Nonparametric Instrumental Variable Methods
When a regressor is correlated with the error, as price is in a demand equation, ordinary regression cannot capture the causal relationship. Instrumental variables are the standard answer to that. In the nonparametric version (NPIV), which drops the assumption that the relationship is linear, both estimation and the assessment of uncertainty become harder. My work on this topic covers learning NPIV models and constructing prediction intervals that come with finite-sample guarantees. The central result is Conformal Prediction for Nonparametric Instrumental Regression (Kato, 2026, arXiv:2603.25509).
Problems addressed
Estimators for NPIV run from sieve two-stage least squares to minimax methods built on neural networks, but saying how far a prediction from the estimated function can be trusted, without assuming a distribution, has been a hard problem. I carry the idea of conditional guarantees from conformal prediction into the instrumental variable setting and construct prediction intervals whose coverage holds in finite samples over a class of shifts the user chooses. The construction pairs with any NPIV estimator. Learning causal models from conditional moment restrictions belongs to the same thread.
Core research
The Conformal Prediction for NPIV page explains how the intervals are built and what the guarantee covers.
Research thread
- 2022
- Learning Causal Models from Conditional Moment Restrictions by Importance Weighting (ICLR 2022). Learning causal models by handling conditional moment restrictions through weighting.
Relation to earlier work
Newey and Powell laid the groundwork for identification and estimation in NPIV (2003, Instrumental Variable Estimation of Nonparametric Models). Estimation with machine learning grew from there, through the deep models of Hartford and coauthors, Deep IV (2017, Deep IV: A Flexible Approach for Counterfactual Prediction), and the minimax estimation of Dikkala and coauthors (2020, Minimax Estimation of Conditional Moment Models). Those methods aim at the function itself, and my work adds on top of them a guarantee for prediction intervals that does not rest on distributional assumptions. Conditional guarantees cannot be achieved as they stand, as Foygel Barber and coauthors showed (2021, The limits of distribution-free conditional predictive inference), and restricting the class of shifts is a formulation that respects that limit.