Title: Inference in High-Dimensional IV Regressions After Lasso Selection
by Firmin Doko Tchatoka and Yuguo Ma; School of Economics and Public Policy, University of Adelaide
Abstract:
We study Lasso-based inference in instrumental variable (IV) regression with many potentially weak instruments. We establish oracle risk bounds and a sharp selection boundary, showing that Lasso recovers the relevant instruments under moderate or strong identification but selects no instruments under weak identification. However, using the selected to conduct inference renders standard inference unreliable
because Lasso selection invalidates the exclusion restrictions. To address this, we propose a simple split-sample approach: One random half of the sample is used for selection, while inference on the structural parameters is conducted with the other half, treating the selected instruments as fixed. This restores orthogonality of the selected instruments, yielding valid identification-robust tests under the usual fixed-number-of-moment conditions setting. Monte Carlo evidence confirms these theoretical findings. These results provide practical guidance for applied work with many instruments.