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Regression Discontinuity Design

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Regression Discontinuity Design

Session Report
Riya Shah

Mr. Rakesh Pandey began by suggesting some of the research papers based on the topic by various renowned professors, for example, Persistent Effects of Mita Mining. The economics paper tries to study Mita’s economic system in Latin America. The paper written by Melissa Del talks about the persistent effects of Matha, a very innovative way of doing it and that is employing the Regression discontinuity. Mita happened in 1500-1600 AD, 400 years ago.

She was trying to see the areas where Mita mining happened, so she went back 400 years and tried to draw the area Map of Chile identifying the region where the Mita was operational and then serves every household which requires some technicalities of geographic GIS and GPS coordinates. Still, she serves individuals in those regions right now and then also serves people outside the region.

Then she calculates the shortest distance between the border of the person whom she has surveyed inside the Mita area and outside the Mita area, so it can range from zero because everyone in both the groups which is outside and inside the Mita boundary if everyone is say, or say if there are two people on the same boundary that distance is zero but if you go farther and farther in terms of where they are located you can see the distance increasing becoming a setup for doing regression discontinuity.

Discontinuity and Treatment

  • When someone is assigned treatment on one side of a line and people on the other side don’t get it.
  • The individuals who receive the treatment based upon the cutoff and those who don’t may be similar.
  • The possibility of similarity at the cutoff point is the crux of setting up a regression discontinuity design.

RDD Vocabulary and the Core Idea

  • Running Variable: The running variable is the variable that determines whether you’re treated or not.
  • Cutoff: The cutoff is the value of the running variable that determines whether you get treatment.
  • Bandwidth: how much area around the cutoff we are willing to consider comparable.

The core of the research design of regression discontinuity is to:

  • Account for how the running variable normally affects the outcome.

Focus on observations right around the cutoff, inside the bandwidth.

  • Compare the just-barely-treated against the just-barely-didn’t to get the effect of treatment.

Examples of Cut-offs

  • Geographic – Border.
  • Politics – Winning margins
  • Age Retirement

In each of these cases, we can pretty reasonably imagine that cases that are just barely to either side of the cutoff are comparable, and any differences between them are the fault of treatment. In other words, we’ve identified the effect of treatment.

When we can apply regression discontinuity?

We are looking for some sort of treatment that is assigned based on a cutoff.

  • There is a running variable that determines treatment.
  • Our strategy is going to be assuming that people close to the cutoff are effectively randomly assigned, there shouldn’t be any obvious impediments to that randomness people shouldn’t be able to manipulate the running variable to choose their treatment.
  • People who choose what the cutoff is shouldn’t be able to make that choice in response to finding out who has which running variable values

How does regression discontinuity work?

  • Choose a method for predicting the outcome on each side of the cut-off.
  • Choose a bandwidth (optional

Setting up a regression discontinuity

  • The running variable does seem to be related to the outcome even when we’re not around the cutoff, which is fine.
  • We also have a cutoff value at which treatment was applied. And we see a jump in the outcome at that cutoff! That’s exactly what we want to see.

Fuzzy regression continuity

  • In a lot of regression discontinuity applications, being on one side or another of the cutoff only changes the probability of treatment.
  • In these cases, we have what’s called a fuzzy regression discontinuity, as opposed to a “sharp” regression discontinuity where treatment rates jump from 0 to 100 percent.

Takeaways

  • First, as with any other method where we isolate just the part of the variation where we can identify the effect, we need to assume that nothing fishy is going on in that variation.
  • We’re estimating the effect of treatment, sure, but we’re estimating the effect of the cutoff and attributing that (or part of that, if it’s fuzzy) to the treatment.
  • So if anything else is changing at the cutoff, we’re in trouble.
  • This assumption is the assumption that the outcome is smooth at the cutoff.
  • That is, if treatment status hadn’t changed at the cutoff (if nobody near the cutoff had gotten treated, or everyone had, or everyone had the same chance of being treated), then there would be no jump or discontinuity to speak.

Empirical Model

Ỵ = β01(Running – Cutoff) + β₂Treated+ β3(Running – Cutoff) ×Treated +ε

  • (Running cutoff) takes a negative value to the left of the cutoff, zero at the cutoff, and a positive value to the right.
  • Notice the lack of control variables in Equation – it’s to help focus your attention on the design.
  • The whole idea of regression discontinuity is that you have a nearly random assignment on either side of the cutoff.
  • It’s not that adding controls is wrong, but you should think carefully about whether you need them if you think that treatment is completely assigned by the cutoff.
  • Controls may be more necessary in fuzzy regression discontinuity, where there are determinants of treatment other than the cutoff.

Conclusion:

Mr. Rakesh Pandey further explained the topics illustrating the data and clearing the doubts of the students.

Acknowledgment: Reet Lath is a research Intern at IMPRI.

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