Nonparametric Jackknife Instrumental Variable Estimation and Confounding Robust Surrogate Indices

TL;DR

This paper extends jackknife instrumental variable methods to nonparametric models with many weak IVs, providing a bias reduction technique and enabling reliable inference on treatment effects with confounding.

Contribution

It introduces a split-IV approach for nonparametric IV models, addressing bias issues and establishing learning rates for semiparametric inference on treatment effects.

Findings

Bias reduction in nonparametric IV estimation with many weak IVs

Establishment of learning rates based on hypothesis class complexity

Asymptotically normal estimates for treatment effects enabling inference

Abstract

Jackknife instrumental variable estimation (JIVE) is a classic method to leverage many weak instrumental variables (IVs) to estimate linear structural models, overcoming the bias of standard methods like two-stage least squares. In this paper, we extend the jackknife approach to nonparametric IV (NPIV) models with many weak IVs. Since NPIV characterizes the structural regression as having residuals projected onto the IV being zero, existing approaches minimize an estimate of the average squared projected residuals, but their estimates are biased under many weak IVs. We introduce an IV splitting device inspired by JIVE to remove this bias, and by carefully studying this split-IV empirical process we establish learning rates that depend on generic complexity measures of the nonparametric hypothesis class. We then turn to leveraging this for semiparametric inference on average treatment effects (ATEs) on unobserved long-term outcomes predicted from short-term surrogates, using historical experiments as IVs to learn this nonparametric predictive relationship even in the presence of confounding between short- and long-term observations. Using split-IV estimates of a debiasing nuisance, we develop asymptotically normal estimates for predicted ATEs, enabling inference.