  This paper studies the identifying power of bunching at kinks when the
researcher does not assume a parametric choice model. I find that in a general
choice model, identifying the average causal response to the policy switch at a
kink amounts to confronting two extrapolation problems, each about the
distribution of a counterfactual choice that is observed only in a censored
manner. I apply this insight to partially identify the effect of overtime pay
regulation on the hours of U.S. workers using administrative payroll data,
assuming that each distribution satisfies a weak non-parametric shape
constraint in the region where it is not observed. The resulting bounds are
informative and indicate a relatively small elasticity of demand for weekly
hours, addressing a long-standing question about the causal effects of the
overtime mandate.
