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I have a set of cities for which approximately half received an intervention and half did not. The intervention was a drug treatment program. All the cities that received the intervention received it at the same time.

I would like to setup a DiD where the Outcome is overdose deaths in cities and control for a few covariates. Based on my understanding, in DiD the impact of the intervention is based on the interaction of a treatment versus control variable and pre/post intervention variable.

My problem is the interaction term I create (Treatment*PrevsPost) is identical to the treatment variable. As a result, I’m not sure how to interpret the treatment effect. Would it simply be represented by the treatment variable? Any help would be greatly appreciated. Below is a simplified version of my dataset to illustrate the issue I’m having.

All the best

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  • $\begingroup$ I have the same problem but the software R plm is dropping the interaction, which of-course with difference in differences is precisely what one is interested in. This makes me think difference in differences is unsuited to this problem. I've seen some people using Regression discontinuity in time, so I'm going to try that with with a parametric RDD to see if it works. $\endgroup$
    – Rodney Beard
    Commented Jun 1, 2022 at 0:36

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The simplest DID as a regression consists of regressing the outcome on

  1. an ever_treated dummy (constant for each observation)
  2. a post_treatment_period dummy (defined in the same way for everyone)
  3. the interaction between (1) and (2)
  4. Covariates

For example, here is the setup of the Card and Krueger minimum wage study from Scott Cunningham's The Mixtape.

If you use a panel fixed-effects model, the time-invariant variables get absorbed into the fixed effect, but since the interaction is the parameter of interest, that is not really a problem when your software drops them.

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