Aggregate group-time average treatment effects

Combines the ATT(g, t) of an attgt() fit into summary effects, as in Callaway and Sant'Anna (2021, Section 3) and did::aggte():

• "simple": the average of all post-treatment ATT(g, t) weighted by cohort size;

• "dynamic": the event study, ATT(e) for each event time e = t - g, averaging across cohorts weighted by cohort size; the overall effect is the mean of the post-treatment ATT(e), e >= 0;

• "group": the average effect of each cohort over its post-treatment periods; the overall effect weights cohorts by size;

• "calendar": the average effect in each calendar period across the cohorts treated by then (weighted by size); the overall effect is the mean over periods.

Usage

# S3 method for class 'panglm_attgt'
summary(
  object,
  type = c("simple", "dynamic", "group", "calendar"),
  min_e = -Inf,
  max_e = Inf,
  balance_e = NULL,
  level = object$level,
  ...
)

Arguments

object

a "panglm_attgt" fit from attgt()

type

"simple", "dynamic", "group" or "calendar"

min_e, max_e

for "dynamic": event-time window

balance_e

for "dynamic": if not NULL, only cohorts observed for at least balance_e periods after treatment are used, so that the composition of cohorts is the same at every event time up to balance_e

level

confidence level; defaults to that of the fit

...

unused

Value

an object of class "summary.panglm_attgt": a list with overall (a one-row data frame with estimate, se, lower, upper), estimates (the effects by event time, cohort or period: column level plus the same columns; NULL for "simple"), type, pretrend, inf (the influence functions of the overall effect), crit (the simultaneous critical value of the uniform bands, or NULL), boot and the fit settings. The influence functions of the effects by level are the attribute "inf" of estimates.

Details

Standard errors come from the influence functions and account for the estimation of the cohort-size weights. When the fit was bootstrapped (attgt() with bstrap = TRUE), the standard errors of the aggregated effects come from the same multiplier draws and, with cband = TRUE, the effects by level get uniform confidence bands (band_lower, band_upper) from the simultaneous critical value crit, as in did::aggte(). Clustering follows the fit.

See also

Other attgt methods: plot.panglm_attgt()

Examples

set.seed(2)
d <- expand.grid(id = 1:150, t = 1:8)
d$first <- rep(c(4, 6, NA), each = 50)[d$id]
d$y <- rnorm(150)[d$id] + 0.2 * d$t +
  ifelse(!is.na(d$first) & d$t >= d$first, 1, 0) + rnorm(nrow(d))
fit <- attgt(y ~ 1, d, index = c("id", "t"), treat = "first")
summary(fit, type = "dynamic")
#> 
#> Callaway and Sant'Anna group-time ATT
#> Aggregation: event study (by time since treatment)
#> Control group: never treated  Estimator: unconditional  Individuals: 150 
#> 
#> ATT (mean of e >= 0): 1.176 (SE 0.163, 95% CI 0.8569 to 1.496)
#> 
#>  event estimate     se    lower    upper
#>     -4   0.4697 0.2704 -0.06039  0.99972
#>     -3  -0.5765 0.2717 -1.10908 -0.04401
#>     -2   0.1442 0.1984 -0.24472  0.53316
#>     -1  -0.2597 0.2103 -0.67194  0.15259
#>      0   0.8400 0.2041  0.44001  1.24005
#>      1   1.1887 0.1602  0.87475  1.50275
#>      2   1.3308 0.1882  0.96196  1.69970
#>      3   1.2700 0.2685  0.74374  1.79633
#>      4   1.2525 0.2656  0.73181  1.77311
#> 
#> Pre-trend test (pre-treatment ATT(g, t) = 0): Chi-squared = 22.19, df = 6, p-value = 0.001119
#> 
summary(fit, type = "calendar")
#> 
#> Callaway and Sant'Anna group-time ATT
#> Aggregation: by calendar period
#> Control group: never treated  Estimator: unconditional  Individuals: 150 
#> 
#> ATT (mean over periods): 1.141 (SE 0.1613, 95% CI 0.825 to 1.457)
#> 
#>  time estimate     se  lower upper
#>     4   0.8908 0.2821 0.3378 1.444
#>     5   1.2792 0.2631 0.7635 1.795
#>     6   1.0762 0.2131 0.6585 1.494
#>     7   1.1842 0.1931 0.8056 1.563
#>     8   1.2755 0.2099 0.8641 1.687
#> 
#> Pre-trend test (pre-treatment ATT(g, t) = 0): Chi-squared = 22.19, df = 6, p-value = 0.001119
#>