High-dimensional instrumental variables regression and confidence sets

Abstract: This article considers inference in linear instrumental variables models with many regressors, all of which could be endogenous. We propose the STIV estimator. Identification robust confidence sets are derived by solving linear programs. We present results on rates of convergence, variable selection, confidence sets which adapt to the sparsity, and analyze confidence bands for vectors of linear functions using bias correction. We also provide solutions to some instruments being endogenous. The application is to the EASI demand system.