 In a two-stage linear regression model with Normal noise, I consider James-Stein type shrinkage in the estimation of the first-stage instrumental variable coefficients. For at least four instrumental variables and a single endogenous regressor, I show that the standard two-stage least-squares estimator is dominated with respect to bias. I construct the dominating estimator by a variant of James-Stein  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.
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.
A
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.
D
James-Stein type
R
show
establish
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two-stage least-squares
2SLS
R
I construct the dominating estimator by a variant of
The dominating IV estimator applies
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type
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