Econometrica Vol. 84 No. 6 2016
Conditional Linear Combination Tests for Weakly Identified Models
Abstract
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.
- DOI
- 10.3982/ecta12407
- Volume
- 84
- Issue
- 6
- Pages
- 2155-2182
- Language
- en
- Sources
- bibtex:phds-export.bib openalex crossref