Inference on Causal Effects in a Generalized Regression Kink Design

David Card, David S. Lee, Zhuan Pei, Andrea Weber

Research output: Contribution to journalArticlepeer-review

156 Scopus citations


We consider nonparametric identification and estimation in a nonseparable model where a continuous regressor of interest is a known, deterministic, but kinked function of an observed assignment variable. We characterize a broad class of models in which a sharp "Regression Kink Design" (RKD or RK Design) identifies a readily interpretable treatment-on-the-treated parameter (Florens, Heckman, Meghir, and Vytlacil (2008)). We also introduce a "fuzzy regression kink design" generalization that allows for omitted variables in the assignment rule, noncompliance, and certain types of measurement errors in the observed values of the assignment variable and the policy variable. Our identifying assumptions give rise to testable restrictions on the distributions of the assignment variable and predetermined covariates around the kink point, similar to the restrictions delivered by Lee (2008) for the regression discontinuity design. Using a kink in the unemployment benefit formula, we apply a fuzzy RKD to empirically estimate the effect of benefit rates on unemployment durations in Austria.

Original languageEnglish (US)
Pages (from-to)2453-2483
Number of pages31
Issue number6
StatePublished - Nov 1 2015

All Science Journal Classification (ASJC) codes

  • Economics and Econometrics


  • Nonparametric estimation
  • Nonseparable models
  • Regression discontinuity design
  • Regression kink design
  • Treatment effects


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