# Can I still call this as a difference-in-difference analysis?

I have a regression which has treatment and control groups. I want to test how the treatment group (binary variable) reacts during crises periods compared to control group.

The crisis variable is a summation of several crises dummy variables that the maximum value is two (showing only values of 0, 1 and 2) as there are some overlapping two crises periods in my sample. Thus, this crisis variable shows a non-zero value only if the time is during the crisis periods.

I interact this crisis variable with the treatment group.

If so, can I still call this a difference-in-differences regression?

I assume the crisis impact overlaps if two crises happen in the same period which is a necessary assumption I need to keep.

• Why do you sum over the crisis dummy variables? Are these three separate treatments, with overlap between all of them? Commented Mar 16, 2023 at 22:05
• Do you treat the aggregate crisis variable as numeric? Doesn't this imply that the effects of crises add up? Alternatively, you could define the crisis variable as binary: is there at least one crisis or not. In any case, much depends on the details of the actual problem. For example: Since the groups (seem to) undergo multiple crisis periods separated by non-crises periods, do you assume that the crisis effect on Y is sharply over as soon as the crisis is over? And do you assume that the crisis effect remains the same in multiple crises over time? Commented Mar 17, 2023 at 20:44
• I assume the crisis impact overlaps if two crises happen in the same period.
– Eric
Commented Mar 24, 2023 at 17:34

Say that $$D_{it}\in\{0,1,\ldots,K\}$$ is a categorical variable denoting whether unit $$i$$ at time $$t$$ got treatment $$k=0,1,\ldots,K,$$ where 0 denotes the absence of treatment (control group).
The answer to your question is yes, if by difference-in-differences you mean estimating via least squares the regression \begin{align*} Y_{it} = \alpha_i + \lambda_t + \sum_{\ell=1}^K\tau_\ell D^{\ell}_{it} + \epsilon_{it},\quad i\in[N],t\in[T] \end{align*} where $$Y_{it}$$ is the outcome of interest, $$\alpha_i$$ and $$\lambda_t$$ are unit and time fixed effects, and $$D_{it}^\ell=\mathbb{1}(D_{it}=\ell)$$. You can add control variables if you feel you need to.
1. the SUTVA (Stable Unit Treatment Value Assumption) would be violated if your shocks are too big/aggregate. The SUTVA require unit $$i$$'s treatment status to not affect unit $$j$$'s ($$i\neq j$$) potential outcomes. This is extremely unlikely if your crisis are systemic or at the local labor market level for example. Much more likely if you are working with small firms, for example, and your definition of crisis is related, say, to the outstanding debt of the company. Again context matters.