The exact distribution of the conditional likelihood-ratio test in instrumental variables regression
Econometrics
2025-09-09 v2 Statistics Theory
Statistics Theory
Abstract
We derive the exact asymptotic distribution of the conditional likelihood-ratio test in instrumental variables regression under weak instrument asymptotics and for multiple endogenous variables. The distribution is conditional on all eigenvalues of the concentration matrix, rather than only the smallest eigenvalue as in an existing asymptotic upper bound. This exact characterization leads to a substantially more powerful test if there are differently identified endogenous variables. We provide computational methods implementing the test and demonstrate the power gains through numerical analysis.
Keywords
Cite
@article{arxiv.2509.04144,
title = {The exact distribution of the conditional likelihood-ratio test in instrumental variables regression},
author = {Malte Londschien},
journal= {arXiv preprint arXiv:2509.04144},
year = {2025}
}