mspe.test {SCtools}

Function to compute the post/pre treatment MSPE ratio for the treated unit and placebos

Description

Computes the post/pre treatement mean square prediction error ratio for a treated unit in a synthetic control analysis and all placebos produced with generate.placebos. Returns a matrix with ratios and a p-value of how extreme the treated unit's ratio is in comparison with that of placebos. Equivalent to a significance testing of a synthetic controls result.

Usage

mspe.test(tdf, discard.extreme = FALSE, mspe.limit = 20)

mspe_test(tdf, discard.extreme = FALSE, mspe.limit = 20)

Arguments

tdf

An object constructed by generate.placebos

discard.extreme

Logical. Whether or not placebos with high pre-treatement MSPE should be excluded from the count and significance testing.

mspe.limit

Numerical. Used if discard.extreme is TRUE. It indicates how many times the pretreatment MSPE of a placebo should be higher than that of the treated unit to be considered extreme and discarded. Default is 20.

Details

Post/pre-treatement mean square prediction error ratio is the difference between the observed outcome of a unit and its synthetic control, before and after treatement. A higher ratio means a small pre-treatment prediction error (a good synthetic control), and a high post-treatment MSPE, meaning a large difference between the unit and its synthetic control after the intervention. By calculating this ratio for all placebos, the test can be interpreted as looking at how likely the result obtained for a single treated case with a synthetic control analysis could have occurred by chance given no treatement. For more detailed description, see Abadie, Diamond, and Hainmueller (2011, 2014).

Value

p.val

The p-value of the treated unit post/pre MSPE ratio. It is the proportion of units (placebos and treated) that have a ratio equal or higher that of the treated unit

test

Dataframe with two columns. The first is the post/pre MSPE ratio for each unit. The second indicates unit names

See Also

generate.placebos, mspe.plot, synth

Examples

## Example with toy data from 'Synth'
library(Synth)
# Load the simulated data
data(synth.data)

# Execute dataprep to produce the necessary matrices for 'Synth'
dataprep.out<-
  dataprep(
    foo = synth.data,
    predictors = c("X1"),
    predictors.op = "mean",
    dependent = "Y",
    unit.variable = "unit.num",
    time.variable = "year",
    special.predictors = list(
      list("Y", 1991, "mean")
    ),
    treatment.identifier = 7,
    controls.identifier = c(29, 2, 13, 17),
    time.predictors.prior = c(1984:1989),
    time.optimize.ssr = c(1984:1990),
    unit.names.variable = "name",
    time.plot = 1984:1996
)

# run the synth command to create the synthetic control
synth.out <- synth(dataprep.out, Sigf.ipop=2)

## run the generate.placebos command to reassign treatment status
## to each unit listed as control, one at a time, and generate their
## synthetic versions. Sigf.ipop = 2 for faster computing time. 
## Increase to the default of 5 for better estimates. 
tdf <- generate.placebos(dataprep.out,synth.out, Sigf.ipop = 2)

## Test how extreme was the observed treatment effect given the placebos:
ratio <- mspe.test(tdf)
ratio$p.val

mspe.plot(tdf, discard.extreme = FALSE)