Using Notches to Uncover Optimization Frictions and Structural Elasticities: Theory and Evidence from Pakistan*

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.