Synth (version 0.1-2)

synth: Constructs Synthetic Control Unit

Description

This function constructs Synthetic Control Groups according to the methods outlined in Abadie and Gardeazabal (2003) and Abadie, Diamond, Hainmueller (2007). The main input is the object list that results from calling dataprep. Accordingly, a usual sequence of commands to implement the synthetic control method is to first call dataprep to prepare the data to be loaded into synth. Then synth is called to run the synthetic control algorithm. Finally, results are obtained using synth.tab, path.plot, or gaps.plot. An example of this sequence is provided in the documentation to dataprep. Notice that by first running dataprep the user creates a data.prep.obj, which is an object list that contains all essential data information to run synth. This procedure is strongly recommended. Alternativley, the user may provide his own preprocessed data matrices and load them into synth via the X0, X1, Z1, and Z0 options. In this case, no data.prep.obj should be specifcied. As proposed in Abadie and Gardeazabal (2003) and Abadie, Diamond, Hainmueller (2007), the synth function routinley searches for the set of weights that generate the best fitting convex combination of the control units such that the path of outcomes for the treated unit prior to treatment is as close as possible to the path for the synthetic control unit for that same period. In other words, V is chosen among all positive definite diagonal matrices such that mean squared prediction error of the outcome variable is minimized for the pre-intervention period. Instead of using this data-driven procedures to search for the best fitting synthtic control group, the user may supply his own V weights, based on his subjective assessment of the predictive power of the variables in $X_{1}$ and $X_{0}$. In this case, the vector of V weights for each variable should be supplied via the custom.V option in synth and the optimization over the V matrices is bypassed. The output from synth is a list containing 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 = NA, X1 = stop("X0 missing"), X0 = stop("X1 missing"), 
Z0 = stop("Z0 missing"), Z1 = stop("Z1 missing"), 
custom.v = FALSE, Margin.ipop = 5e-04, Sigf.ipop = 4, Bound.ipop = 10, ...)

Arguments

data.prep.obj

the object that comes from running dataprep. This object contains all information about X0, X1, Z1, and Z0. Therefore, if data.prep.obj is supplied, none of X0, X1, Z1, and Z0 should be manually spe

X1

vector of treated predictor data, length = number of predictors and special predictors.

X0

matrix of controls' predictor data. nrows = number of predictors & special predictors ncols = number of control units.

Z0

matrix of controls' outcome data. nrows = number of pre-treatment years ncols = number of control units.

Z1

vector of treated predictor data. length = number of pre-treatment years .

custom.v

vector of weights for predictors supplied by the user. uses synth to bypass optimization for solution.V.

Margin.ipop

Settings for Quadratic Programming Solver ipop(): Margin for contraint violation tolerance. See ?ipop for details

Sigf.ipop

Settings for Quadratic Programming Solver ipop(): Precision (no of significant figures). See ?ipop for details.

Bound.ipop

Settings for Quadratic Programming Solver ipop(): Clipping bound for the variables. See ?ipop for details.

...

Additional arguments to be passed to optim to adjust optimization

Value

• solution.V
  vector of predictor weights.
• solution.W
  vector of weights across the controls.
• loss.v
  Loss.v.
• loss.w
  Loss.w.
• custom.V
  if this was specified in the call to synth, this outputs the weight vector specified.
• rgV.optim
  Results from optim() minimization. Could be used for diagnostics.

Details

Please consult the papers in the reference section for detailed information on the exact algorythm used to construct synthetic control groups.

References

Abadie, A. and Gardeazabal, J. (2003) Economic Costs of Conflict: A Case Study of the Basque Country American Economic Review 93 (1) 113--132 http://ksghome.harvard.edu/~.aabadie.academic.ksg/ecc.pdf Abadie, A., Diamond, A., Hainmueller, J. (2007) Synthetic Control Methods for Comparative Case Studies: Estimating the Effect of California's Tobacco Control Program NBER Technical Working Paper no 335 http://www.people.fas.harvard.edu/~jhainm/

See Also

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

Examples

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