Model Restrictiveness in Functional and Structural Settings
Drew Fudenberg, Wayne Yuan Gao, Zhiheng You
TL;DR
This paper generalizes the notion of model restrictiveness beyond finite-dimensional, reduced-form settings to infinite-dimensional functional spaces and structural econometric models. It operationalizes restrictiveness through Bayesian nonparametric priors (notably Gaussian Processes) and a context-specific discrepancy $d$ evaluated via $\lambda_{\mathcal{F}}$, extending the framework to endogeneity, multiple equilibria, and semiparametric components, and linking it with the average-case learning curve. The authors provide computational methods for sampling from constrained priors and derive estimation and inference procedures, including when $d$ is data-driven. Across applications to Cumulative Prospect Theory and multinomial choice models with and without endogeneity, the results show how endogeneity and nonparametric components shape the restrictiveness frontier and model rankings, offering a unified way to assess the structural content of economic models. The framework enables a population-level, interpretable comparison of theoretical restrictions and suggests using restrictiveness as a regularization device to balance structure and predictive flexibility in empirical work and machine learning.
Abstract
We generalize the notion of model restrictiveness in Fudenberg, Gao and Liang (2026) to a wider range of economic models with semi/non-parametric and structural ingredients. We show how restrictiveness can be defined and computed in infinite-dimensional settings using Gaussian process priors (including with shape restrictions) and other alternativess in Bayesian nonparametrics. We also extend the restrictiveness framework to structural models with endogeneity, instrumental variables, multiple equilibria, and nonparametric nuisance components. We discuss the importance of the user-specific choice of discrepancy functions in the context of Rademacher complexity and GMM criterion function, and relate restrictiveness to the limit of the average-case learning curve in machine learning. We consider applications to: (1) preferences under risk, (2) exogenous multinomial choice, and (3) multinomial choice with endogenous prices: for (1), we obtain results consistent with those in Fudenberg, Gao and Liang (2026); for (2) and (3), our findings show that nested logit and mixed logit exhibit similar restrictiveness under standard parametric specifications, and that IV exogeneity conditions substantially increase overall restrictiveness while altering model rankings.