Identifying Causal Effects under Kink Setting: Theory and Evidence

This paper develops a generalized framework for identifying causal impacts in a reduced-form manner under kinked settings when agents can manipulate their choices around the threshold. The causal estimation using a bunching framework was initially developed by Diamond and Persson (2017) under notched settings. Many empirical applications of bunching designs involve kinked settings. We propose a model-free causal estimator in kinked settings with sharp bunching and then extend to the scenarios with diffuse bunching, misreporting, optimization frictions, and heterogeneity. The estimation method is mostly non-parametric and accounts for the interior response under kinked settings. Applying the proposed approach, we estimate how medical subsidies affect outpatient behaviors in China.