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I am trying to estimate the impact of a minimum wage policy in a given region and I was initially thinking of only using a DiD design. However, I came across this causal inference post on synthetic control methods SCM, and I am now considering but was curious if one method is "superior" to the other. Specifically, I want to know if I should pick my own control group based on institutional knowledge, as in the case of a DiD. Or use SCM to create an artificial control group based on a dataset of all 8 regions in X country I am studying.

I have several macro variables/indicators at the region-level on both my treated and control regions, and both before and after treatment. These variables include:

unemployment rate
Labor fore participation rate
employment rate 
Gini coefficient
share of prime-age workers
median household income
median individual income
poverty rate
% of population on food stamps
% of workforce receiving unemployment insurance
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The advantages over DID:

  • It relaxes the parallel trends assumption.
  • It can work with fewer treated units, often just one
  • Easier to explain compared to a table of regression coefficients.

You can select your potential donor group using institutional knowelede, and then let SC algorithm reweight those selected units. This is recommended in the SC literatuire. Personally I would pre-register the set of potential donors and then check "all regions" version for robustness.

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    $\begingroup$ dimitriy, do you have a good recommendation for understanding the SC weighting algorithm? I think Abadie does too much abbreviation in the technical sections from the 2003, 2007, and 2021 articles on synthetic controls, and I would love to be able to learn it with enough depth to program the weights-estimations algorithm myself. $\endgroup$
    – Alexis
    Dec 14, 2021 at 0:39
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    $\begingroup$ Those are all the same papers I've read. I would take a look at Synth: An R package for synthetic control methods in comparative case studies A Abadie, A Diamond, J Hainmueller - Journal of Statistical Software, 2011 and the code (or another implementation). $\endgroup$
    – dimitriy
    Dec 14, 2021 at 1:00

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