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Title: Better bunching, nicer notching Authors:  Marinho Bertanha - University of Notre Dame (United States) [presenting]
Andrew McCallum - Board of Governors of the Federal Reserve System (United States)
Nathan Seegert - University of Utah (United States)
Abstract: Bunching estimators use mass points in an observed distribution to estimate parameters of a structural model, such as the elasticity of taxable income with respect to tax rates. The distribution of income typically shows mass points at income values with a change in the tax regime: either a change in marginal tax rate (kink) or a change in lump-sum tax (notch). Identification of the elasticity parameter in a setting with both kinks and notches is studied. First, we find that inference methods for the elasticity that focus on one kink may still be valid, as long as there are no notches near that kink. Second, contrary to what was previously thought, it is impossible to identify the elasticity using a kink, when the distribution of agents is non-parametric. We show the same is not true for notches. Third, we propose practical solutions for the lack of identification. We derive partial identification bounds on the elasticity using non-parametric shape restrictions on the distribution of agents. Then, we connect the bunching problem to the literature on censored regressions, namely Tobit and censored quantile regressions. This allows us to combine covariates with semi-parametric restrictions on the distribution of agents to point-identify the elasticity. We compare our estimates to previous estimates based on tax return data in the context of the ``earned income tax credit'', and find economically meaningful differences.