The bunching estimator cannot identify the taxable income elasticity

Saez (2010) introduced an influential estimator that has become known as the bunching estimator. 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 in a budget set can be consistent with any 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 to the data in Saez (2010). We also consider identification from budget set variation. We find that kinks alone are still not 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 linear segments of budget sets.