Goodman-Bacon three-way composition of the TWFE DiD coefficient

Collapses the Goodman-Bacon (2021, Theorem 1, eqs. 7-9) decomposition to its three comparison types: a timing cohort against never-treated units, an earlier cohort against a later one before the later adopts, and a later cohort against an already-treated earlier one – the forbidden comparison whose weight is how a TWFE coefficient can land below every clean comparison when effects grow over time. Reports total weight, weighted-average 2x2 estimate and contribution per type; the three contributions sum back to the TWFE coefficient and the weights sum to 1, both computed and reported rather than assumed.

Usage

Gbtcom(data, outcome, treatment, unit, time)

Arguments

data: Long-format balanced panel data frame.
outcome: Name of the outcome column.
treatment: Name of the absorbing 0/1 treatment column.
unit: Name of the unit identifier column.
time: Name of the period column.

Value

List with estimate (TWFE coefficient), weight, mean_beta and contribution (named vectors over the three types), weight_sum, identity_residual, forbidden_weight and n_components_by_type.

Details

Classification rule (identical to the Python arm): a component with an infinite control cohort is treated-vs-never; otherwise a treated cohort adopting before its control cohort is early-vs-late, and one adopting after its (already treated) control cohort is late-vs-early.

References

Goodman-Bacon, A. (2021). Difference-in-differences with variation in treatment timing. Journal of Econometrics, 225(2), 254-277. doi:10.1016/j.jeconom.2021.03.014. Implemented from Theorem 1 and eqs. (7)-(9) of NBER Working Paper 25018;

Examples

u <- rep(1:9, each = 8L)
tt <- rep(1:8, times = 9L)
g <- rep(c(3, 3, 3, 5, 5, 5, Inf, Inf, Inf), each = 8L)
rel <- ifelse(is.finite(g), pmax(0, tt - g), 0)
y <- u * 0.3 + tt * 0.2 + ifelse(tt >= g, 1 + 0.5 * rel, 0)
d <- data.frame(y = y, d = as.numeric(tt >= g), unit = u, time = tt)
out <- Gbtcom(d, "y", "d", "unit", "time")
round(out$weight[["treated vs never-treated"]], 10)
#> [1] 0.7