Econometrics Seminar Series - Firmin Doko Tchatoka (University of Adelaide)

Title: Inference in High-Dimensional IV Regression After Lasso Selection

Abstract: We study Lasso-based inference in linear IV models with many potentially correlated and weak instruments. We derive necessary and sufficient conditions for Lasso selection consistency in this setting and show that these conditions are automatically violated under weak identification. Even under moderate identification, exact recovery of the relevant instrument set may fail in finite samples, inducing a non-negligible selection bias in the sample moment conditions and thereby invalidating post-selection moment-based inference. This includes conventional weak-identification-robust procedures, whose asymptotic size may approach one under weak identification. To overcome this problem, we propose a sample-splitting approach in which instrument selection and inference are performed on independent subsamples. This restores valid moment conditions for the inference sample and delivers asymptotically valid identification-robust inference. Monte Carlo simulations confirm our theoretical findings.