Exercise 1 (20 minutes)

You practice: a treatment × country interaction — did one natural experiment hit ten countries the same way? When you're done, assist some of the others …

Back to Legewie's Bali natural experiment — but this time across ten countries. Was the effect of the terror attack on xenophobia the same everywhere, or did it depend on the country? That is an interaction between the treatment and country.

1. Prepare the data. This keeps ten countries and makes Portugal the reference (it had the clearest effect, so it is the natural baseline to compare the others against).

pacman::p_load(tidyverse, haven, estimatr, modelsummary)
ESS_raw <- read_dta("Legewie_ESS_02.dta") # from your project folder

event_date <- as.Date("2002-10-13")   # the Bali attack
win_begin  <- as.Date("2002-09-14")
win_end    <- as.Date("2002-10-20")

ESS <- ESS_raw %>%
  mutate(
    int_date = as.Date(sprintf("%s-%s-%s", inwyr, inwmm, inwdd)),
    treat = case_when(
      int_date > event_date & int_date <= win_end   ~ "After the attack",
      int_date < event_date & int_date > win_begin  ~ "Before the attack",
      TRUE ~ NA_character_) %>% fct_relevel("Before the attack", "After the attack"),
    anti_immi = rowMeans(across(c(imtcjob, imbleco, imbgeco, imueclt,
                                  imwbcnt, imwbcrm, imbghct)), na.rm = TRUE) %>%
      scale() %>% as.numeric(),
    anti_immi = max(anti_immi, na.rm = TRUE) - anti_immi,
    across(c(brncntr, mocntr, facntr), as_factor),
    age  = inwyr - yrbrn,
    empl_stat = case_when(
      pdwrk == 1 ~ "Working", uempla == 1 ~ "Unemployed",
      rtrd == 1 ~ "Retired", TRUE ~ "Other"),
    pspwght = pweight * dweight
  ) %>%
  filter(!cntry %in% c("DK", "IL", "HU") &                # keep 10 countries
           brncntr == "yes" & mocntr == "yes" & facntr == "yes") %>%
  select(treat, anti_immi, cntry, pspwght, age, empl_stat) %>%
  drop_na() %>%
  mutate(cntry = fct_relevel(cntry, "PT"))               # Portugal = reference

Stuck?

• Did pacman::p_load(...) run without red errors? Fix that first.
• read_dta() can't find the file? Legewie_ESS_02.dta must sit in your project folder.
• Odd results? Session → Restart R, then rerun from the top.
• Still stuck? Ask in the t-R-ouble forum on Absalon.

2. Predict before you compute. You are about to fit anti_immi ~ treat * cntry. In that model, what will the plain treatAfter the attack coefficient represent? The attack effect in Portugal, the reference countryThe average attack effect across all ten countriesThe attack effect in every country

3. Fit the interaction and look at whether the country-specific terms differ from Portugal.

Hint

lm_robust(anti_immi ~ treat * cntry, data = ESS, weights = pspwght) — the treat:cntryXX rows are how much each country's effect differs from Portugal's.

R solution <U+2014> don't peek too early ;) !

ols_int <- lm_robust(anti_immi ~ treat * cntry, data = ESS, weights = pspwght)

modelsummary(list("Xenophobia" = ols_int),
             stars = TRUE, gof_map = c("nobs", "r.squared"),
             output = "kableExtra")

Compared with Portugal, are the effects in the other countries mostly weaker or stronger? No significant differencesMost are significantly smallerMost are significantly larger

4. Read a main term. What was the effect of the Bali attack in Portugal (the reference)?

5. Read a conditional effect. The effect in Slovenia (SI) is the Portugal effect plus the treatAfter the attack:cntrySI interaction term. Compute it:

R solution

coef(ols_int)["treatAfter the attack"] +
  coef(ols_int)["treatAfter the attack:cntrySI"]

6. Write one sentence as a # comment explaining, in plain words, what a significant treat:cntryXX interaction means — then compare:

Model answer

A significant treat:cntryXX term means the effect of the Bali attack in country XX was significantly different from its effect in Portugal — the attack's impact on xenophobia depended on the country. Because most of these terms are negative and significant, the strong Portuguese reaction was unusual: in most other countries the same attack moved xenophobia much less, or not at all. The interaction is what lets one model carry ten different effects at once.

7. Bonus, for the fast. Add age and empl_stat as additive controls to the interaction model. Do the country differences survive?

R solution

ols_int2 <- lm_robust(anti_immi ~ treat * cntry + age + empl_stat,
                      data = ESS, weights = pspwght)

modelsummary(list("No controls" = ols_int, "+ controls" = ols_int2),
             stars = TRUE, gof_map = c("nobs"), output = "kableExtra")

The interaction pattern is broadly robust — some countries even become statistically indistinguishable from Portugal once age and employment are held constant. Note you can freely mix an interaction (treat * cntry) with ordinary additive controls (+ age + empl_stat) in the same model.

8. Discuss with your neighbour.

   • Why is it more honest to interact treatment with country than to run ten separate country-by-country regressions?
   • The Portuguese effect is the reference. If we had made Sweden the reference instead, would any of the underlying country effects change?
   • A significant treatment × country interaction tells us the effect varies. Does it tell us why it varies?

Talking points

• One interaction model uses all the data to estimate a common baseline and lets each country deviate from it, with proper standard errors for the differences. Ten separate regressions throw away that shared information and make it awkward to test whether countries really differ.
• No. Changing the reference relabels the coefficients — every country's actual predicted effect is identical; only which one is called "the baseline" changes. The model is the same.
• No. The interaction establishes that the effect depends on country, not why. Explaining it — history, media, prior immigration — is the substantive sociology that begins where the regression ends.