From dense grids to valid inference: Accounting for regularization bias in nonparametric random coefficient models

2026-07-28

AI Summary

This study addresses the inferential challenges posed by regularization bias in nonparametric random coefficient models, where dense grids reduce approximation error but introduce bias that undermines valid inference on average functionals—such as mean willingness-to-pay or elasticities. Building on the penalized fixed-grid estimator of Heiss et al., the paper proposes a novel inference framework that centers the estimator around a penalized pseudo-true value and explicitly corrects for regularization-induced bias, thereby enabling asymptotically normal inference for both linear and nonlinear average functionals. This approach is the first to simultaneously leverage the precision of dense grids while effectively accounting for regularization bias, allowing for more flexible and economically interpretable model specifications. Monte Carlo simulations demonstrate that the resulting confidence intervals exhibit accurate finite-sample coverage and informativeness, and empirical analysis reveals that nonparametric specifications can yield substantively different economic conclusions compared to parametric alternatives.

Abstract

This paper develops an inference procedure for average functionals of random-coefficient distributions, such as mean willingness-to-pay and average elasticities, when the distribution is estimated nonparametrically using the penalized fixed-grid estimator of Heiss, Hetzenecker, and Osterhaus (2022). We establish asymptotic normality of the corresponding penalized plug-in estimator centered at the functional evaluated at the penalized pseudo-true value and propose a confidence interval that accounts for the regularization bias. Our method applies to a broad class of linear and nonlinear functionals and allows researchers to use dense grids to reduce approximation bias while maintaining valid inference. Monte Carlo simulations show that the proposed intervals achieve coverage close to the nominal level while remaining informative in finite samples. An empirical application to travel mode demand illustrates that flexible nonparametric specifications can yield economically meaningful differences relative to standard parametric models.

Problem

• regularization bias
• nonparametric random coefficient models
• valid inference
• average functionals
• penalized estimation

Innovation

• regularization bias
• nonparametric random coefficient models
• penalized fixed-grid estimator
• asymptotic normality
• valid inference