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Synthetic Control Gaps and Inference Plot

sc_inference_plot.Rd

Reproduces the visual inference approach from Abadie, Diamond & Hainmueller (2010). Placebo gaps (donor unit gaps or permutation draws) are overlaid in grey to provide a null distribution for assessing statistical significance.

Usage

sc_inference_plot(
  Y_treated,
  Y_synthetic,
  time_points,
  treat_time,
  donor_gaps = NULL,
  title = NULL,
  alpha = 0.05
)

Arguments

Y_treated

Numeric vector. Observed outcome for the treated unit.

Y_synthetic

Numeric vector. Synthetic control outcome (same length as Y_treated).

time_points

Numeric or integer vector. Time periods (same length as Y_treated).

treat_time

Numeric. The first treatment period.

donor_gaps

A numeric matrix or data frame where each column is the gap (actual minus synthetic) for one placebo/donor unit. NULL to omit placebo overlay and p-value.

title

Character or NULL. Title prefix for both panels.

alpha

Numeric. Significance level for RMSPE-ratio p-value. Default 0.05.

Value

A named list:

plot

A patchwork or list of ggplot2 objects (level + gap panels).

p_value

Permutation p-value (fraction of placebos with post/pre RMSPE ratio >= treated unit ratio). NA if no donors.

rmspe_ratio

Post/pre RMSPE ratio for the treated unit.

level_plot

ggplot2 level panel.

gap_plot

ggplot2 gap panel.

Details

Synthetic Control Inference Plot (Abadie-Diamond-Hainmueller Style)

Creates the canonical two-panel synthetic control figure: (1) the level plot showing the treated unit against its synthetic control, and (2) the gap plot showing the difference between them, overlaid with donor/placebo gaps in grey. A permutation-based p-value is computed as the fraction of placebos with a post/pre RMSPE ratio at least as large as the treated unit.

References

Abadie, A., Diamond, A., & Hainmueller, J. (2010). Synthetic control methods for comparative case studies: Estimating the effect of California's tobacco control program. Journal of the American Statistical Association, 105(490), 493-505.

Examples

# Simulate treated and synthetic outcomes
set.seed(7)
time_pts <- 1990:2005
treat_t  <- 1997
Y_tr     <- c(seq(40, 55, length.out = 7),
              seq(55, 70, length.out = 9)) + rnorm(16, 0, 1.5)
Y_sc     <- c(seq(40, 55, length.out = 7),
              seq(55, 59, length.out = 9)) + rnorm(16, 0, 1.5)

# Simulate 10 donor gaps
donor_mat <- matrix(rnorm(16 * 10, 0, 3), nrow = 16)

result <- sc_inference_plot(
  Y_treated    = Y_tr,
  Y_synthetic  = Y_sc,
  time_points  = time_pts,
  treat_time   = treat_t,
  donor_gaps   = donor_mat
)
result$plot

result$p_value
#> [1] 0