Treatment Effects in Bunching Designs: The Impact of Mandatory Overtime Pay on Hours

Abstract: 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.