Model Restrictiveness in Functional and Structural Settings

TL;DR

This paper extends the restrictiveness measure to functional and structural econometric models using Gaussian process priors, revealing that models are more restrictive over continuum domains and highlighting the impact of endogeneity and model choice on restrictiveness.

Contribution

It introduces a generalized restrictiveness framework for complex econometric models, including endogeneity and nonparametric components, and clarifies the role of discrepancy functions.

Findings

Models are more restrictive over continuum domains than finite sets.

Endogeneity and moment restrictions increase model restrictiveness.

Choice of discrepancy function significantly affects restrictiveness assessment.

Abstract

We extend the restrictiveness measure of Fudenberg, Gao & Liang (2026) to functional and structural econometric settings using Gaussian process priors. We find that models evaluated over continuum domains appear more restrictive than when evaluated over finite sets of observations. We also extend the restrictiveness framework to structural models with endogeneity, instrumental variables, multiple equilibria, and nonparametric nuisance components. We explain why the choice of discrepancy function is a substantive modeling decision, and why the Rademacher complexity and GMM criterion functions are unsuitable as discrepancies. We further show that restrictiveness equals the normalized limit of the noise-free average-case learning curve. In applications to preferences under risk, and multinomial choice under exogenous and endogenous settings, we find that the same models exhibit uniformly higher restrictiveness when evaluated over continuum domains than based on their predictions on finite sets, and that moment restrictions from endogeneity substantially increase restrictiveness and alter model rankings.