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.

bunching估计量由塞兹（2010年）、切蒂等人（2011年）以及克莱文和瓦西姆（2013年）开发并扩展。使用这种方法，可以从弯折点周围的聚集模式中估计应税收入弹性。bunching估计量已变得很流行，有大量论文应用了该方法。在本文中，我们表明当偏好异质性分布的函数形式未知时，bunching估计量无法识别应税收入弹性。我们发现，如果异质性分布不受限制，在弯折点周围或整个预算集上观察到的应税收入分布可以与任何正的应税收入弹性相一致。如果愿意对异质性密度施加限制，就可以获得一些关于应税收入弹性的信息。我们基于异质性密度的单调性给出了应税收入弹性的界限，并在一个例子中应用了这些界限。我们还考虑了从预算集变化中进行识别。我们发现，即使预算集发生变化，仅弯折点可能也没有信息量。然而，如果应税收入的设定被限制为塞兹（2010年）中假设的参数等弹性形式，那么可以从预算集之间的变化很好地识别应税收入弹性。关键条件是，对于某些个人，所选应税收入的税率在不同预算集之间存在差异。