Penalized GMM Framework for Inference on Functionals of Nonparametric Instrumental Variable Estimators
arXiv:2603.29889v1 Announce Type: cross 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. Sim
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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.
Comments: Previously circulated as "Automatic Debiased Machine Learning in Presence of Endogeneity"
Subjects:
Econometrics (econ.EM); Machine Learning (stat.ML)
Cite as: arXiv:2603.29889 [econ.EM]
(or arXiv:2603.29889v1 [econ.EM] for this version)
https://doi.org/10.48550/arXiv.2603.29889
arXiv-issued DOI via DataCite (pending registration)
Submission history
From: Edvard Bakhitov [view email] [v1] Tue, 31 Mar 2026 15:38:27 UTC (77 KB)
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