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I am running a 2 period difference in differences model on a repeated cross section.

I want to test the parallel trend assumption using a placebo test. I have read that to do this

"you perform an additional difference-in-differences estimation using a “fake” treatment group, that is, a group that you know was not affected by the program. "

I only have 2 groups, the treated (treatment group) and the untreated (control group) and no other groups or data that shouldn't be affected by the program.

Is it okay to create a placebo treatment group by randomly assigning members of the control group to the placebo group, then running the difference in difference model on the placebo group against the remaining members of the control group. I know that the placebo group should not be affected by the program but I am suspicious that this may not be theoretically sound.

Does anyone know if this is okay to do?

Chris

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  • $\begingroup$ You have 3 groups: treated, untreated, and control. $\endgroup$
    – user158565
    Commented Dec 14, 2018 at 19:10
  • $\begingroup$ just to clarify when I say control group what I mean is the group of untreated individual. $\endgroup$
    – user9903833
    Commented Dec 14, 2018 at 19:13
  • $\begingroup$ Unnecessary to create a placebo group. If treated group and untreated group are comparable, then just compare two groups directly. If not comparable, creating a placebo group randomly from untreated group cannot resolve the incomparable problem. $\endgroup$
    – user158565
    Commented Dec 14, 2018 at 19:17
  • $\begingroup$ Just to be clear, have you collected your data yet? (It is not clear from your description of the problem.) So can you actually re-allocate subjects to other groups for purposes of the experiment, or is it too late for this? $\endgroup$
    – Ben
    Commented Jan 8, 2019 at 22:24

2 Answers 2

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You want to confirm that the counterfactual trends look parallel in treatment and control by looking at a random subset of the control group. There is little reason to believe that tells you anything about the treatment group if there is non-random selection into treatment. Suppose treatment group was on a different untreated trajectory than the control. Why would looking at the control group tell you anything about that?

The best you can do is test the trends assumption in pre-treatment data (if you have enough data to do this, i.e., more than a single pre period). If it looks good there, you might be more willing to believe it would hold in the counterfactual, post-treatment data, but this is really an unverifiable assumption. There is no guarantee that it continues to hold.

You might also consider using synthetic cohort and matrix completion methods that can relax the parallel trends assumptions.

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Placebo control isn't the same as "do nothing" control. In a clinical trial, for example, some patients actually do improve by seeing the doctor and taking a sugar pill, which is the bar to beat for a new medication. Placebo-treated patients often significantly outperform patients who receive nothing, hence the "placebo effect". Is there a sham intervention in the control group that's outwardly similar to the treatment group? If not, you're probably not justified in calling untreated controls as placebo treated controls.

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