Regression Discontinuity Design Flashcards
Lecture 9 (23 cards)
RDD treatment
the treatment (D) is not randomly assigned, but it is determined, at least
partly, by the value of an observed covariate X lying on either side of a fixed threshold c.
used in?
rule-based settingas
design is reliant on?
us knowing about and having access to a running variable that
determines the treatment status.
what is a running variable (X)?
a score which determines treatment
Cutoff (C) is?
the value of the running variable at which treatment is
▶ assigned when unit running variable score (X) is above cutoff
▶ not assigned when unit running variable score (X) is below cutof
Sharp?
All units with a score above a cutoff is assigned to treatment
Fuzzy
Propensity to be treated increases at cutoff point but compliance with
treatment is imperfect (not fully determined treatment assignment). Use running variable
as an instrumental variable
in an RDD treatment not randomly designed but…
determined at least partly by the value of an observed covariate x lying on either side of a fixed threshold
identification assumption?
that potential outcomes are continuous in X around c
around the cut off, what happens
random assignment essentially near the cut-off
forcing variable
same as running variable
In SRD the assignment to treatment Di is ?
Completely determined by the value of the covariate Xi being on either side of the threshold C
If Xi > C
Treated
If Xi < C
not treated
Potential outcomes at the cut-off?
Very similar and continuous
What do we calculate at the cut-off?
The LATE
Issue with the LATE?
Dont observe both quantities at the cut-off
Potential Outcomes at the cut-off
lim
x↓c
E[Y | X = x] − lim
x↑c
E[Y | X = x]
Implications
We extrapolate to infer potential outcomes at c.
▶ Without further assumptions, the LATE only identifies the ATE at c.
Continuity Assumption
. Trim the sample to a reasonable window around the cutpoint c
▶ c − h ≤ Xi ≤ c + h, were h is some positive value that determines the size of the
window
2. Generate X˜ which measures the distance to the threshold:
X˜ = X − c so X˜i =
X˜ = 0 if X = c
X >˜ 0 if X > c and thus D=1
X <˜ 0 if X < c and thus D=0
3. Decide on a model for E[Y | X]
▶ linear, same slope for E[Y0 | X] and E[Y1 | X]
▶ linear, different slopes for E[Y0 | X] and E[Y1 | X]
▶ non-linear
Linear Same-Slope
E[Y0 | X] is linear: E[Y0 | X] = µ + βX
bias -variance tradeoff
SMall window = treatment effects variable, large window = sensitive to model
