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Can I use a synthetic control method in the following settings:

  1. Treatment on one aggregate unit causes some of the individuals in that aggregate unit to migrate to the control unit
  2. The individuals in the control unit are cognizant of the treatment and react to the treatment within the control unit

How would I go about modeling this situation? Some examples of what I'm thinking:

  1. Tobacco ban in say, Florida, causes a subset of the Florida population to move to the control states, leading to a rise in tobacco-related health problems in the control units
  2. Tobacco ban in Florida causes the individuals in the control unit to react negatively (may be get outraged) and smoke more and increase health problems there

I'll be very grateful if anyone can point out to papers that consider similar situations and how to deal with them. Thanks!

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The key assumption to synthetic controls is that the weighted average of controls trends the way the treated would have trended in the absence of treatment.

If the treatment affects all of the components of your synthetic control, this assumption likely fails. There are a few things you could do.

(1) Restrict the set of potential control states to those for which this problem is unlikely.

(2) Not change your method at all, but acknowledge there may be bias. You'll want to think in context about the direction of the bias. If the direction of the bias is opposite that of your treatment effect, then your estimates are conservative, which is typically not an issue.

For example, if you are trying to quantify the health benefits of a tobacco ban in Florida, presumably the treatment effect is an increase in health in Florida relative to controls.

If the ban causes people to move from Florida to Georgia to smoke, that will make it seem like the controls are even less healthy, and bias your estimates toward finding a positive effect (this is not conservative).

If the ban causes people in Georgia to recognize smoking is harmful, and they start smoking less, that will make it seem like the controls are even more healthy, and bias your estimates toward not finding a positive effect (this is conservative).

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