# Lecture 22 Regression Discontinuity

## Nick Huntington-Klein

### March 17, 2019

## Recap

- We’ve been going over ways in which we can use control groups to isolate causal effects
- We can select similar control groups using matching or controlling (what economists call “selection on observables”)
- We can use a treated group at a different time as its own control group with fixed effects
- When a treatment is applied at a particular time, we can select a reasonable control to account for the effects of time using difference-in-difference (a “natural experiment”)

## Today

- We’re going to go over one other way in which we can find and isolate a very convincing control group
- Like DID, it’s also an example of a natural experiment
*Regression discontinuity*

## Regression Discontinuity

- For regression discontinuity to work, we need the Treatment to be assigned based on a
*cutoff* of what’s called a “running variable”
- For example, imagine we want to know the effects of being in a Gifted and Talented (GATE) program on your adult earnings
- Being admitted to the program is based on your test score (running variable)
- If you score above 75, you’re in the program. 75 or below, you’re out!

## Regression Discontinuity

- Notice that the y-axis here is
*In GATE*, not the outcome

## Regression Discontinuity

- Here’s how it look when we look at the actual outcome

## Regression Discontinuity

- Now, we have a bit of a problem!
- If we look at the relationship between treatment and going to college, we’ll be picking up the fact that higher test scores make you more likely to go to college anyway