Bias Reduction in Instrumental Variable Estimation through First-Stage Shrinkage

TL;DR

This paper proposes a shrinkage-based method for the first stage of instrumental variable estimation to reduce bias, especially effective with multiple instruments, by applying James-Stein type shrinkage in a high-dimensional Normal setting.

Contribution

It introduces a novel bias reduction technique for 2SLS using shrinkage in the first stage, improving estimation accuracy with multiple instruments.

Findings

Shrinkage reduces bias in 2SLS estimates.

Dominance over standard 2SLS with four or more instruments.

Method preserves invariances of IV equations.

Abstract

The two-stage least-squares (2SLS) estimator is known to be biased when its first-stage fit is poor. I show that better first-stage prediction can alleviate this bias. In a two-stage linear regression model with Normal noise, I consider shrinkage in the estimation of the first-stage instrumental variable coefficients. For at least four instrumental variables and a single endogenous regressor, I establish that the standard 2SLS estimator is dominated with respect to bias. The dominating IV estimator applies James-Stein type shrinkage in a first-stage high-dimensional Normal-means problem followed by a control-function approach in the second stage. It preserves invariances of the structural instrumental variable equations.