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

TL;DR

This paper introduces a penalized GMM framework for automatic, debiased inference on functionals of nonparametric instrumental variable estimators, ensuring reliable coverage and applicability to demand elasticity estimation.

Contribution

It develops a novel PGMM approach with convergence guarantees for debiased inference on both linear and nonlinear functionals, validated through simulations and real data.

Findings

Monte Carlo experiments show 90-96% coverage for the PGMM estimator.

Debiased estimates are approximately 20% more elastic than logit benchmarks.

Debiasing corrections vary significantly across products.

Abstract

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.