<p>The slope for <span class="math-container">$f_i \leq f_z$</span> is <span class="math-container">$- \eta$</span>, as the difference is reversed, with <span class="math-container">$f_i$</span> being the term with the negative sign.</p>
<p>From the cutoff, these two new terms “activate”:</p>
<ul>
<li><span class="math-container">$\alpha$</span>, which is a constant. Assuming <span class="math-container">$\alpha &gt; 0$</span>, 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 <span class="math-container">$\delta$</span>, this “would-be-intercept” is <span class="math-container">$\delta + \alpha$</span>.</li>
<li><span class="math-container">$\lambda (f_i - f_z)$</span> which is a linear term on the difference: From the cutoff, this term adds a slope of <span class="math-container">$\lambda$</span>. With this, we get that the slope of the regression (on <span class="math-container">$f_i$</span>) becomes <span class="math-container">$\lambda - \eta$</span>.</li>
</ul>

CC BY-SA 4.0
2023-05-16T12:58:37.263Z
2023-05-17T13:00:41.597Z
2023-05-17T13:00:41.597Z
Nicolas Torres
<p><a href="https://i.sstatic.net/7QhSq.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/7QhSq.png" alt="enter image description here" /></a>Dear all,
I found this equation to estimate a RDD in a paper. <span class="math-container">$(f_i-f_z)$</span> is the running variable, hence <span class="math-container">$\alpha$</span> should be the slope to the left of the cutoff and <span class="math-container">$\lambda$</span> 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 <span class="math-container">$\eta$</span>?</p>

CC BY-SA 4.0
2023-05-16T12:43:21.890Z
look again. Is $\alpha$ a slope or an intercept?
user18214
<regression><applied-econometrics><rdd>
Regression Discontinuity Design equation
userF
# Regression Discontinuity Design equation

(Asked by: username_0 on 2023-05-16)

[![enter image description here](https://i.sstatic.net/7QhSq.png)](https://i.sstatic.net/7QhSq.png)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 $\eta$?

**Tags:** regression, applied-econometrics, rdd
> **Comments:**
> **username_1**: look again. Is $\alpha$ a slope or an intercept?  

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## 1 answers

### Answer by username_2 on 2023-05-16. Score: 1

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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