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Imagine I want to reconstruct a counterfactual euro-dollar exchange rate in 2010 using a synthetic control variable to assess the impact of some policy. Could I use, for example, the exchange rates from 2000 to 2009 as a sample to create my SC?

More generally, when it's impossible to use similar subjects (e.g. neighboring countries) for a control group, can the historical series of the variable of interests serve as a control group?

raving-bandit
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  • You might find this paper of interest, though its topic may not directly answer your question: Phillips, P. C. (2006). [Optimal estimation of cointegrated systems with irrelevant instruments](https://cowles.yale.edu/sites/default/files/files/pub/d15/d1547.pdf). Discussion Paper 1547, Cowles Foundation. – Alexis May 20 '18 at 21:43
  • Take a look at the Causal Impact R package that does something like this. You would be assuming that those other time series are not touched by the intervention, which might be a strong assumption. – dimitriy May 22 '18 at 16:34

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