Conformal Prediction for Nonparametric Instrumental Regression

Masahiro Kato. 2026. Preprint (arXiv:2603.25509). 日本語版

Nonparametric instrumental variable regression (NPIV) recovers a structural function under endogeneity without assuming its shape. This study builds prediction intervals for it that hold in finite samples without distributional assumptions, and the construction works with any NPIV estimator, from sieve two-stage least squares to estimators built on machine learning.

The problem

When a regressor is correlated with the error term, ordinary regression does not identify the structural relationship, and NPIV is the standard remedy. Estimation methods for it have advanced considerably. What was missing was a way to say how much a prediction from the estimated function can be trusted, without leaning on distributional assumptions. The instrumental variable setting also breaks the exchangeability that ordinary conformal prediction relies on, so the guarantee itself has to be reformulated rather than transplanted.

The proposed method

We carry the conditional-guarantee framework of conformal prediction over to the instrumental variable setting. Conditional coverage is restated as marginal coverage against a class of instrument shifts that the user chooses. Under that formulation, we give a construction of prediction intervals that can be combined with any NPIV estimator.

Main results and conditions

The intervals carry distribution-free finite-sample coverage for the chosen shift class. The guarantee is relative to that choice: a wider class makes the intervals more conservative. This design follows from a known theoretical limit, namely that full conditional coverage cannot be achieved without distributional assumptions.

Relation to earlier work

Newey and Powell established the identification and estimation of NPIV (2003, Instrumental Variable Estimation of Nonparametric Models). Estimation with machine learning was developed by Hartford and coauthors with Deep IV (2017, Deep IV: A Flexible Approach for Counterfactual Prediction) and by Dikkala and coauthors with a minimax formulation (2020, Minimax Estimation of Conditional Moment Models). Separately, Foygel Barber and coauthors showed that distribution-free conditional coverage has a fundamental limit (2021, The limits of distribution-free conditional predictive inference). This study draws on both lines and formulates a coverage guarantee for NPIV that is achievable given that limit.

Where it applies

Think of pricing or demand estimation, where endogeneity is present and the estimated relationship is used to predict. The construction attaches to an existing NPIV pipeline after the fact, so it reports the uncertainty of those predictions with a guarantee rather than replacing the estimator.

Paper and materials

BibTeX

@misc{conformal-prediction-npiv,
  author       = {Masahiro Kato},
  title        = {Conformal Prediction for Nonparametric Instrumental Regression},
  year         = {2026},
  eprint       = {2603.25509},
  archivePrefix = {arXiv},
  url          = {https://arxiv.org/abs/2603.25509},
}