<p>If your question is the broad: &quot;How do I estimate the differences between these two groups under these problematic contexts?&quot; I recommend taking a look at event study literature, which has a lot of similarities to the DiD literature, but is frequently applied in the context of stocks (which can be non-stationary).</p>
<p><a href="https://www.jstor.org/stable/pdf/2729691.pdf?casa_token=Hwm77w3rIMEAAAAA:Yydbr28qKdY1qMKfc-UtOgYuZge_b3jSoFYpevwfPABEPcFCiQXTWrTe_fEzGej8ej8VIhdnF9kBWts9jGfV1lgfC6KdMPhwAL64eHN0x6ZcFU4ylgY" rel="nofollow noreferrer">MacKinlay, A. Craig. &quot;Event studies in economics and finance.&quot; Journal of economic literature 35.1 (1997): 13-39.</a></p>

CC BY-SA 4.0
2020-08-07T00:33:45.380Z
2020-08-07T00:33:45.380Z
RegressForward
<p>I would like to run a DID regression between two periods where each period spans multiple years. For example:
Period 1: 1970Q1-1990Q4
Period 2: 1991Q1-2010Q4.</p>
<p>My treatment and control variables are non-stationary, but they are cointegrated. Thus, the error term is stationary and normally distributed. All assumptions of OLS also hold for DID. However, in a standard setting where you have two cointegrated variables one would have to use a DOLS or FMOLS to properly estimate the standard errors. Yet, the setup of a DID regression is different than the standard assumptions of regressing Y on X (with both being I(1) and cointegrated) which is what all of the theory on cointegration (in levels) is based on.</p>
<p>My question is if the variables are non-stationary, but cointegrated is the DID estimation valid? If it is, then the estimates would be superconsistent as is the case with an OLS between cointegrated variables, however, I am not sure if one can correct for the standard errors in this setup.</p>
<p>Any help would be much appreciated!</p>

CC BY-SA 4.0
2020-08-05T22:45:11.887Z
How can your treatment be non-stationary? If you are using DiD the treatment will be a dummy variable. A dummy variable will be non-stationary only if probability of 1/0 is not constant in each time period. I cannot imagine any way how that would be possible with a treatment dummy, which is arguably not even stochastic if you apply treatment at some given time t and in other times its just always set to 0 or 1, and even if that would be the case how would you run DiD on it?
1muflon1
CC BY-SA 4.0
2020-08-05T23:55:48.813Z
I am sorry I didn't mean that the treatment dummy is non-stationary (it is either 0 or 1 as you said). What I meant is that both my treatment and control groups ( the actual data process describing the two groups) are not stationary, but cointegrated.
user29937
CC BY-SA 4.0
2020-08-13T23:09:38.523Z
@1muflon1 Assuming my previous comment clears up the confusion does this regression make sense econometrically given the non-stationary nature of the treatment and control groups. If this was simply a regression of the type: y_t=alpha+beta_t+e and Y and X are cointegrated the esitmates will be superconsistent although one would have to correct for the standard errors. In my case, however, the X and the Y processes are my treatment and control respectively which are non-stationary, but cointegrated.
user29937
<econometrics><regression><co-integration>
Difference-in-Difference (DID) Regression with Non-Stationary (but Cointegrated) Treatment and Control Groups
user29937
# Difference-in-Difference (DID) Regression with Non-Stationary (but Cointegrated) Treatment and Control Groups

(Asked by: username_0 on 2020-08-05)

I would like to run a DID regression between two periods where each period spans multiple years. For example:
Period 1: 1970Q1-1990Q4
Period 2: 1991Q1-2010Q4.

My treatment and control variables are non-stationary, but they are cointegrated. Thus, the error term is stationary and normally distributed. All assumptions of OLS also hold for DID. However, in a standard setting where you have two cointegrated variables one would have to use a DOLS or FMOLS to properly estimate the standard errors. Yet, the setup of a DID regression is different than the standard assumptions of regressing Y on X (with both being I(1) and cointegrated) which is what all of the theory on cointegration (in levels) is based on.

My question is if the variables are non-stationary, but cointegrated is the DID estimation valid? If it is, then the estimates would be superconsistent as is the case with an OLS between cointegrated variables, however, I am not sure if one can correct for the standard errors in this setup.

Any help would be much appreciated!

**Tags:** econometrics, regression, co-integration
> **Comments:**
> **username_1**: How can your treatment be non-stationary? If you are using DiD the treatment will be a dummy variable. A dummy variable will be non-stationary only if probability of 1/0 is not constant in each time period. I cannot imagine any way how that would be possible with a treatment dummy, which is arguably not even stochastic if you apply treatment at some given time t and in other times its just always set to 0 or 1, and even if that would be the case how would you run DiD on it?  
> **username_0**: I am sorry I didn't mean that the treatment dummy is non-stationary (it is either 0 or 1 as you said). What I meant is that both my treatment and control groups ( the actual data process describing the two groups) are not stationary, but cointegrated.  
> **username_0**: @1muflon1 Assuming my previous comment clears up the confusion does this regression make sense econometrically given the non-stationary nature of the treatment and control groups. If this was simply a regression of the type: y_t=alpha+beta_t+e and Y and X are cointegrated the esitmates will be superconsistent although one would have to correct for the standard errors. In my case, however, the X and the Y processes are my treatment and control respectively which are non-stationary, but cointegrated.  

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## 1 answers

### Answer by username_2 on 2020-08-07. Score: 2

If your question is the broad: "How do I estimate the differences between these two groups under these problematic contexts?" I recommend taking a look at event study literature, which has a lot of similarities to the DiD literature, but is frequently applied in the context of stocks (which can be non-stationary).

[MacKinlay, A. Craig. "Event studies in economics and finance." Journal of economic literature 35.1 (1997): 13-39.](https://www.jstor.org/stable/pdf/2729691.pdf?casa_token=Hwm77w3rIMEAAAAA:Yydbr28qKdY1qMKfc-UtOgYuZge_b3jSoFYpevwfPABEPcFCiQXTWrTe_fEzGej8ej8VIhdnF9kBWts9jGfV1lgfC6KdMPhwAL64eHN0x6ZcFU4ylgY)


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