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enter image description hereDear 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 $\eta$?

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  • $\begingroup$ look again. Is $\alpha$ a slope or an intercept? $\endgroup$
    – user18214
    May 16, 2023 at 12:43

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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.

From the cutoff, these two new terms “activate”:

  • $\alpha$, 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 $\lambda - \eta$.
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