Diffuse Bunching with Frictions: Theory and Estimation
72 Pages Posted: 12 Jul 2022 Last revised: 13 Oct 2022
Date Written: October 13, 2022
We incorporate a model of frictions into the bunching-based elasticity estimator to rationalize diffuse bunching around kinks and mass above notches in empirical distributions. Model agents draw a sparse set of opportunities from a Poisson process, approximating a broad class of frictions including search costs, inattention, and lumpy adjustment; the predicted density depends on the standard structural elasticity and a money-metric “lumpiness parameter.” We estimate the model using administrative tax data on South African small-businesses, recovering moderate elasticities of taxable income between 0.2 and 0.3 at higher incomes, and larger elasticities at low incomes. Firms appear to treat the bottom kink as a notch, and firms with paid tax practitioners exhibit sharper bunching, driven primarily by lower frictions rather than a higher elasticity.
Keywords: diffuse bunching, sparsity, lumpy adjustment, optimization frictions, elasticity of taxable income, tax, small business, South Africa
JEL Classification: D22, H20, H25, H30, O55
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