Difference in differences for treatments that switch on and off

De Chaisemartin and D'Haultfoeuille's estimator of the effect at the moment units switch: in every period, units that switch into treatment are compared with units untreated in both periods, and units that switch out with units treated in both; with the placebo that runs the same comparison one period earlier.

Usage

swtdid(
  data,
  unit,
  time,
  y,
  trtd,
  cl = NULL,
  reps = 499L,
  seed = NULL,
  conflvl = 0.95
)

Arguments

data: A data frame, one row per unit and period.
unit, time, y: Column names: the unit, the period (numeric, for example a year or a month index) and the outcome.
trtd: Column name of the treatment indicator (0 or 1).
cl: Column name of the clusters (default the unit), or two column names for two-way clustering (Cameron, Gelbach and Miller 2011): $V_a + V_b - V_{ab}$, each term with the small-sample factor of the dimension with fewer clusters, and t on its $G - 1$ degrees of freedom. A composite cluster (district by month, say) is one column made with interaction(). Fewer than ten clusters give a warning (CR1 errors are unreliable with so few; wcb is made for that case), and so does a cluster that changes within a unit.
reps: Bootstrap replications (default 499; 0 for none).
seed: Optional seed for the bootstrap.
conflvl: Confidence level of the intervals reported (default 0.95).

Value

A data frame of class rmbl_switching_did, two rows (effect, placebo): estimate, se, lower, upper, switchers.

Details

For each period $t$ with joiners ($D_{t-1} = 0, D_t = 1$) and stayers untreated in both, $DID_{+,t}$ is the joiners' mean change in the outcome minus the stayers'; with leavers (1 to 0) and stayers treated in both, $DID_{-,t}$ is the stayers' change minus the leavers'. The estimate is $$DID_M = \sum_t \frac{N_{J,t}}{N_S} DID_{+,t} + \frac{N_{L,t}}{N_S} DID_{-,t},$$ over the $N_S$ switchers. The placebo compares, between $t - 2$ and $t - 1$, the change of the units that switch at $t$ with that of the units whose treatment did not change over $t - 2$ to $t$; it should be near zero. Standard errors come from the cluster bootstrap. Unlike the two-way estimator, $DID_M$ never uses a unit whose treatment changed as a control in the period it changed.

References

de Chaisemartin C, D'Haultfoeuille X (2020). Two-way fixed effects estimators with heterogeneous treatment effects. American Economic Review 110(9):2964-2996. doi:10.1257/aer.20181169

Applied as a placebo check on ward redistricting: Ternullo S, Zorro-Medina A, Vargas R (2024). How political dynasties concentrate advantage within cities. Social Forces 102(4):1310-1331. doi:10.1093/sf/soae029

Examples

p <- polex()
swtdid(p, "district", "month", "crmrate", "reformed", reps = 99, seed = 1)
#> ╭── Difference in differences, switching treatment ──────────────────────╮
#> │   Method     de Chaisemartin and D'Haultfoeuille, switchers vs stayers │
#> │   Switchers  15                                                        │
#> │                                                                        │
#> │   term     estimate      se  interval          switchers               │
#> │   -------  --------  ------  ----------------  ---------               │
#> │   effect     -3.135  0.4556  [-4.028, -2.243]         15               │
#> │   placebo    -0.517  0.4430  [-1.385, 0.351]          15               │
#> │                                                                        │
#> │   At the moment units switch, the effect is -3.135 (its interval       │
#> │   [-4.028, -2.243]): the interval excludes 0, so the data distinguish  │
#> │   it from no effect. The placebo, the same comparison one period       │
#> │   earlier, is -0.5169; near zero supports the design.                  │
#> │                                                                        │
#> │   Intervals are normal, from the cluster-bootstrap standard error.     │
#> ╰────────────────────────────────────────────────────────────────────────╯

# your own panel: eight towns over ten years, four adopting a by-law (two
# in 2019, two in 2021), with each town's population, county and income
own <- data.frame(
  town = rep(c("A", "B", "C", "D", "E", "F", "G", "H"), each = 10),
  year = rep(2015:2024, times = 8)
)
i <- match(own$town, unique(own$town))
own$first <- c(2019, 2019, 2021, 2021, NA, NA, NA, NA)[i]
own$bylaw <- as.integer(!is.na(own$first) & own$year >= own$first)
own$pop <- c(12, 30, 8, 22, 15, 40, 9, 18)[i] * 1000
own$county <- rep(c("North", "South"), 4)[i]
own$income <- 50 + own$year - 2015 + cos(seq_len(80))
own$rate <- 30 + i + 0.5 * (own$year - 2015) - 4 * own$bylaw +
  0.2 * own$income + sin(seq_len(80))
swtdid(own, "town", "year", "rate", "bylaw", reps = 49, seed = 1)
#> ╭── Difference in differences, switching treatment ──────────────────────╮
#> │   Method     de Chaisemartin and D'Haultfoeuille, switchers vs stayers │
#> │   Switchers  4                                                         │
#> │                                                                        │
#> │   term     estimate      se  interval          switchers               │
#> │   -------  --------  ------  ----------------  ---------               │
#> │   effect     -4.022  0.3802  [-4.767, -3.277]          4               │
#> │   placebo    -0.062  0.4099  [-0.865, 0.742]           4               │
#> │                                                                        │
#> │   At the moment units switch, the effect is -4.022 (its interval       │
#> │   [-4.767, -3.277]): the interval excludes 0, so the data distinguish  │
#> │   it from no effect. The placebo, the same comparison one period       │
#> │   earlier, is -0.06159; near zero supports the design.                 │
#> │                                                                        │
#> │   Intervals are normal, from the cluster-bootstrap standard error.     │
#> ╰────────────────────────────────────────────────────────────────────────╯