84, Issue 6

Conditional Linear Combination Tests for Weakly Identified Models

https://doi.org/10.3982/ECTA12407
p. 2155-2182

Isaiah Andrews

We introduce the class of conditional linear combination tests, which reject null hypotheses concerning model parameters when a data‐dependent convex combination of two identification‐robust statistics is large. These tests control size under weak identification and have a number of optimality properties in a conditional problem. We show that the conditional likelihood ratio test of Moreira, 2003 is a conditional linear combination test in models with one endogenous regressor, and that the class of conditional linear combination tests is equivalent to a class of quasi‐conditional likelihood ratio tests. We suggest using minimax regret conditional linear combination tests and propose a computationally tractable class of tests that plug in an estimator for a nuisance parameter. These plug‐in tests perform well in simulation and have optimal power in many strongly identified models, thus allowing powerful identification‐robust inference in a wide range of linear and nonlinear models without sacrificing efficiency if identification is strong.


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Supplemental Material

Supplement to "Conditional Linear Combination Tests for Weakly Identified Models"

This appendix contains asymptotic results and proofs for the paper.

Supplement to "Conditional Linear Combination Tests for Weakly Identified Models"

This zip file contains replication files for the manuscript and additional material not found within the main manuscript.