Re-assigns the adoption dates across clusters (all the distinct assignments when there are few, random ones otherwise), re-estimates the difference in differences each time, and gives the share of assignments with an effect at least as large; for several outcomes, also the Westfall-Young stepdown p-values that hold the family-wise error rate.
Arguments
- data
A data frame, one row per unit and period.
- unit, time
Column names: the unit and the period (numeric).
- y
One outcome column, or several.
- ftreat
Column name of the period a unit is first treated (
NA, 0 orInffor a unit never treated). Treatment is taken as staying on.- 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;wcbis made for that case), and so does a cluster that changes within a unit.- stat
"t"(default) or"estimate".- reps
The number of random assignments (default 999).
- seed
Optional seed for the random assignments, or NULL for none.
- ties
"count"(default): an assignment whose statistic equals the observed one counts (the observed assignment is among those enumerated, so the exact p-value is at least \(1/N\));"strict": only larger ones count.
Value
A data frame of class rmbl_permutation, one row per outcome:
outcome, estimate, statistic, p_value,
pstpdn, assignments, exact; attribute null (the
matrix of permuted statistics).
Details
The adoption period of each cluster (for example a judicial
district's stage of a reform) is shuffled among the clusters, keeping the
number of clusters adopting at each date, and plndid's estimate
(statistic = "estimate") or t statistic ("t", the default) is
recomputed. With \(b\) of \(R\) random assignments at least as extreme as
observed, \(p = (b + 1)/(R + 1)\); when every distinct assignment is
enumerated (their number is at most reps), \(p\) is the exact share.
The test is Fisher's: it is valid in any sample when adoption dates were
assigned at random across clusters.
For several outcomes, the same assignments give stpdnpv.
A placebo date is the same analysis with ftreat moved earlier, on the
periods before the real adoption.
References
Fisher RA (1935). The Design of Experiments. Oliver and Boyd, Edinburgh.
Applied with the four stages of a reform permuted across districts: Acosta,
Mejia and Zorro Medina (2023), see plndid.
Examples
p <- polex()
perminf(p, "district", "month", c("crmrate", "arrrate"),
"refmonth",
cl = "region", reps = 199, seed = 3)
#> ╭── Permutation inference ───────────────────────────────────────────────╮
#> │ Method randomisation inference on the adoption dates │
#> │ Assignments 24 │
#> │ Draws every assignment (exact) │
#> │ Outcomes 2 │
#> │ │
#> │ outcome estimate statistic p_value stepdown_p │
#> │ ------- -------- --------- ------- ---------- │
#> │ crmrate -3.232 -19.52 0.042 0.042 │
#> │ arrrate -0.214 -3.64 0.125 0.125 │
#> │ │
#> │ The p-value is the share of reassigned adoption dates that give a │
#> │ statistic at least as extreme as the one observed; it needs no model │
#> │ of the errors. The stepdown p-values (Westfall and Young) hold for │
#> │ all the outcomes tested together. │
#> ╰────────────────────────────────────────────────────────────────────────╯
# 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))
# every assignment of the two adoption dates to the eight towns
perminf(own, "town", "year", "rate", "first", reps = 99, seed = 1)
#> ╭── Permutation inference ───────────────────────────────────────────────╮
#> │ Method randomisation inference on the adoption dates │
#> │ Assignments 99 │
#> │ Draws random draws │
#> │ Outcomes 1 │
#> │ │
#> │ outcome estimate statistic p_value stepdown_p │
#> │ ------- -------- --------- ------- ---------- │
#> │ rate -4.039 -16.86 0.010 0.010 │
#> │ │
#> │ The p-value is the share of reassigned adoption dates that give a │
#> │ statistic at least as extreme as the one observed; it needs no model │
#> │ of the errors. │
#> ╰────────────────────────────────────────────────────────────────────────╯