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Staggered adoption

Source: vignettes/articles/staggered.Rmd
staggered.Rmd

When units adopt treatment at different times, coresynth fits each adoption cohort separately and aggregates the cohort ATTs with weights proportional to N_treated × T_post (Clarke et al. 2023):

τ̂=∑gNtr,gTpost,gτ̂g∑gNtr,gTpost,g.\hat\tau = \frac{\sum_g N_{tr,g}\, T_{post,g}\, \hat\tau_g}{\sum_g N_{tr,g}\, T_{post,g}}.

All six estimators support this; staggered timing is detected automatically from the treatment column — no extra flag is needed.

A staggered panel

Here u1 is treated from period 11 and u2 from period 16.

set.seed(42)
N <- 12; TT <- 20
f   <- cumsum(rnorm(TT, 0, 0.5))
lam <- rnorm(N, 1, 0.3)
dat <- expand.grid(time = seq_len(TT), id = paste0("u", seq_len(N)))
dat$y <- as.vector(outer(f, lam)) + rnorm(nrow(dat), 0, 0.3)

dat$d <- 0L
dat$d[dat$id == "u1" & dat$time > 10] <- 1L
dat$d[dat$id == "u2" & dat$time > 15] <- 1L
dat$y[dat$d == 1] <- dat$y[dat$d == 1] + 2.0   # true ATT = 2.0

Fitting 

fit <- scm_fit(y ~ d | id + time, data = dat, method = "sdid")
fit$estimate          # aggregate ATT
#> [1] 1.872835
fit$staggered         # TRUE
#> [1] TRUE

Per-cohort detail is in cohort_estimates:

fit$cohort_estimates
#>   cohort n_treated T_pre T_post estimate    weight
#> 1     11         1    10     10 1.839381 0.6666667
#> 2     16         1    15      5 1.939744 0.3333333

Choosing the control group

control_group controls which units serve as donors for each cohort:

  • "clean" (default) — never-treated units plus not-yet-treated units (those adopting later than the current cohort).
  • "never_treated" — never-treated units only.
fit_clean <- scm_fit(y ~ d | id + time, data = dat, method = "sdid",
                     control_group = "clean")
fit_nt    <- scm_fit(y ~ d | id + time, data = dat, method = "sdid",
                     control_group = "never_treated")
c(clean = fit_clean$estimate, never_treated = fit_nt$estimate)
#>         clean never_treated 
#>      1.872835      1.962071

Across estimators

The same call works for every method:

methods <- c("scm", "sdid", "gsc", "mc", "tasc", "si")
sapply(methods, function(m)
  scm_fit(y ~ d | id + time, data = dat, method = m)$estimate)
#>      scm     sdid      gsc       mc     tasc       si 
#> 1.835229 1.872835 1.760712 2.292777 3.153267 1.934303

Inference under staggered adoption

sdid_inference(), gsc_inference(), and si_inference() all extend to staggered fits. jackknife_global is the staggered-specific variant that removes each unique control unit across all cohorts at once, correctly capturing cross-cohort correlation.

library(broom)
tidy(sdid_inference(fit, method = "bootstrap", n_boot = 100, seed = 1))
#>   term estimate  std.error statistic      p.value conf.low conf.high    method
#> 1  ATT 1.872835 0.09273774  20.19496 1.084054e-90 1.711155  2.060448 bootstrap
#>   alternative n_controls staggered
#> 1   two.sided       10.5      TRUE
tidy(sdid_inference(fit, method = "jackknife_global"))
#>   term estimate std.error statistic      p.value conf.low conf.high
#> 1  ATT 1.872835 0.1186042  15.79063 3.609468e-56 1.640375  2.105295
#>             method alternative n_controls staggered
#> 1 jackknife_global   two.sided         11      TRUE

Notes

  • plot() and augment() for staggered fits operate per cohort; the aggregate synthetic series is not defined (Y_synth = NULL).
  • SCM staggered adoption supports covariates = (partial-out) but not the predictors = pred(...) interface.
  • SI additionally supports staggered and multi-arm simultaneously — see Estimators.