# Regression Discontinuity Design equation

Dear all, I found this equation to estimate a RDD in a paper. $$(f_i-f_z)$$ is the running variable, hence $$\alpha$$ should be the slope to the left of the cutoff and $$\lambda$$ the variation in the slope between the left and the right of the cutoff for the function. But what does it mean the term associated with $$\eta$$?

• look again. Is $\alpha$ a slope or an intercept? May 16, 2023 at 12:43

The slope for $$f_i \leq f_z$$ is $$- \eta$$, as the difference is reversed, with $$f_i$$ being the term with the negative sign.
• $$\alpha$$, which is a constant. Assuming $$\alpha > 0$$, the would-be-intercept (assuming the right regression extended all the way to the left) would be higher than the intercept of the left regression. The original intercept is $$\delta$$, this “would-be-intercept” is $$\delta + \alpha$$.
• $$\lambda (f_i - f_z)$$ which is a linear term on the difference: From the cutoff, this term adds a slope of $$\lambda$$. With this, we get that the slope of the regression (on $$f_i$$) becomes $$\lambda - \eta$$.