pensynth {pensynth}

Penalized synthetic control estimator

Description

For a given set of variable weights (v) this function estimates the unit weights for a synthetic control with penalization according to Abadie & L'Hour (2021). This function deals with only a single treated unit.

Usage

pensynth(
  X1,
  X0,
  v = 1,
  lambda = 0,
  opt_pars = clarabel::clarabel_control(),
  standardize = TRUE
)

Arguments

X1

⁠N_covars by 1 matrix⁠ of treated unit covariates

X0

⁠N_covars by N_donors matrix⁠ of donor unit covariates

v

⁠N_covars vector⁠ of variable weights (default 1)

lambda

numeric penalization parameter

opt_pars

clarabel settings using clarabel::clarabel_control()

standardize

boolean whether to standardize the input matrices (default TRUE)

Details

This routine uses the same notation of the original Synth::synth() implementation but uses a different, faster quadratic program solver (namely, clarabel::clarabel()). Additionally, it implements the penalization procedure described in Abadie & L'Hour (2021), such that the loss function is as in equation 5 of that paper (but for a single treated unit).

Variable weights are not optimized by this function, meaning they need to be pre-specified. This is by design.

The original synthetic control method can be recovered by setting lambda = 0. For determining lambda based on data, see cv_pensynth().

Value

A list with two values: w, the estimated weights; and solution, the result of the optimization.

References

Abadie, A., & L’Hour, J. (2021). A penalized synthetic control estimator for disaggregated data. Journal of the American Statistical Association, 116(536), 1817-1834.

See Also

cv_pensynth(), placebo_test(), simulate_data(), Synth::synth()

Examples

# generate some data
X0 <- matrix(
  c(1, 1.3,
    0.5, 1.8,
    1.1, 2.4,
    1.8, 1.8,
    1.3, 1.8), 2)
X1 <- matrix(c(0.8, 1.65), 2)

# run classic synthetic control (no penalization)
res <- pensynth(X1, X0)

# plot donor units in covariate space
plot(t(X0), asp = 1, xlab = "X1", ylab = "X2",
     main = "Covariate space plot")
# add the treated unit
points(t(X1), pch = 2)
# add the synthetic control
points(t(X0%*%res$w), pch = 3)

# run synthetic control with penalty
res <- pensynth(X1, X0, lambda = 0.5)
# the resulting synthetic control is
# biased towards its closest neighbours
points(t(X0 %*% res$w), pch = 4)