Model Restrictiveness in Functional and Structural Settings

2026-02-07

AI Summary

This study addresses the definition and quantification of model restrictiveness in semi- and nonparametric structural economic models featuring endogeneity, instrumental variables, and multiple equilibria. We extend the restrictiveness framework to settings with endogenous regressors and nonparametric disturbances, integrating Bayesian nonparametric methods—such as shape-constrained Gaussian processes—with generalized method of moments (GMM) criteria and user-specified discrepancy functions to compute restrictiveness in infinite-dimensional spaces. Our approach reveals a formal connection between restrictiveness and the asymptotic average-case learning curves in machine learning. Applications to risk preference and multinomial choice models show that nested logit and mixed logit exhibit similar levels of restrictiveness, while the exogeneity assumption on instrumental variables substantially increases model restrictiveness and alters the ranking of competing models.

Technology Category

Machine Learning: Bayesian LearningReasoning under Uncertainty: Graphical ModelsGame Theory and Economic Paradigms: Mechanism Design

Application Category

Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphsEconomics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystemsSemantics and Knowledge: Methods, algorithms and applications for the development of semantic models, knowledge graphs and other forms of structured data models with machine-interpretable semantics

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.

Problem

• model restrictiveness
• structural models
• nonparametric models
• endogeneity
• Bayesian nonparametrics

Innovation

• model restrictiveness
• Gaussian process priors
• Bayesian nonparametrics
• structural econometric models
• endogeneity