Diffuse Bunching with Frictions: Theory and Estimation

Abstract

We incorporate a general model of frictions into the bunching-based elasticity estimator. This model relies on fewer parameters than the conventional approach, replacing bunching window bounds with a single "lumpiness parameter," while matching rich observed bunching patterns such as sharp-peaked diffusion around tax kinks and depressed density in the dominated region above a notch. Simulations suggest that in the presence of frictions, conventional methods may underestimate elasticities with overstated confidence. Our method draws information from the spread of bunching mass around kinks and asymmetry around notches, revealing the size of frictions, unobserved costs, and kink vs. notch misperceptions. Estimating this model on South African administrative tax data, we find that individuals and firms appear to treat the bottom zero-to-positive tax kink like a notch, and we uncover differences in lumpiness between wage earners vs. the self-employed and between firms with vs. without paid tax practitioners. 

Keywords: diffuse bunching, sparsity, lumpy adjustment, optimization frictions, elasticity of taxable income, tax, small business, South Africa, bunching estimators

JEL Classification: D22, H20, H25, H30, O55