# Nonparametric Instrumental Variable Inference with Many Weak Instruments

arXiv: https://arxiv.org/abs/2505.07729 · HTML: https://mlsanity.com/paper/2505.07729/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 12 May 2025.

## Built on by (most cited first, 5 of 5)

- [Bellman Calibration for V-Learning in Offline Reinforcement Learning](https://mlsanity.com/paper/2512.23694/) (2025)
- [Fitted Q-Evaluation without Bellman Completeness via Occupancy Weighting](https://mlsanity.com/paper/2512.23805/) (2025)
- [Efficient Inference after Directionally Stable Adaptive Experiments](https://mlsanity.com/paper/2602.21478/) (2026)
- [Canonical correlation regression with noisy data](https://mlsanity.com/paper/2512.22697/) (2025)
- [Nonparametric Instrumental Variable Analysis Without Structural Equations: Debiased Inference on Functionals of Inverse Problems with No Solutions](https://mlsanity.com/paper/2604.24660/) (2026)

## Abstract (arXiv)

We study inference on linear functionals in the nonparametric instrumental variable (NPIV) problem with a discretely-valued instrument under a many-weak-instruments asymptotic regime, where the number of instrument values grows with the sample size. A key motivating example is estimating long-term causal effects in a new experiment with only short-term outcomes, using past experiments to instrument for the effect of short- on long-term outcomes. Here, the assignment to a past experiment serves as the instrument: we have many past experiments but only a limited number of units in each. Since the structural function is nonparametric but constrained by only finitely many moment restrictions, point identification typically fails. To address this, we consider linear functionals of the minimum-norm solution to the moment restrictions, which is always well-defined. As the number of instrument levels grows, these functionals define an approximating sequence to a target functional, replacing point identification with a weaker asymptotic notion suited to discrete instruments. Extending the Jackknife Instrumental Variable Estimator (JIVE) beyond the classical parametric setting, we propose npJIVE, a nonparametric estimator for solutions to linear inverse problems with many weak instruments. We construct automatic debiased machine learning estimators for linear functionals of both the structural function and its minimum-norm projection, and establish their efficiency in the many-weak-instruments regime. To do so, we develop a general semiparametric efficiency theory for regular estimators under weak identification and many-weak-instrument asymptotics.