GV249 Seminar WT8: Regression Discontinuity Design

Outline

• Introducing quasi-experiments

Online resources

In addition to the lecture, seminar and core readings there good online textbooks for causal inference. When writing your research designs, it’s worth looking at what these say on the design you are using for more details.

• Huntington-Klein - The Effect

Quasi-experiments

• The three assumptions needed for causal inference - (1) independence (2) excludability (3) non-interference - are easiest to meet with a randomised experiment.
  • Quasi-experiments do not involve randomisation.
  • They use additional assumptions to meet the conditions.
• When are quasi-experiments useful?

RDD - What we need

1. Continuous “running” variable \(X\)
2. Treatment status (\(D\)) determined by a cut-off (\(C\)) based on a value of \(X\)
3. A bandwidth around the cutoff (\(H\))

RDD - What we need

RDD

• Core idea: individuals very close to the cut-off are “as-if” randomly assigned to treatment of control.

• If our assumptions hold, we can identify the ATE for individuals close to the cutoff -> LATE

RDD - Graphically

Source: Huntington-Klein - The Effect

RDD - Key assumptions

• No sorting around the threshold
  • As this would mean individuals are selecting into treatment
• No discontinuity in covariates
  • Otherwise, changes might be caused by differences in these variables
• Treatment is the only thing that changes at the threshold
  • To fulfil the excludability assumption

RDD - Robustness checks

Robustness checks are tests that increase our confidence the

• Balance checks to check for continuity in other covariates
• Density tests to check for (sorting)

Further robustness (which we will cover in the lab)

• Different bandwidths
• Polynomial specifications
• Placebo outcomes; placebo cutoffs

Fuzzy RDD

RDD - Estimation

• We could fit one model with two lines - one for before and one for after, However, this can mask “non-linearity”:

RDD - Estimation

• Local linear regression
  • Weighted regression restricted to small bandwidths around a value of \(X\). Observations closer to the value are weighted more.
  • The “kernel” determines the weights, we use an algorithm to choose the best kernel.

RDD - Example 1

What is the effect of a radical right party winning seats in parliament?

• In many PR systems, there is a minimum vote threshold (e.g. 5%) a party needs before it gains seats.

Abou-Chadi & Krause (2018)

RDD - Example 2

What is the effect of living with others on turn out?

Dahlgaard et al (2021)

🏃 Exercise

How might you use an RDD to study this?

1. What is your running variable and cut-off?
2. What assumptions need to be met?
3. Might people be able to sort across the boundary? How could you show they aren’t?
4. What robustness checks would you need to do?