Can CausalImpact package be used in lieu of the Synth package to create a synthetic control ? The R implementation of the Synth package is very confusing compared to the Stata demo for the Synth function.
The authors of the
Synth package may have much more to add, but in principle,
Synth address the same fundamental problem: How can we draw causal inferences in settings where there is only one treated unit, and where treatment was not necessarily assigned at random? Typical examples include a new policy that's instituted in a particular state, or an advertising campaign that targets a particular market.
Both packages infer the causal effect of such interventions by constructing a synthetic control: a time series of what a control probably would have looked like had it been available. The difference between the two packages lies in how they go about constructing such synthetic controls:
Synthuses pre-treatment variables for matching. For example, you might consider the overall state of other markets prior to the beginning of the advertising campaign to construct a synthetic market resembling the treated market.
CausalImpact, in contrast, uses the full pre- and post-treatment time series of predictor variables for matching. For example, you could consider using demand, sales, or even general GDP time series in other markets to construct a synthetic control for the market that was treated. For more details from the perspective of
CausalImpact, see the paragraph starting at the bottom of p. 250 in the manuscript.