Using Nonlinear Budget Sets to Estimate Extensive Margin Responses: Method and Evidence from the Earnings Test

We estimate the impact of the Social Security Annual Earnings Test (AET) on older workers' employment. The AET reduces social security claimants' current benefits in proportion to their earnings in excess of an exempt amount. Using a regression kink design and Social Security Administration data, we document that the discontinuous change in the benefit reduction rate at the exempt amount causes a corresponding change in the slope of the employment rate, suggesting that the extensive margin of labor supply is more sensitive to this policy than commonly thought. We develop a model and method that allow us to translate the behavioral responses into a lower bound estimate of 0.49 for the extensive margin elasticity, which implies more than a 1 percentage point increase in work in the absence of the AET.