The kink and notch bunching estimators cannot identify the taxable income elasticity

Bunching estimators were developed and extended by Saez (2010), Chetty et al. (2011) and Kleven and Waseem (2013). Using this method one can get an estimate of the taxable income elasticity from the bunching pattern around a kink point. The bunching estimator has become popular, with a large number of papers applying the method. In this paper, we show that the bunching estimator cannot identify the taxable income elasticity when the functional form of the distribution of preference heterogeneity is unknown. We find that an observed distribution of taxable income around a kink point or over the whole budget set can be consistent with any positive taxable income elasticity if the distribution of heterogeneity is unrestricted. If one is willing to assume restrictions on the heterogeneity density some information about the taxable income elasticity can be obtained. We give bounds on the taxable income elasticity based on monotonicity of the heterogeneity density and apply these bounds in an example. We also consider identification from budget set variation. We find that kinks alone may not be informative even when budget sets vary. However, if the taxable income specification is restricted to be of the parametric isoelastic form assumed in Saez (2010) the taxable income elasticity can be well identified from variation among budget sets. The key condition is that the tax rates at chosen taxable income differ across budget sets for some individuals.