# Does "Regression Discontinuity" Require the Presence of an Intervention?

I have been trying to learn more about "Regression Discontinuity". This appears to be a statistical method designed at testing the effectiveness of some sort of intervention. The Wikipedia article (https://en.wikipedia.org/wiki/Regression_discontinuity_design) states that "regression discontinuity design (RDD) is a quasi-experimental pretest-posttest design that aims to determine the causal effects of interventions by assigning a cutoff or threshold above or below which an intervention is assigned."

I had the following question: For the Regression Discontinuity framework to be valid - does an intervention have to be present?

As an example - suppose you are interested in studying if neighborhoods with higher median incomes have more hospital-to-population ratios. At first glance, the following analysis options seem possible:

• Decide some arbitrary cut-off (e.g. median income less than 50k and median income greater than 50k) and perform a hypothesis test to examine if the average hospital-to-population ratios in neighborhoods above and below this cut-off are statistically similar.

• Assuming linear correlation, you can calculate Pearson's Correlation Coefficient to study the correlation between both variables.

• You can also fit a standard regression model to study the general effect of median income on the hospital-to-patient ratio.

However, I am interested about performing analysis around some cut-off value (e.g. \$50,000).

I have heard many professors on YouTube lectures mention that in real world examples, individuals just below some arbitrary cut-off are likely to similar to individuals just above this same arbitrary cut-off (in all other observable aspects).

Using a similar thought process, it could be thought that neighborhoods with a median income of 49k are likely very similar to neighborhoods with a median income of 51k. Thus, if the hospital-to-population ratio were to suddenly "jump" around the 50k mark - we might have reasons to believe that something special happens at the 50k median income mark that could be worth further investigating.

However, in this example, there does not seem to be an active intervention. I have usually seen Regression Discontinuity presented in examples where students who score above 90% on an exam were (deliberately) awarded a scholarship (i.e. an intervention) and those who scored below 90% were not given a scholarship, and the researchers were interested in studying the effect of receiving this scholarship on whether the graduation rates between both students. In my example, the people in charge of deciding if a hospital should be built in a specific neighborhood were likely not actively making this decision by explicitly consulting the median income of each neighborhood - thus, I am not sure if this can be considered as an active intervention and if Regression Discontinuity is appropriate in such a problem as mine (i.e. median income vs hospital-patient ratio over some arbitrary cutoff).

Can someone please comment on this? In my example that I have outlined - is the Regression Discontinuity design a suitable approach, given this "indirect intervention"?

PS: I found this R package online (https://cran.r-project.org/web/packages/rdmulti/rdmulti.pdf) - apparently Regression Discontinuity can be used to analyze the "jumps" in multiple cut-offs?

• It is hard to see anything in the theory which supposes an intervention. Commented Nov 26, 2022 at 17:06
• I share your skepticism about arbitrary cutoffs based on convenient or “round” numbers. If there are real threshold effects (e.g., a company over a certain size has to report certain data), then the approach seems more reasonable.
– Dave
Commented Nov 30, 2022 at 3:35
• Assuming linear correlation, you can calculate Pearson's Correlation Coefficient to study the correlation between both variables. You do not have to assume linear correlation for linear correlation to be well defined. You could assume a linear relationship / a linear model, but again that is not necessary. Commented Dec 5, 2022 at 10:08
• @Dave Yes, if the answer is still marked as accepted when the grace period expires, half the bounty will be awarded. But if you look at the post history, you can see that the answer was accepted after I wrote my initial comment, but before you wrote your most recent comment.
– Sycorax
Commented Dec 7, 2022 at 21:10
• @stats_noob Upvoting answers that are helpful is great. I'm asking why you haven't awarded a bounty on several of your recently bountied questions. A person might make the inference that it is not worth the effort to write a high-quality answer to your bountied questions, because they may not be rewarded with the bounty. For instance, dimitry has not yet received the bounty, and only 6 hours of grace period remain. Why is that?
– Sycorax
Commented Dec 7, 2022 at 21:12

You need an intervention/treatment for RD to make sense. The basic idea is that by looking around the cutoff, you are comparing people with similar unobservables, with the only difference coming from the intervention. This is why you see people run various false placebo tests with RD.

Since you are looking for an authoritative source, I recommend A Practical Introduction to Regression Discontinuity Designs: Foundations. On page 3 of the draft version, they write

There are three fundamental components in the RD design—a score, a cutoff, and a treatment.

To use your example, suppose you want to figure out the causal effect of local income on the hospital beds to population ratio. The concern is that people must be paid more to take on riskier or more stressful work because it makes them sicker. Hospitals choose to locate near sicker and wealthier people. So some of the observed relationship between income and hospitals may be because of this omitted job risk-health factor. If you went out and just gave people bags of money, it would have a smaller effect on hospital construction and availability than the richer vs. poorer neighborhood comparison you propose.

There is something called Geographic RD, which is similar in spirit to what you have in mind. Here the running variable is two-dimensional (latitude and longitude). For example, some counties in the US state of Colorado have all-mail elections where voting can only be conducted by mail, and in-person voting is not allowed. In contrast, other counties have traditional in-person voting. Where the two types of counties are adjacent, the administrative border between the counties induces a discontinuous treatment assignment between in-person and all-mail voting. A Geographic RD design can be used to estimate the effect of adopting all-mail elections on voter turnout. This is covered in A Practical Introduction to Regression Discontinuity Designs: Extensions (the second unpublished volume of the pubkushec book I mentioned above). Note that there is still a treatment of different laws here.

• @ Dimitriy : thank you for your answer! Just to reiterate - in my original question, the way I have described the problem: Regression Discontinuity is not appropriate because there is no "direct intervention" - correct? Commented Nov 30, 2022 at 8:05
• Yes, that’s right. Commented Nov 30, 2022 at 8:07
• This is a good answer, but it suggest that the theory requires an intervention to make sense. Regression discontinuity is just fitting different lines to different regions of the data. That idea makes sense without an intervention. It can be used as an interpretable approximation to a more complex function. Piecewise linear splines are essentially the same model with more knots/lines, and no one would say you need interventions corresponding to each knot point.
– Eli
Commented Dec 4, 2022 at 17:57
• @Eli The point of RD is not to approximate a complex function, but estimate an effect by a gap between lines at the threshold. We don’t even care about the whole line, just the neighborhood around the threshold. PLS would not work here since it forces the pieces to connect, though that could be useful in a kink RD design where we are interested in a change in a slope at the threshold rather than in the level. Commented Dec 4, 2022 at 18:21
• To make it concrete, suppose we are interested in how unions change wages. RD compares post-unionization wages in firms with a 49% pro vote with wages in firms that had a 51% pro vote. We are not just fitting curves on two regions of the data. The threshold is meaningful because the probability of intervention/unionization changes when there is a majority in favor. We are also not trying to approximate a whole curve that speaks to what would happen to wages had a firm with a pro vote of 5% unionized. The two curves are necessary, but you need lots of other stuff before it becomes RD. Commented Dec 4, 2022 at 19:00