Guggenberger would like to thank the NSF for research support under Grant SES-1021101. Mavroeidis would like to thank the European Commission for research support under a FP7 Marie Curie Fellowship CIG 293675. We would like to thank Jim Stock for valuable advice.
On the Asymptotic Sizes of Subset Anderson–Rubin and Lagrange Multiplier Tests in Linear Instrumental Variables Regression
Article first published online: 26 NOV 2012
© 2012 The Econometric Society
Volume 80, Issue 6, pages 2649–2666, November 2012
How to Cite
Guggenberger, P., Kleibergen, F., Mavroeidis, S. and Chen, L. (2012), On the Asymptotic Sizes of Subset Anderson–Rubin and Lagrange Multiplier Tests in Linear Instrumental Variables Regression. Econometrica, 80: 2649–2666. doi: 10.3982/ECTA8953
- Issue published online: 26 NOV 2012
- Article first published online: 26 NOV 2012
- Manuscript received November, 2009; final revision received July, 2012.
- Asymptotic size;
- linear IV model;
- size distortion;
- subset inference;
- weak instruments
We consider tests of a simple null hypothesis on a subset of the coefficients of the exogenous and endogenous regressors in a single-equation linear instrumental variables regression model with potentially weak identification. Existing methods of subset inference (i) rely on the assumption that the parameters not under test are strongly identified, or (ii) are based on projection-type arguments. We show that, under homoskedasticity, the subset Anderson and Rubin (1949) test that replaces unknown parameters by limited information maximum likelihood estimates has correct asymptotic size without imposing additional identification assumptions, but that the corresponding subset Lagrange multiplier test is size distorted asymptotically.