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This vignette illustrates the usage of improveSynth
. For a more general introduction to package MSCMT
see its main vignette.
Estimating an SCM model involves searching for an approximate solution of a nested optimization problem. Although the formulation of the optimization problem is quite simple, finding a (good approximate) solution can be hard for several reasons, see Becker and Klößner (2017) and Becker and Klößner (2018). While implementing package MSCMT
we put a lot of effort into the design of a smart and robust (but still fast) optimization procedure.
Apart from function mscmt
for the estimation of SCM models based on our model syntax, we also included the convenience function improveSynth
, which implements checks for feasibility and optimality of results delivered by package Synth
. Below, we illustrate how to use improveSynth
.
We exemplify the usage of improveSynth
based on the first example of function synth
in package Synth
.
Synth
The following code is thus essentially borrowed from the example
section of the corresponding help page (all comments have been removed):
library(Synth)
## ##
## ## Synth Package: Implements Synthetic Control Methods.
## ## See http://www.mit.edu/~jhainm/software.htm for additional information.
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 = c(1984:1989),
time.optimize.ssr = c(1984:1990),
unit.names.variable = "name",
time.plot = 1984:1996
)
synth(dataprep.out) synth.out <-
##
## X1, X0, Z1, Z0 all come directly from dataprep object.
##
##
## ****************
## searching for synthetic control unit
##
##
## ****************
## ****************
## ****************
##
## MSPE (LOSS V): 4.720551
##
## solution.v:
## 0.003972032 0.00222758 0.1288856 0.3277689 0.008144768 0.5290011
##
## solution.w:
## 0.001006191 0.005246634 0.1691651 0.2136205 0.6109586 2.9586e-06
We check the result by applying function improveSynth
to synth.out
and dataprep.out
:
library(MSCMT)
improveSynth(synth.out,dataprep.out) synth2.out <-
## Results reported by package Synth
## =================================
##
## Optimal V : 0.00397203172199428 0.0022275802340665 0.128885551930044
## 0.327768944797584 0.00814476840194525 0.529001122914366
## Optimal W*(V): 0.00100619117797987 0.00524663354000337 0.169165120873083
## 0.213620460951039 0.610958634379188 2.95858187768921e-06
## with corresponding predictor loss ('loss W') of 0.004733129
## and corresponding dependent loss ('loss V') of 4.720551.
##
##
## Components of W*(V) do not sum to 1, dependent loss ('loss V') of
## rescaled W*(V) is 4.720551.
##
##
## Feasibility of W*(V)
## ====================
##
## WARNING: W*(V) is NOT optimal and thus infeasible!
## 'True' W*(V): 0 0.00338943037392679 0.158483318047272 0.217351422652097
## 0.620775828926704 0
## with corresponding predictor loss ('loss W') of 0.004715856
## and corresponding dependent loss ('loss V') of 4.719351.
##
##
## Optimality of V
## ===============
##
## WARNING: 'Optimal' V (as reported by package Synth) is not optimal (W*(V) was
## infeasible), (one of potentially many) 'true' optimal V* (with
## sum(V*)=1):
## Optimal V* : 5.60003568150536e-09 0.560003568150536 1.77473253948985e-08
## 5.60003568150536e-09 5.60285964068872e-08 0.439996346873471
## Optimal W*(V*): 0 0 0.045688074469268 0.250556360555955 0.627179685612033
## 0.0765758793627435
## with corresponding predictor loss ('loss W') of 7.597302e-09
## and corresponding dependent loss ('loss V') of 4.440946.
Package Synth
generated a (slightly) infeasible solution, returning a (slightly) suboptimal weight vector w
for the control units. However, the predictor weights v
are (considerably) suboptimal anyway, because the original dependent loss of 4.720551 (as well as the dependent loss for the corrected w
4.719351) is considerably larger than the dependent loss 4.440946 for the optimal predictor weights obtained by improveSynth
.
In the second example, we modify the first example by allowing package Synth
to use genoud
as (outer) optimization algorithm.
Synth
genoud
is switched on by the corresponding function argument. We capture the output with capture.output
because it is very verbose. Furthermore, the calculation is quite lengthy, therefore the results have been cached.1
if (file.exists("synth3.out.RData")) load ("synth3.out.RData") else {
set.seed(42)
capture.output(synth3.out <- synth(dataprep.out,genoud=TRUE))
out <- }
We again check the result by applying function improveSynth
to synth3.out
and dataprep.out
:
improveSynth(synth3.out,dataprep.out) synth4.out <-
## Results reported by package Synth
## =================================
##
## Optimal V : 2.0267533885719e-10 0.282598702518196 0.0021778890504857
## 0.00278189732871801 0.000373699249646763 0.712067811650278
## Optimal W*(V): 0.0420138249827668 0.0112849868071455 0.0223432791829297
## 0.218134146153805 0.595395073764248 0.110828688687666
## with corresponding predictor loss ('loss W') of 0.0001350879
## and corresponding dependent loss ('loss V') of 4.328506.
##
##
## Components of W*(V) do not sum to 1, dependent loss ('loss V') of
## rescaled W*(V) is 4.328506.
##
##
## Feasibility of W*(V)
## ====================
##
## WARNING: W*(V) is NOT optimal and thus infeasible!
## 'True' W*(V): 0 0 0 0.229091487590933 0.715755416007496 0.0551530964015711
## with corresponding predictor loss ('loss W') of 4.4355e-05
## and corresponding dependent loss ('loss V') of 6.09574.
##
##
## Optimality of V
## ===============
##
## WARNING: 'Optimal' V (as reported by package Synth) is not optimal (W*(V) was
## infeasible), (one of potentially many) 'true' optimal V* (with
## sum(V*)=1):
## Optimal V* : 5.60003568150536e-09 0.560003568150536 1.77473253948985e-08
## 5.60003568150536e-09 5.60285964068872e-08 0.439996346873471
## Optimal W*(V*): 0 0 0.045688074469268 0.250556360555955 0.627179685612033
## 0.0765758793627435
## with corresponding predictor loss ('loss W') of 7.597302e-09
## and corresponding dependent loss ('loss V') of 4.440946.
Now, package Synth
generated a solution with a dependent loss of 4.328506 which is even smaller than the dependent loss 4.440946 obtained by improveSynth
. However, the solution generated by Synth
is severely infeasible: the inner optimization failed, returning a suboptimal weight vector w
for the control units, which itself lead to a wrong calculation of the dependent loss (which, of course, depends on w
). Implanting the true optimal w
(depending on v
) leads to a large increase of the dependent loss, which uncovers the suboptimality of v
.
improveSynth
is able to detect this severe problem and calculates an improved and feasible solution (the improved solution matches the solution obtained from the first call to improveSynth
above, with a dependent loss of 4.440946).
Issues with the inner and outer optimizers used in synth
from package Synth
may lead to infeasible or suboptimal solutions. This vignette illustrated the usage of the convenience function improveSynth
from package MSCMT
for checking and potentially improving results obtained from synth
.
Becker, Martin, and Stefan Klößner. 2017. “Estimating the Economic Costs of Organized Crime by Synthetic Control Methods.” Journal of Applied Econometrics 32 (7): 1367–9. http://dx.doi.org/10.1002/jae.2572.
———. 2018. “Fast and Reliable Computation of Generalized Synthetic Controls.” Econometrics and Statistics 5: 1–19. https://doi.org/10.1016/j.ecosta.2017.08.002.
To reproduce from scratch, please delete "synth3.out.RData"
from the vignettes
folder.↩︎
These binaries (installable software) and packages are in development.
They may not be fully stable and should be used with caution. We make no claims about them.
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