Synthetic control for a single treated area or force

Builds a weighted average of untreated donor units whose pre-period path matches the treated unit's, and reads the gap between them afterwards as the effect. Inference is by permutation: the same procedure is run pretending each donor was treated, and the treated unit's post-period fit is compared with that distribution.

Usage

lamp_synth(
  panel,
  outcome = "crime_total",
  treated_unit,
  treatment_start,
  donors = NULL,
  method = c("internal", "synth", "gsynth"),
  placebo = TRUE,
  min_pre = 6L
)

Arguments

panel

A lamp_panel.

outcome

The outcome column.

treated_unit

The area that was treated.

treatment_start

The first treated month.

donors

Candidate donor areas; NULL uses every other area that has a complete series.

method

"internal" (default), "synth" or "gsynth".

placebo

Run in-space placebos over the donors for the permutation p value.

min_pre

Months of pre-period required.

Value

A list of class lamp_synth with weights, path (a tibble of month, observed, synthetic and gap), effect (mean post-period gap), rmspe_pre, rmspe_post, rmspe_ratio, p_value (the share of donors with a ratio at least as large), placebos and assumption.

Identifying assumption

The weighted donors reproduce what the treated unit would have done without the intervention. This is credible only when the pre-period fit is close over a long window, no donor was itself affected by the intervention, and nothing else happened to the treated unit at the same time. A poor pre-period fit invalidates the comparison, which is why the pre-period root mean squared error is reported first.

References

Abadie, A., Diamond, A. and Hainmueller, J. (2010). Synthetic control methods for comparative case studies. Journal of the American Statistical Association 105(490), 493-505.

Xu, Y. (2017). Generalized synthetic control method. Political Analysis 25(1), 57-76.

See also

Other estimators: lamp_allocation(), lamp_crimes_prevented(), lamp_did_staggered(), lamp_displacement_quotient(), lamp_elasticity(), lamp_event_study(), lamp_spillover(), lamp_twfe(), tidy.lamp_estimate()

Examples

sim <- lamp_simulate(n_areas = 20, n_months = 30, design = "event", effect = -0.4, seed = 1)
truth <- attr(sim, "truth")
sc <- lamp_synth(
  sim, "crime_total",
  treated_unit = truth$treated_areas[1],
  treatment_start = truth$event_date,
  donors = setdiff(unique(sim$area), truth$treated_areas),
  placebo = FALSE
)
sc
#> 
#> ── streetlamp synthetic control 
#> Treated unit: "S00001" from 2019-03
#> Donors: 8; pre-period months: 14; post-period months: 16
#> Identifying assumption: The weighted donors reproduce what the treated unit
#> would have done without the intervention; no donor is itself affected by it.
#> Pre-period fit (root mean squared error): 3.23; post-period: 2.84; ratio 0.878
#> Mean post-period gap: -0.964
#> The synthetic unit does not track the treated unit before the intervention, so
#> the gap afterwards is not evidence of an effect.
#> Largest weights: S00014 0.66, S00019 0.24, S00017 0.06, S00015 0.04