Estimating E[z|c] nonparametrically and either residualizing the instrument or adding it as a control guarantees the rich-covariates condition and yields √n-consistent causal complier-weighted estimates.
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Nonparametric "rich covariates" without saturation
Estimating E[z|c] nonparametrically and either residualizing the instrument or adding it as a control guarantees the rich-covariates condition and yields √n-consistent causal complier-weighted estimates.