Arindrajit Dube has an excellent twitter thread on synthetic control methods. Super-informative throughout. I really like the discussion at the end with Wojtek Kopczuk who writes, "My preference, when possible, is to first see a variant of diff-in-diff (as simple as practical for the context) to show the presence of an effect and only then run SC to get precision. Then you hopefully get both transparent identification and tight estimates."
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