Difference-in-Difference (DID) Regression with Non-Stationary (but Cointegrated) Treatment and Control Groups 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!
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).
MacKinlay, A. Craig. &quot;Event studies in economics and finance.&quot; Journal of economic literature 35.1 (1997): 13-39.