Exercise 2 (15 minutes)

You practice: a non-parametric RDD with rdrobust(), and what the bandwidth does to your answer. When you're done, assist some of the others …

Same study as exercise 1 — Uruguay's cash transfer and the question of whether welfare buys political loyalty — but now the state-of-the-art estimator: rdrobust(), which fits a local linear regression inside an optimal bandwidth with triangular-kernel weights.

pacman::p_load(tidyverse, rdrobust, causaldata)
data("gov_transfers", package = "causaldata")

1. Run it. Estimate the RDD with rdrobust(): outcome Support, running variable Income_Centered, cutoff c = 0. Read the Conventional coefficient. The estimate is about . Is it statistically significant? NoYes

R solution — don't peek too early ;) !

RDD <- rdrobust(gov_transfers$Support, gov_transfers$Income_Centered, c = 0)
summary(RDD)

2. Why so uncertain? In exercise 1 the parametric model — using all the data — found a clear, significant effect of about 0.10. Here rdrobust() cannot even reach significance. Look at the bandwidth it chose (h ≈ 0.005) and the number of observations left inside it. The most likely reason the non-parametric estimate is so imprecise is that the optimal bandwidth is tiny, so very few households are used — low reliabilityrdrobust ignores the running variablethe effect is genuinely zero

3. Turn the bandwidth up by hand. rdrobust() takes an argument h to set the bandwidth yourself. Re-run it with h = 0.02. The estimate is now about , and it is statistically significant. The wider window changed the studyA wider window uses far more households, so the estimate becomes precise enough to detect the effect

R solution

RDD_wide <- rdrobust(gov_transfers$Support, gov_transfers$Income_Centered, c = 0, h = 0.02)
summary(RDD_wide)

4. Mind the sign. In exercise 1 the parametric \(\lambda\) was +0.10; here rdrobust() reports about −0.10 for the same effect. rdrobust() always estimates (value just above the cutoff) − (value just below). In this study the households who received the transfer are below the cutoff. So the negative sign means: the transfer reduced supportthe same finding as exercise 1 — support is higher on the treated (below-cutoff) side, just measured above-minus-belowrdrobust made an error

5. Write one sentence as a # comment reconciling the two exercises — then compare:

Model answer

Both exercises say the transfer raised government support by roughly 0.10 on the 0–1 scale. The parametric model reported it as +0.10 for a below-cutoff dummy; rdrobust() reports it as −0.10 because it measures the jump as above-minus-below, and the treated sit below. The sign is bookkeeping — the substantive finding is identical. The lesson is that at the MSE-optimal bandwidth the local estimate was too imprecise to detect, and widening the window traded a little bias for the precision needed to see the effect.

6. Discuss with your neighbour.

   • rdrobust() picked a smaller bandwidth than the one that finally revealed the effect. Is the algorithm "wrong"? What is it optimising, and why might that differ from "find me a significant result"?
   • You could keep widening h until the stars pile up. Why would that be p-hacking, and what protects an honest RDD against it?
   • Which estimate would you report in a paper — the parametric 0.10, the optimal-bandwidth rdrobust, or the hand-widened one? Defend your choice.

Talking points

• The optimal bandwidth minimises expected error (bias + variance), not the p-value. A tiny window here means minimal bias but high variance — a wide, honest confidence interval. It is not "wrong"; it is telling you this dataset cannot pin the effect down tightly at the cutoff.
• Choosing the bandwidth after seeing which one gives significance is fishing — you are no longer running one test but many, and a "significant" result becomes meaningless. The protection is to pre-commit to the algorithm's bandwidth (and report robustness across a reported range), exactly as you would pre-register an analysis.
• Defensible answers differ. Best practice is to lead with the rdrobust optimal-bandwidth estimate (the principled default), and show the estimate is stable across a range of bandwidths — honesty about uncertainty beats a single starred number.