Model Restrictiveness in Functional and Structural Settings

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.