Interpretation coefficients fixed-effects model when time dummies are included

[Marina Jenny]

Dear community!

I need your help I have been reading many posts in this forum and generally on the world wide web but I failed to find an answer to my question. Maybe it is too simple and that is why I cannot find it..

I ran a FE regression without time dummies first:

I do know that the interpretation then would be "for a given firm as the Members-to-beneficiaries-ratio (MBRatio) varies across time by 1 unit, the Return (Y) changes by 0.221 units (%)."

However, if I include time dummies with i.year (I did testparm i.year to test for time fixed-effects) then I get confused about the interpretation of the coefficients. First of all, I have to leave out "interest rate (IntRate)" and "inflation (infl)" as those factors are equal for all firms and will then, as I understand it, be part of the time fixed-effects (year d. coefficients) - but correct me on that if I misinterpret this (too).

So the regression with the year dummies looks as follows:

1) Would it the interpretation then still be "for a given firm as the Members-to-beneficiaries-ratio (MBRatio) varies across time by 1 unit, the Return (Y) changes by 0.0997 units (%)."?

and 2) how do I interpret the time dummies? Because obviously the interpretation as above does not really make any sense. Does it mean something like that the year 2020 (itself with its factors) had an influence of 13.065 unit increase in Return (Y) relative to 2016. Or how do I interpret these? Do I even or do they just tell me that some factors (i.e. interest rates) that are equal for all funds in a certain year singificantly influenced my dependent variable (return)?

I am not sure where I make the error in thinking exactly, but I hope someone of you out there can help me with it

Thanks a lot in advance already!

Best,
Marina

[Rhys Williams]

Hi Marina,

1) You are correct that including time fixed effects means variables that only vary over time but not firm will be omitted. It is not possible to disentangle the variation from, say, interest rates on your dependent variable when you have a year fixed effect. That being said, so long as you aren't trying to study the effect of, say, interest rates, it is preferable to use a year fixed effect as a kind-of catch-all.
2.) In terms of interpretation, I do not think you need to say about it varying across time: a 1-unit increase in MBRatio is associated with a 0.0997 unit change in Return. Obviously, you need to be careful whether this is % change or percentage point change.
3.) I don't think you need to mention the effect of the time dummies in your report/paper. However, the interpretation is that - compared to the baseline (2016 in your case) - the return was greater in 2017, 2018 (not statistically significant), 2019 and 2020 than in 2016 (by the respective coefficients). This could be for a variety of reasons but basically it is something which occurred in a given year that affected all firms equally (a macro shock).

Best,
Rhys

[Marina Jenny]

Hi Rhys Williams,

Thank you very much for your your clarifying and helpful answer!! It is really much appreciated, especially also the hint about the percentage point change.. as I believe, in my case I actually have to deal with percentage point changes since pretty much all variables, independent and dependent, are originally expressed in percent (i.e. MBRatio is in the dataset a percentage, so is the return, hence it would be a 0.0997 percentage point change, I believe?).

Would you mind if ask another question that came up in the meantime? If you do, no problem, you already helped a lot
I did first run a pooled OLS, then FE and FE with time fixed effects, also to compare the different results with each other. I know that often from pooled OLS to FE models the coefficients become smaller because FE can eliminate some effects bc some before unobserved effect is responsible (and we control for that now). But could it also be the that coefficients get higher? because I get higher coefficients for some ind. variables when using FE and then even for some a bit more when using FE and time effects.

Best,
Marina

[Rhys Williams]

Hi Marina,

Yes, I think it is fine if your FE estimates are higher than OLS. FE removes time-invariant omitted variable bias. If this omitted variable bias was positive then you would expect FE>OLS, which your results suggest.

Hope this helps.

Best,
Rhys

[Marina Jenny]

Hi Rhys Williams,

Yes, that helps a lot again - THANKYOU!!

Have a successful day.

Best,
Marina