Exercise 1 (20 minutes)

You practice: building and reading a parametric RDD — did a cash transfer buy political support? When you're done, assist some of the others …

Can a government buy the loyalty of the poor? Whether welfare and patronage translate into political support — or whether citizens keep the help they receive separate from the party that governs — is one of the oldest questions in political sociology (clientelism, the "moral economy" of redistribution). Uruguay's PANES programme is a natural experiment on exactly that: a monthly cash transfer went to poor households, and eligibility ran off a predicted income score — score below the threshold and you got the money; above it, nothing. Did receiving it raise political support for the government that sent it? Marco Manacorda, Edward Miguel and Andrea Vigorito studied this, and you get their data to replicate it.

Manacorda, Marco, Edward Miguel, and Andrea Vigorito. 2011. "Government Transfers and Political Support." American Economic Journal: Applied Economics 3(3):1–28.

pacman::p_load(tidyverse, estimatr, modelsummary, causaldata)

# The data ship inside the causaldata package — no file to download.
data("gov_transfers", package = "causaldata")

The running variable is Income_Centered: income relative to the threshold, already centred at 0 and in logarithmic units (so 0.01 ≈ 1 % above the threshold). The outcome Support runs from 0 to 1 (both adults said "no" = 0, one each = 0.5, both "yes" = 1).

Watch the treated side. In the drinking-age lecture the treated were above the cutoff. Here it is the other way round: households below the threshold (Income_Centered < 0) are the ones who received the transfer. RDD does not care which side is treated — only that a rule splits it.

1. Plot the discontinuity. Draw Support against Income_Centered, add a vertical line at the cutoff (0), and use geom_smooth(method = "lm") fitted separately on each side. Does support appear to jump at the cutoff? No, the two sides line upYes, support is higher just below the cutoffIt is impossible to tell

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

gov_transfers <- gov_transfers %>%
  mutate(rule = if_else(Income_Centered < 0, "Received transfer", "No transfer"))

ggplot(gov_transfers, aes(y = Support, x = Income_Centered)) +
  geom_jitter(alpha = 0.15, height = 0.02, width = 0) +
  geom_vline(xintercept = 0, colour = "red", linetype = "dashed") +
  geom_smooth(aes(group = rule), method = "lm") +
  labs(title = "Uruguay PANES programme",
       x = "Income relative to cutoff (0.01 ≈ 1%)",
       y = "Support for the government") +
  theme_minimal()

2. Predict before you compute. The eye is easily fooled. Before running any regression, commit to a guess: did receiving the transfer raise support, lower it, or do nothing? There is no wrong guess — pick one, then test it.

3. Estimate the jump. Create a dummy D that is 1 when Income_Centered < 0 (received the transfer) and 0 otherwise. Fit a parametric RDD: Support on D, the running variable, and their interaction, with lm_robust().

Hint

lm_robust(Support ~ D * Income_Centered, data = gov_transfers) — after you have built D.

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

gov_transfers <- gov_transfers %>%
  mutate(D = if_else(Income_Centered < 0, 1, 0))

RDD <- lm_robust(Support ~ D * Income_Centered, data = gov_transfers)

modelsummary(list("Support for the government" = RDD),
             coef_rename = c("D" = "Received transfer (λ)",
                             "Income_Centered" = "Income (centred)",
                             "D:Income_Centered" = "Transfer × income"),
             stars = TRUE, gof_map = c("nobs", "r.squared"), output = "kableExtra")

The local effect of the transfer, \(\lambda\) (the coefficient on D), is about . Is it statistically significant? NoYes

4. Write one sentence as a # comment interpreting \(\lambda\) — then compare:

Model answer

Receiving the PANES transfer raised support for the government by about 0.10 on the 0–1 scale, right at the eligibility cutoff — and the effect is statistically significant. Because the comparison is between households just below and just above the threshold, who are otherwise alike, we can read this causally: the cash bought goodwill.

5. How far does this generalise? Suppose the government had set a far higher income threshold, letting many richer households in too. What does your estimate tell us about the effect there? The effect would be the same everywhereSince more households would benefit, the effect would be largerWe do not know — the estimate is local to the cutoff

6. Discuss with your neighbour.

   • Why is a household on Income_Centered = -0.01 a good comparison for one on +0.01, but a household on -0.5 a poor one?
   • The "no sorting" assumption says households must not be able to place themselves just below the line. How might that fail for an income-based rule — and how would it break the design?
   • Support is revealed, not the household's private opinion. Does that change what we have shown?

Talking points

• Near the cutoff the two households are near-identical in income and everything correlated with it, so the only systematic difference is the transfer — as good as random. Far apart, -0.5 is a much poorer household that differs in many ways, reintroducing selection bias.
• Income can be under-reported or timed to fall just under an eligibility line, especially once the rule is known. Households who manipulate their way below are self-selected (perhaps more motivated or better informed), so a jump could reflect who sorts below, not the transfer itself.
• It shifts the interpretation from private attitudes to expressed/behavioural support, which is arguably what matters politically — but it is a different construct, and worth being precise about.

7. Bonus, for the fast. The parametric model used all the data. Re-fit on a narrow window around the cutoff (e.g. abs(Income_Centered) < 0.05). Does \(\lambda\) change much? What happens to the standard error, and why?

R solution

RDD_narrow <- lm_robust(Support ~ D * Income_Centered,
                        data = gov_transfers %>% filter(abs(Income_Centered) < 0.05))
modelsummary(list("Narrow window" = RDD_narrow),
             stars = TRUE, gof_map = c("nobs", "r.squared"), output = "kableExtra")

The point estimate stays in the same ballpark, but the standard error grows — fewer observations mean less precision. That is the bias–reliability trade-off in miniature, and it is exactly what next week's rdrobust() bandwidth automates.