NPIV

The package supports Debiased Machine Learning (DML) for the semiparametric model where the parametric part is a functional of a standard nonparametric instrumental variables (NPIV) inverse problem.

Localization

When V is supplied, DML_npiv estimates the finite-bandwidth target

\[\theta_\lambda(v) =\frac{\mathbb{E}[K\{(V-v)/\lambda\}H]} {\mathbb{E}[K\{(V-v)/\lambda\}]},\]

where \(H\) is the uncentered MR, OR, or IPW score selected by the user. Writing \(\ell_{\lambda,v}=K/\mathbb{E}[K]\), the centered score contribution is \(\ell_{\lambda,v}\{H-\theta_\lambda(v)\}\), not \(\ell_{\lambda,v}H-\theta_\lambda(v)\). Pointwise and uniform inference use this ratio centering. Without V, the loading is one and the estimator reduces to the ordinary average-score calculation.

All routes use this centering; see Localized Ratio Targets for the influence-function distinction and nuisance requirements. Use include_V=True for the usual conditional causal interpretation.

nnpiv.semiparametrics.DML_npiv(Y, D, Z, W[, ...])

Debiased Machine Learning for Nonparametric Instrumental Variables (DML-npiv) class.

References