Title: Bias Reduction in Instrumental Variable Estimation through First-Stage Shrinkage,
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.