RDD in Edx

Regression Discontinuity Design

There is a limitation, however, is that we can’t say much about the impact of the intervention for those who are far from the cutoff. So we learn about a select subset of the population.

Implementing the RD Approach

\(S_i\) being the \(r_i - r^c\), meaning it is the variable measuring the difference between the the difference between the running variable (a score for example) and the cutoff value (eligility limit)

Individuals who are ineligible for the intervention have values of \(S_i\) less than 0. And those who are eligible have values of \(S_i\) greater than 0.

Our assumption is that there are no jumps at 0 without the intervention. In the presence of the intervention, we’re going to try to describe the relationship between \(S_i\) and \(y\) in two parts, one below the cutoff and one above it, and see if they match up.

Implementing the RD Approach

A visual inspection of the data with these fitted lines gives us a first indication of whether the outcome variable exhibits a kind of a jump at the cutoff. In this first example, there seems to be a jump in the outcome variable at s equals 0.

The size of the impact is the difference in the estimated intercepts : \(\hat{\alpha}_{below}\) and \(\hat{\alpha}_{above}\)

But if our analysis has yielded a figure more like this one, then we might not be so confident that the intervention had made a difference. It’s true that those who are eligible have higher outcomes than those who are not, but this difference probably reflects the fact that people with higher values of the running variable are inherently different to those with lower values and is unlikely to be attributable to the intervention being studied.