<p>For those interested, there is work on this: <a href="https://link.springer.com/article/10.1007/s00181-018-1465-0" rel="nofollow noreferrer">Kim, K., &amp; Lee, M. J. (2019). Difference in differences in reverse. Empirical Economics, 57(3), 705-725.</a></p>

CC BY-SA 4.0
2021-07-05T08:50:31.870Z
2021-07-05T09:22:59.607Z
2021-07-05T09:22:59.607Z
Papayapap
<p>In principle yes, but you would not use 'reverse treatment' but standard terminology. Here just withdrawal of some stimuli is the treatment. That is you would still code the withdrawal as <span class="math-container">$D=1$</span>.</p>
<p>For example, suppose you have two groups of people where everyone drink. If you implement policy that forces one group to stop consuming alcohol, that will be the treatment (with <span class="math-container">$D=0$</span> for groups that drink and <span class="math-container">$D=1$</span> for abstinence). This would give you the effect of withdrawal of  alcohol consumption.</p>
<p>In the case you mention in the question there is just one extra twist that you also reverse order of the time periods, but that itself should not affect the properties of the estimator. Only interpretation is different.</p>
<p>Also, you do not have just analogue of parallel trend assumption, you still need to satisfy the parallel trend assumption, except since you reversed the order of time periods the parallel trend assumption needs to hold not before but after.</p>
<p>So for example, if you would run this DiD with 2 time period 2020 and 2021, you would need data on outcomes for 2022, 2023, 2024, 2025... and so on and see if there is common/parallel trend assumption.</p>

CC BY-SA 4.0
2021-06-24T10:56:29.527Z
2021-06-24T11:03:35.190Z
2021-06-24T11:03:35.190Z
1muflon1
<p>I would be interested also in the generalised case, but let's start with 2x2 to keep it simple.</p>
<p>Say you have two groups <span class="math-container">$i \in \{1,2\}$</span> and two time periods <span class="math-container">$t$</span> and <span class="math-container">$t-1$</span>, as the classical DiD case. One group is untreated in <span class="math-container">$t-1$</span>, i.e. <span class="math-container">$D_{t-1}=0$</span>, and starts receiving treatment in <span class="math-container">$t$</span>, i.e. <span class="math-container">$D_{t}=1$</span>. However, the other group is treated in both periods <span class="math-container">$D_t=1$</span>. We are interested in the Average Treatment Effect on the Treated (ATT) <span class="math-container">$ATT = E[Y_t(1)-Y_t(0)|D=1]$</span>.</p>
<p>Can we do some kind of &quot;reverse&quot; DiD here? And if so, what would be the analogue of the parallel trends assumption?</p>

<econometrics><causal-inference><difference-in-difference>
Reverse DiD: or using always treated as control
Papayapap
# Reverse DiD: or using always treated as control

(Asked by: username_0 on 2021-06-24)

I would be interested also in the generalised case, but let's start with 2x2 to keep it simple.

Say you have two groups $i \in \{1,2\}$ and two time periods $t$ and $t-1$, as the classical DiD case. One group is untreated in $t-1$, i.e. $D\_{t-1}=0$, and starts receiving treatment in $t$, i.e. $D\_{t}=1$. However, the other group is treated in both periods $D\_t=1$. We are interested in the Average Treatment Effect on the Treated (ATT) $ATT = E[Y\_t(1)-Y\_t(0)|D=1]$.

Can we do some kind of "reverse" DiD here? And if so, what would be the analogue of the parallel trends assumption?

**Tags:** econometrics, causal-inference, difference-in-difference

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## 2 answers

### Answer by username_1 on 2021-06-24. Score: 4 | Accepted answer

In principle yes, but you would not use 'reverse treatment' but standard terminology. Here just withdrawal of some stimuli is the treatment. That is you would still code the withdrawal as $D=1$.

For example, suppose you have two groups of people where everyone drink. If you implement policy that forces one group to stop consuming alcohol, that will be the treatment (with $D=0$ for groups that drink and $D=1$ for abstinence). This would give you the effect of withdrawal of alcohol consumption.

In the case you mention in the question there is just one extra twist that you also reverse order of the time periods, but that itself should not affect the properties of the estimator. Only interpretation is different.

Also, you do not have just analogue of parallel trend assumption, you still need to satisfy the parallel trend assumption, except since you reversed the order of time periods the parallel trend assumption needs to hold not before but after.

So for example, if you would run this DiD with 2 time period 2020 and 2021, you would need data on outcomes for 2022, 2023, 2024, 2025... and so on and see if there is common/parallel trend assumption.


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### Answer by username_0 on 2021-07-05. Score: 2

For those interested, there is work on this: [Kim, K., & Lee, M. J. (2019). Difference in differences in reverse. Empirical Economics, 57(3), 705-725.](https://link.springer.com/article/10.1007/s00181-018-1465-0)


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