synth: Constructs synthetic control units for comparative case...

In Synth: Synthetic Control Group Method for Comparative Case Studies

Constructs synthetic control units for comparative case studies

Description

Implements the synthetic control method for causal inference in comparative case studies as developed in Abadie and Gardeazabal (2003) and Abadie, Diamond, and Hainmueller (2010, 2011, 2014). synth estimates the effect of an intervention by comparing the evolution of an aggregate outcome for a unit affected by the intervention to the evolution of the same aggregate outcome for a synthetic control group.

synth constructs this synthetic control group by searching for a weighted combination of control units chosen to approximate the unit affected by the intervention in terms of characteristics that are predictive of the outcome. The evolution of the outcome for the resulting synthetic control group is an estimate of the counterfactual of what would have been observed for the affected unit in the absence of the intervention.

synth can also be used to conduct a variety of placebo and permutation tests that produce informative inference regardless of the number of available comparison units and the number of available time periods. See Abadie and Gardeazabal (2003), Abadie, Diamond, and Hainmueller (2010, 2011, 2014) for details.

synth requires the user to supply four matrices as its main arguments. These matrices are named X0, X1, Z1, and Z0 accordingly. X1 and X0 contain the predictor values for the treated unit and the control units respectively. Z1 and Z0 contain the outcome variable for the pre-intervention period for the treated unit and the control units respectively. The pre-intervention period refers to the time period prior to the intervention, over which the mean squared prediction error (MSPE) should be minimized. The MSPE refers to the squared deviations between the outcome for the treated unit and the synthetic control unit summed over all pre-intervention periods specified in Z1 and Z0.

Creating the matrices X1, X0, Z1, and Z0 from a (panel) dataset can be tedious. Therefore, the Synth package offers a preparatory function called dataprep that allows the user to easily create all inputs required for synth. By first calling dataprep, the user creates a single list object called data.prep.obj that contains all essential data elements to run synth.

A usual sequence of commands to implement the synthetic control method is to first call dataprep to prepare the data, then call synth to construct the synthetic control group, and finally summarize results using the functions synth.tab, path.plot, or gaps.plot.

An example of this sequence is provided in the documentation to dataprep. This procedure is strongly recommended. Alternatively, the user may provide their own preprocessed data matrices and load them into synth via the X0, X1, Z1, and Z0 arguments. In this case, no data.prep.obj should be specified.

The output from synth is a list object that contains the weights on predictors (solution.V) and weights on control units (solution.W) that define contributions to the synthetic control unit.

Usage

synth(data.prep.obj = NULL,
      X1 = NULL, X0 = NULL,
      Z0 = NULL, Z1 = NULL,
      custom.v = NULL,
      optimxmethod = c("Nelder-Mead", "BFGS"),
      genoud = FALSE, quadopt = "ipop",
      Margin.ipop = 5e-04,
      Sigf.ipop = 5,
      Bound.ipop = 10,
      verbose = FALSE, ...)

Arguments

data.prep.obj	The object produced by dataprep. This object contains all information about X0, X1, Z1, and Z0. If data.prep.obj is supplied, none of X0, X1, Z1, and Z0 should be manually specified.
X1	Matrix of treated predictor data. Rows correspond to predictors, columns to a single treated unit.
X0	Matrix of control units’ predictor data. Rows correspond to predictors, columns to control units (>=2).
Z1	Matrix of treated outcome data for the pre-treatment periods over which MSPE is minimized.
Z0	Matrix of control units’ outcome data for the pre-treatment periods over which MSPE is minimized.
custom.v	Vector of weights for predictors supplied by the user. Uses synth to bypass optimization for solution.V. See Details.
optimxmethod	Character vector specifying optimization algorithms to be used. Permissible values are all optimization algorithms currently implemented in the function optimx (see that function for details). If multiple algorithms are specified, synth will run all chosen algorithms and return the best-performing result. If "All" is specified, all algorithms in optimx are tried.
genoud	Logical flag. If TRUE, synth performs a two-step optimization. In the first step, genoud is used to obtain a global solution. In the second step, the results are passed to the algorithm(s) chosen in optimxmethod for local optimization. This two-step procedure is slower but may yield lower loss for irregular search spaces.
quadopt	Character specifying the routine for quadratic optimization over W weights. Possible value: "ipop" (see ipop for details).
Margin.ipop	Setting for the ipop optimization routine: how close we get to the constraints (see ipop for details).
Sigf.ipop	Setting for the ipop optimization routine: precision in significant figures (default: 7; see ipop for details).
Bound.ipop	Setting for the ipop optimization routine: clipping bound for variables (see ipop for details).
verbose	Logical flag. If TRUE, intermediate results are displayed.
...	Additional arguments passed to optimx or genoud.

Details

As proposed in Abadie and Gardeazabal (2003) and Abadie, Diamond, and Hainmueller (2010), synth searches for the set of weights that generate the best-fitting convex combination of control units. The predictor weight matrix V is chosen among positive definite diagonal matrices such that MSPE is minimized for the pre-intervention period.

Alternatively, the user may supply a vector of V weights based on a subjective assessment of the predictive power of the variables in X1 and X0. In this case, specify custom.V in synth, and the optimization over V matrices is bypassed.

Value

solution.v	Vector of predictor weights.
solution.w	Vector of weights across control units.
loss.v	MSPE from optimization over V and W weights.
loss.w	Loss from optimization over W weights.
custom.v	If specified, returns the user-supplied weight vector.
rgV.optim	Results from optimx() minimization, useful for diagnostics.

Author(s)

Jens Hainmueller and Alexis Diamond

References

Abadie, A., Diamond, A., Hainmueller, J. (2014). Comparative Politics and the Synthetic Control Method. American Journal of Political Science.

Abadie, A., Diamond, A., Hainmueller, J. (2011). Synth: An R Package for Synthetic Control Methods in Comparative Case Studies. Journal of Statistical Software, 42(13), 1–17.

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.

Abadie, A., and Gardeazabal, J. (2003). Economic Costs of Conflict: A Case Study of the Basque Country. American Economic Review, 93(1), 113–132.

See Also

dataprep, gaps.plot, path.plot, synth.tab

Examples

data(synth.data)
dataprep.out <- dataprep(foo = synth.data,
   predictors = c("X1","X2","X3"),
   predictors.op = "mean",
   dependent = "Y",
   unit.variable = "unit.num",
   time.variable = "year",
   special.predictors = list(
      list("Y",1991,"mean"),
      list("Y",1985,"mean"),
      list("Y",1980,"mean")),
   treatment.identifier = 7,
   controls.identifier = c(29,2,13,17,32,38),
   time.predictors.prior = 1984:1989,
   time.optimize.ssr = 1984:1990,
   unit.names.variable = "name",
   time.plot = 1984:1996)
synth.out <- synth(dataprep.out)
path.plot(dataprep.res = dataprep.out, synth.res = synth.out)
gaps.plot(dataprep.res = dataprep.out, synth.res = synth.out)

Synth documentation built on Nov. 5, 2025, 6:35 p.m.