Regression Dicontinuity

Question 1

When use RDD?

Distinction between Sharp and Fuzzy RDD

Answer 1

Assignment to treatment is determined completely/partly by the value of a (running) variable being on either side of a known threshold
Sharp RDD: assignment completely determined by value of running variable
Fuzzy RDD: assignment partly determined by value of running variable

Question 2

Example: Sharp RDD estimates the ATT at the threshold

Answer 2

Jump in the outcome at the threshold is interpreted as a causal effect: in small neighborhood around threshold treatment is as good as randomly assigned
Cum-laude example: natural comparison group (counterfactual), any difference in earnings can be attributed to cum-laude effect

Question 3

Example: Fuzzy RDD estimated LATE at threshold

Answer 3

Incentives to participate change but not sufficient to move all individuals from non-treatment to treatment
If the jump in the running variable is accompanied by a jump in the outcome at exactly the same point, interpreted as evidence of causal effect
Example: minimum drinking age of 21, (1) increase in drinking (2) increase in mortality, argued that increase in mortality due to increase in alcohol consumption
Change in the outcome at the threshold should be weighted by the fraction of compliers: if only few individuals affected, estimated impact is larger - almost all individuals are affected, very close to Sharp RDD

Question 4

How does RDD obtain the counterfactual and why is there no problem with omitted variables?

Answer 4

Take a bunch of people arbitrarily close to the threshold to obtain the counterfactual
If you compare individuals within a very local bandwidth, treated and controls are as good as randomly assigned
As treatment depends only on running variable, no omitted variable bias

Question 5

Regression equations for RDD

Answer 5

Sharp: identify ATT for individuals with X value equal to c: E[Y(1) - Y(0) | X = c]
Fuzzy RDD:
First stage: jump in treatment variable
Reduced form: jump in outcome variable
Treatment effect = jump in outcome / jump in treatment

Question 6

Checks and balances when implementing RDD

Answer 6

Graphical analysis should be integral part of RDD
Vary the bandwidth to check robustness of your results
Check the behavior of other variables at the threshold
Is there sorting around the threshold: can individuals manipulate around the threshold?

Question 7

Relationship between IV and Fuzzy RDD

Relation between RDD and matching

Answer 7

In RDD, as opposed to IV, the instrument (running variable) is allowed to influence to outcome directly - identification comes from distinguishing between the smooth relation between running variable and outcome and the discontinuous jump in the running variable due to the treatment
In contract to matching, RDD does not have common support - identification comes from picking a group of individuals very close to the threshold

Question 8

External validity of RDD

Answer 8

Might not be good (it does have high internal validity)
Estimation is done in very small neighborhood around the threshold
Fuzzy RDD estimated LATE (only for compliers)
Even more local: only individuals near threshold