Using Notches to Uncover Optimization Frictions and Structural Elasticities: Theory and Evidence from Pakistan*
提出一个非参数框架，利用税收政策中的断点（notches）来识别优化摩擦和结构弹性，并应用于巴基斯坦的税收数据，发现尽管观察到的聚集效应很大，但优化摩擦也很大，导致结构弹性较小，揭示了断点的低效率。
Abstract We develop a framework for nonparametrically identifying optimization frictions and structural elasticities using notches—discontinuities in the choice sets of agents—introduced by tax and transfer policies. Notches create excess bunching on the low-tax side and missing mass on the high-tax side of a cutoff, and they are often associated with a region of strictly dominated choice that would have zero mass in a frictionless world. By combining excess bunching (observed response attenuated by frictions) with missing mass in the dominated region (frictions), it is possible to uncover the structural elasticity that would govern behavior in the absence of frictions and arguably capture long-run behavior. We apply our framework to tax notches in Pakistan using rich administrative data. While observed bunching is large and sharp, optimization frictions are also very large as the majority of taxpayers in dominated ranges are unresponsive to tax incentives. The combination of large observed bunching and large frictions implies that the frictionless behavioral response to notches is extremely large, but the underlying structural elasticity driving this response is nevertheless modest. This highlights the inefficiency of notches: by creating extremely strong price distortions, they induce large behavioral responses even when structural elasticities are small.