how to test for multicollinearity after using reghdfe in DID regression model

[Saleh sharmah]

Hi all
how to test for multicollinearity after using reghdfe in DID regression model ?

Thanks for your help

[Clyde Schechter]

Well, if you really can't find anything better to do with your time, multicolinearity is exclusively about the relationships among the independent variables in the model. It has nothing to do with the outcome variable nor the particular kind of regression. So you can run plain old -regress- with the same variables that you used in your -reghdfe- command and then run -estat vif- to see the variance inflation factors.

That said, testing for multicolinearity is a waste of time. It is often present, but usually not a problem. And when it is a problem, there are no easy solutions. All that multicolinearity does is reduce the precision (i.e. increase the standard errors and widen the confidence intervals) of the estimated coefficients of the variables that participate in the multicolinearity. Crucially, it does not cause any bias in the analysis. If the key variables whose effects you are trying to estimate in order to answer your research questions (as opposed to the "control" variables) are not involved in the multicolinearity, then they are not affected and there is no problem. Even if one or more of the key variables does participate in the multicolinearity, if its confidence interval is narrow enough that you can still answer your research question, then there is no problem.

You only have a possible multicolinearity problem if a key variable's coefficient's confidence interval is so wide that your study is inconclusive. In that case, you might want to check the variance inflation factors in order to see if multicolinearity might be the reason the confidence interval is so wide. But be warned, if you determine that this is the case, there is no simple way around this. All the solutions involve either getting a much larger data set, or starting over with a new sampling design that breaks the multicolinearity. Both of these solutions are typically very resource intensive and often completely infeasible.

I strongly recommend you get a copy of Arthur Goldberger's A Course in Econometrics and read chapter 23. That chapter is devoted to an exploration of multicolinearity. It is a very entertaining read, and it thoroughly explains why multicolinearity is a highly overrated problem, and really just boils down to having too small a sample.

[Saleh sharmah]

Thanks, Clyde for your informative response and your suggestion. I will definitely keep that in mind.