High-dimensional instrumental variables regression and confidence sets

Eric Gautier (1) , Christiern Rose (2)

1 TSE-R - Toulouse School of Economics
2 UQ [All campuses : Brisbane, Dutton Park Gatton, Herston, St Lucia and other locations] - The University of Queensland

This article considers inference in linear models with d_X regressors, some or many of which could be endogenous, and d_Z instrumental variables (IVs). d_Z can range from less than d_X to any order smaller than an exponential in the sample size. For moderate d_X, identification robust confidence sets are obtained by solving a hierarchy of semidefinite programs. For large d_X, we propose the STIV estimator. The analysis of its error uses sensitivity characteristics introduced in this paper. Robust confidence sets are derived by solving linear programs. Results on rates of convergence, variable selection, and confidence sets which "adapt" to the sparsity are given. Generalizations include models with endogenous IVs and systems of equations with approximation errors. We also analyse confidence bands for vectors of linear functionals and functions using bias correction. The application is to a demand system with approximation errors, cross-equation restrictions, and thousands of endogenous regressors.

Mots clés: Unknown variance; Variable selection; Instrumental variables; Sparsity; Endogeneity; Confidence intervals; Partial identification; Robustness to identification; Bias correction

Domaines: Statistiques [math.ST]; Théorie [stat.TH]; Economies et finances

Eric Gautier, Christiern Rose. High-dimensional instrumental variables regression and confidence sets. 2018. ⟨hal-00591732v6⟩