Causal Inference under Kink Bunching

Abstract

Kinked policies change marginal incentives at a threshold, and agents respond by adjusting the assignment variable that determines their treatment. The bunching literature uses this response to estimate the elasticity of the assignment variable; policymakers often care about effects on other outcomes. We develop a framework for estimating causal effects of kinked policies on outcomes beyond the assignment variable when agents can fully manipulate it. Average effects are defined for two affected populations: bunchers, who locate at the kink, and shifters, who reduce their assignment values but remain above the threshold; shifter effects compare equal-mass intervals and require only rank invariance. Because a single kink identifies neither the counterfactual assignment density nor the counterfactual outcome function, identification is design-assisted: placebo groups and moving thresholds discipline the local shape of both objects, the focal group's unaffected observations pin down level and slope differences, and the restrictions are testable. Applying the framework to a kinked coinsurance schedule in China's medical insurance, we find that the loss of reimbursement above the annual cap sharply reduces outpatient visits, raises cost per visit, and shifts the composition of care toward hospitals -- effects that are invisible in a density-only bunching analysis.