fn.V: Loss Function for nested optimization of W and V weights

Description

Loss function for the nested optimization of W and V weights used for constructing synthetic control groups according to the methods outlined in Abadie and Gardeazabal (2003) and Abadie, Diamond, Hainmueller (2010, 2011, 2014) (see references). This function is called by synth internally, and should not be called manually by a normal user.

Usage

fn.V(variables.v = stop("variables.v missing"),
X0.scaled = stop("X0.scaled missing"), 
X1.scaled = stop("X1.scaled missing"), 
Z0 = stop("Z0 missing"), 
Z1 = stop("Z1 missing"), 
margin.ipop = 5e-04, 
sigf.ipop = 5, 
bound.ipop = 10, 
quadopt = "ipop")

Value

A scalar that contains the function value.

Arguments

variables.v: 1 by k a vector of v weights.
X0.scaled: matrix of controls' predictor data. nrows = number of predictors and (possibly) special predictors. ncols = number of control units.
X1.scaled: matrix of treated predictor data. nrows = number of predictors and (possibly) special predictors. ncols = one.
Z0: matrix of controls' outcome data for the pre-treatment periods over which MSPE is to be minimized. nrows = number of pre-treatment periods. ncols = number of control units.
Z1: matrix of treated outcome data for the pre-treatment periods over which MSPE is to be minimized. nrows = number of pre-treatment periods. ncols = one.
margin.ipop: setting for ipop optimization routine: how close we get to the constrains (see ipop for details)
sigf.ipop: setting for ipop optimization routine: Precision (default: 7 significant figures (see ipop for details)
bound.ipop: setting for ipop optimization routine: Clipping bound for the variables (see ipop for details)
quadopt: string vector that specifies the routine for quadratic optimization over w weights. possible values are "ipop" (see ipop for details)

Author

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 Forthcoming 2014.

Synthetic : 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. (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.