High-dimensional instrumental variables regression and confidence sets

TL;DR

This paper introduces the STIV estimator for high-dimensional linear instrumental variables models, providing robust confidence sets, variable selection, and bias correction, with applications to demand systems.

Contribution

The paper develops the STIV estimator and derives identification robust confidence sets for high-dimensional IV models with endogenous regressors.

Findings

The STIV estimator achieves favorable convergence rates.

Confidence sets adapt to sparsity in the model.

Bias correction improves confidence band accuracy.

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.