EMET8002 Chap.10 Regression Discontinuity and Kink Designs
Regression Discontinuity and Kink Designs
Thresholds as experiments
When treatment depends on a running variable crossing a known cutoff, units just either side are comparable, and the jump in outcomes at the cutoff estimates the treatment's effect.
The chapter covers sharp and fuzzy designs, the continuity assumption, the McCrary test and the need for large samples near the cutoff.
Cases and kinks
The lecture's cases follow: Norwegian fields of study, Hoekstra's flagship university premium and the regression kink design for Austrian unemployment benefits, where the slope of the benefit formula changes at a maximum.
Showing that a cutoff is credible
A threshold design earns credit when the write-up shows the cutoff is credible: who sets it, why units cannot place themselves precisely on one side, and evidence that observations do not bunch at it.
The lecture adds that visualisation is essential and that large samples near the cutoff are needed, so a strong answer plots both the first stage and the outcome against the running variable and reports how many observations lie close to the threshold.
What this chapter covers
- 01
Running variables and cutoffs
- 02
Sharp regression discontinuity
- 03
Continuity and the McCrary test
- 04
Fuzzy designs as instrumental variables
- 05
Fields of study in Norway
- 06
The flagship university premium
- 07
Regression kink designs
- 08
When to use a kink or a discontinuity
Worked example · free
Reading a jump at a scholarship cutoff
- 1At the cutoff the score is zero, so the predicted completion rate is 60 just below and 66 just above.
- 1The jump of 66 − 60 = 6 points is the estimated effect for students near the cutoff.
- 1It assumes that without the scholarship completion would pass smoothly through the cutoff.
Key terms
- Sharp Design
- A discontinuity design in which treatment switches from 0 to 1 exactly at the cutoff.
- Fuzzy Design
- A discontinuity design in which the probability of treatment jumps by less than one at the cutoff.
- Regression Kink Design
- A design that uses a change in the slope of a treatment rule at a threshold.
- Continuity Assumption
- The requirement that outcomes would pass smoothly through the cutoff without treatment.
Regression Discontinuity and Kink Designs FAQ
What is the difference between a sharp and a fuzzy RDD?
In a sharp design, treatment jumps from 0 to 1 at the cutoff, so the outcome jump is the effect. In a fuzzy design, only the probability of treatment jumps, so the outcome jump is divided by the treatment jump, which is estimated by two-stage least squares.
What did Hoekstra find about flagship universities?
Using the SAT admission cutoff at a state flagship university as a fuzzy discontinuity, he found jumps in both enrolment and later earnings at the cutoff, with an estimated earnings premium of about 9.5% for attending the flagship.
When should I use a regression kink design instead of an RDD?
Use a kink design when the treatment is continuous and only its slope changes at a threshold, as with a benefit formula that pays a share of earnings up to a maximum. Use an RDD when the probability of treatment jumps at the threshold.
Why is an RDD estimate described as local?
It compares units just above and just below the cutoff, so it measures the effect for people near the threshold. The effect for units far above or below may differ, and the estimate says nothing about them without further assumptions.
What is a running variable?
It is the observed score whose position relative to a known cutoff determines treatment, such as a grade point average, an entrance test score, age or income. The outcome is compared just either side of the point where the running variable crosses the cutoff.
Assessment move
For each threshold design, sketch the first stage and the outcome against the running variable before writing any equation. Then list one reason units might sort around the cutoff and the check that would detect it. Finally, find one tax or benefit rule with a maximum or a rate change and describe the kink design it would support.
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