High-dimensional instrumental variables regression and confidence sets -- v2/2012

TL;DR

This paper introduces a variation of the STIV estimator, called C-STIV, which uses multiple conic constraints aligned with the number of instruments to improve high-dimensional instrumental variables regression.

Contribution

It proposes the C-STIV estimator that directly incorporates multiple conic constraints for better handling of endogenous instruments in high-dimensional settings.

Findings

Enhanced estimator with multiple conic constraints

Better handling of endogenous instruments

Improved confidence set construction in high dimensions

Abstract

This was a revision of arXiv:1105.2454v1 from 2012. It considers a variation on the STIV estimator where, instead of one conic constraint, there are as many conic constraints as moments (instruments) allowing to use more directly moderate deviations for self-normalized sums. The idea first appeared in formula (6.5) in arXiv:1105.2454v1 when some instruments can be endogenous. For reference and to avoid confusion with the STIV estimator, this estimator should be called C-STIV.