Before revision:  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.
After revision:  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.