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?

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.
