Regression Kink Design
When the assignment variable is continuous (e.g. student aid) and depends predictably on another observed variable (e.g. family income), one can identify treatment effects using sharp changes in the slope of the treatment function. This technique was coined regression kink design by Turner Nielsen, Sørensen, and Tabe (2009), though they cite similar earlier analyses. They write, "This approach resembles the regression discontinuity idea. Instead of a discontinuity of in the level of the stipend-income function, we have a discontinuity in the slope of the function." Rigorous theoretical foundations were provided by Card et al (2012).
Note that regression kinks (or kinked regression) can also mean a type of segmented regression, which is a different type of analysis.
Read more about this topic: Regression Discontinuity Design, Extensions
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