Event-study leads + lags coefficients

Formula: the dynamic two-way fixed effects specification

  y_it = alpha_i + lambda_t + sum_{e != ref} mu_e 1{t - g_i = e} + eps

where g_i is unit i's treatment cohort and e = t - g_i is event time. One event-time indicator must be dropped for identification against the unit and period effects; e = ref (conventionally -1) is omitted, so every mu_e is read relative to it. Never-treated units (cohort NA or infinite) enter only through alpha_i and lambda_t and act as a clean control group.

Usage

Evstud(y, D, unit, time, cohort, max_lead = NULL, max_lag = NULL, ref = -1)

Arguments

y

Outcome, one entry per unit-period.

D

Treatment indicator (carried for reference; the event dummies are built from cohort and time).

unit, time

Unit and period labels.

cohort

First treated period per observation; NA or Inf marks a never-treated unit.

max_lead, max_lag

Truncate the window to [-max_lead, max_lag].

ref

Omitted event time.

Value

List with estimate, event_times, coef, se, sigma2, resid_df, n_units, n_periods, n, method.

Details

CAVEAT, not a defect of the code: with heterogeneous, dynamic treatment effects these mu_e are contaminated – weighted sums of cohort-specific effects at OTHER relative periods, with weights that can be negative. Sun & Abraham (2021) prove this and give the interaction-weighted alternative.

References

Sun & Abraham (2021), Journal of Econometrics 225(2):175-199, doi:10.1016/j.jeconom.2020.09.006; Borusyak & Jaravel (2017), "Revisiting Event Study Designs", working paper.

Examples

set.seed(8)
units <- 1:30; periods <- 1:6
d <- expand.grid(time = periods, unit = units)
cohort <- rep(c(4, Inf), each = 15)[d$unit]
d$D <- as.integer(d$time >= cohort)
d$y <- rnorm(nrow(d)) + 2 * d$D + d$unit / 10
e <- Evstud(d$y, d$D, d$unit, d$time, cohort)
round(e$coef, 2)
#> [1] 1.04 0.49 1.15 2.04 2.18