Many significant results. But very low r-square. What to do/What does it mean?

[tim hoeflinger]

Dear all,

i am currently working with a panel data set (100 countries, 18 years, about 1800 observations) and seek to run a regression analysis.I employ several control variables...
The Hausman test implies that one should use fixed effects.
When i do that i get several significant results that make a lot of sense. However the r-square value is really low (overall = 0.1221). I was wondering what this means or what i can do ?
I do get significantly higher r-square values when i run a random effects or a between estimator regression....

A further and perhaps separate problem is the fact that there are important time-invariant variables (independent) that i need to incorporate but that are naturally omitted in the fixed effects model... Should i therefore abolish the fixed effects model altogether and instead use other options as recommended in other posts in this forum (e.g. between estimator or hausman-taylor model)....even though hausman test implied fixed effects....

Many thanks for any help, thoughts, recommendations.
Tim

[daniel klein]

The answers to your questions depend on your research questions which you do not state. Are you primarily interested in the association between the predictors and your outcome or are you primarily interested in predicting the outcome?

If your interest is in associations, you should not care much about R-squared as it tells you very little (if anything) about your research question. A low R-squared basically means that your model does do not include all [random] variables that are associated with the outcome. That is not necessarily a problem as long as the omitted variables are not correlated with your predictors.

If you are primarily interested in predicting the outcome, then you should probably not even run a Hausman test and just go with the model that gives you the best predictions. Perhaps you should go for some sort of cross-validation to avoid overfitting.

Concerning the time-invariant variables, it is not clear what "incorporating" them means. If you want to "control" for these variables, then go with fixed-effects because that is what FE-models do: they control for variables that are constant within panel-units. If you are interested in the coefficients of these variables, then you have no choice but to use the RE specification (or within-between models; there is not a big difference regarding the time-invariant predictors) and adopt the additional assumptions.

[tim hoeflinger]

Many Thanks Daniel for your rapid and eloquent reply. My research seeks to identify whether certain country characteristics e.g. GDP determine foreign policy actions by partner countries such as the allocation of development aid.
In this sense, i am indeed primarily interested in the associations between the predictors and the the dependent variable...
Regarding the time-invariant variables.... it would be good to know the coefficients...but i might need to reconsider this part....