vignettes/Event_study_vs_Callaway_vs_Chaisemartin.md

In MatthieuStigler/multiDiff: Multi-year diff-diff and FE decompositions

library(multiDiff)

Preview this file with: link

Comparing DiD, event-study, Callaway Sant’Anna and Chaisemartin and Haultfeuille estimates

In summary, in a non-staggered case:

1. a DiD estimate the average post periods against all pre periods
2. An event study (ES) estimates individual post periods against a single pre period
3. The Callaway Sant’Anna (CS) gives the same estimates as an ES when using base_period = "universal"
4. The CS did::aggte function gives the average of the post periods against a single pre periods

5. Therefore, the link between DiD and ES/CS is:

6. a full DiD is equal to the average ES when the ES is computed against all pre periods (argument trim_low)

7. a truncated DiD is equal to the average ES when the DiD’s input contains only one pre period

8. The Chaisemartin and Haultfeuille (2023) gives the ES coefficients (against the -1 period) BUT:

9. coefficients are rounded to digits=5

10. The CH ATE is therefore equal to the EC/CS coefficients.

example

Simulate data with common treatment (= non-staggered). Treatment happens at T=5.

dat_common <- sim_dat_common(timing_treatment = 5:10, as_mdd = TRUE, seed=123)

Estimate the standard DiD, and a truncated DiD, where we remove all pre-treatment periods except the last one

reg_DD <- mdd_DD_simple(dat_common)
reg_DD_trunc <- mdd_DD_simple(dat_common |>subset(Time>=4))

Estimate the ES coefficents

reg_ES <- mdd_event_study(dat_common)
reg_ES_trunc <- mdd_event_study(dat_common, trim_low = -1)

Estimate the CS coefficients

reg_CS <- mdd_CS(dat_common, base_period = "universal")

Estimate the CH coefficient

reg_CH_24_effct_1 <- mdd_estim_CH(mdd_dat = dat_common, graph_off=TRUE)
reg_CH_24_effct_6 <- mdd_estim_CH(mdd_dat = dat_common, effects =6, placebo=3, graph_off=TRUE)

verify the relationships

The full DiD is the same as the mean ES which considers all pre-periods (trim_low = -1)

all.equal(coef(reg_DD)[[1]],
          mean(coef(reg_ES_trunc)))
#> [1] TRUE

a truncated DiD is the same as the mean ES

all.equal(coef(reg_DD_trunc)[[1]],
          mean(coef(reg_ES)[4:9]))
#> [1] TRUE

a truncated DiD is also the same as the aggte(CS)

all.equal(coef(reg_DD_trunc)[[1]],
          suppressWarnings(did::aggte(reg_CS)$overall.att))
#> [1] TRUE

Individual ES are equal to individual CS when using base_period = "universal"

all.equal(coef(reg_ES)[4:9],
          reg_CS$att[5:10], check.attributes = FALSE)
#> [1] TRUE

Individual ES are equal to individual CS

all.equal(round(coef(reg_ES)[4:9],5),
          reg_CH_24_effct_6$results$Effects[,"Estimate"], check.attributes = FALSE)
#> [1] TRUE

MatthieuStigler/multiDiff documentation built on Feb. 14, 2025, 12:02 a.m.