Card et al. 2015 — Inference on Causal Effects in a Generalized Regression Kink Design

Summary

Develops the formal econometric foundations for the Regression Kink Design (RKD), a quasi-experimental method that identifies causal effects at points where a policy assignment function has a kink (change in slope) rather than a jump. The paper provides identification conditions, asymptotic inference procedures, and a falsification framework. Applied to unemployment insurance (UI) in Austria, it estimates the causal effect of benefit levels on unemployment duration.

Key Claims

• RKD identifies a local average treatment effect at the kink point under the condition that the density of the running variable is smooth and the potential outcomes are continuously differentiable.
• A "fuzzy" RKD generalizes the design to settings where the relationship between the running variable and the treatment is not deterministic (analogous to fuzzy regression discontinuity design (RDD)).
• Inference can be conducted with standard instrumental variables (IV) methods once the design is validated; bandwidth selection follows from local polynomial regression theory.
• The UI application finds that a $10\%$ increase in benefit levels raises unemployment duration by roughly $1.5$–$2$ weeks.

Concepts Introduced or Extended

• Regression Kink Design

Entities Mentioned

• David Card
• David Lee
• Zhuan Pei
• Andrea Weber

Quotes

"The RKD exploits the fact that while the level of a policy variable may be continuous, its slope changes at a known threshold."

My Take

The canonical reference for any study using RKD. Directly undergirds the Gelber, Moore, and Strand (2017) methodology for estimating the causal effect of DI income on mortality using the Social Security benefit kink. Should be cited alongside any RKD application in the DI literature.