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.

Using a novel source of quasi-experimental variation in interest rates, we develop a new approach to estimating the Elasticity of Intertemporal Substitution (EIS). In the U.K., the mortgage interest rate features discrete jumps—notches—at thresholds for the loan-to-value (LTV) ratio. These notches generate large bunching below the critical LTV thresholds and missing mass above them. We develop a dynamic model that links these empirical moments to the underlying structural EIS. The average EIS is small, around 0.1, and quite homogeneous in the population. This finding is robust to structural assumptions and can allow for uncertainty, a wide range of risk preferences, portfolio reallocation, liquidity constraints, present bias, and optimization frictions. Our findings have implications for the numerous calibration studies that rely on larger values of the EIS.