# Penalized GMM Framework for Inference on Functionals of Nonparametric Instrumental Variable Estimators

arXiv: https://arxiv.org/abs/2603.29889 · HTML: https://mlsanity.com/paper/2603.29889/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 4 of its 73 references that are in the map.
- First posted on arXiv 31 Mar 2026.

## Builds on (most cited first, 4 of 4)

- [Learning Deep Features in Instrumental Variable Regression](https://mlsanity.com/paper/2010.07154/) (2020)
- [Minimax Semiparametric Learning With Approximate Sparsity](https://mlsanity.com/paper/1912.12213/) (2019)
- [Regularized DeepIV with Model Selection](https://mlsanity.com/paper/2403.04236/) (2024)
- [Choice Models and Permutation Invariance: Demand Estimation in Differentiated Products Markets](https://mlsanity.com/paper/2307.07090/) (2023)

## Built on by (most cited first, 1 of 1)

- [Debiased Machine Learning: Identification, Estimation, and Shape Constraints](https://mlsanity.com/paper/2607.24472/) (2026)

## Abstract (arXiv)

This paper develops a penalized GMM (PGMM) framework for automatic debiased inference on functionals of nonparametric instrumental variable estimators. We derive convergence rates for the PGMM estimator and provide conditions for root-n consistency and asymptotic normality of debiased functional estimates, covering both linear and nonlinear functionals. Monte Carlo experiments on average derivative show that the PGMM-based debiased estimator performs on par with the analytical debiased estimator that uses the known closed-form Riesz representer, achieving 90-96% coverage while the plug-in estimator falls below 5%. We apply our procedure to estimate mean own-price elasticities in a semiparametric demand model for differentiated products. Simulations confirm near-nominal coverage while the plug-in severely undercovers. Applied to IRI scanner data on carbonated beverages, debiased semiparametric estimates are approximately 20% more elastic compared to the logit benchmark, and debiasing corrections are heterogeneous across products, ranging from negligible to several times the standard error.