Choice models with nonlinear budget sets are important in econometrics.In this paper we propose a nonparametric approach to estimation of choice models with nonlinear budget sets.The basic idea is to think of the choice, in our case hours of labor supply, as being a function of the entire budget set.Then we can ac- count nonparametrically for a nonlinear budget set by estimating a nonparametric regression where the variable in the regression is the budget set.We reduce the dimensionality of this problem by exploiting additive structure implied by utility maximization with convex budget sets.This structure leads to a polynomial con- vergence rate for the estimator.We give asymptotic normality results also.The usefulness of the estimator is demonstrated in Monte Carlo and empirical work, where we find it can have a large impact on estimated effects of tax changes.

Choice models with nonlinear budget sets provide a precise way of accounting for the nonlinear tax structures present in many applications. In this paper we propose a nonparametric approach to estimation of these models. The basic idea is to think of the choice, in our case hours of labor supply, as being a function of the entire budget set. Then we can do nonparametric regression where the variable in the regression is the budget set. We reduce the dimensionality of this problem by exploiting structure implied by utility maximization with piecewise linear convex budget sets. This structure leads to estimators where the number of segments can differ across observations and does not affect accuracy. We give consistency and asymptotic normality results for these estimators. The usefulness of the estimator is demonstrated in an empirical example, where we find it has a large impact on estimated effects of the Swedish tax reform.