Mixed model (random effects) vs pooled OLS with clustered SE

Question

I have a dataset of country-years. I want to find out whether membership in a particular group, say, EU, has an effect on an outcome, say, GDP.

In my initial model, I estimated a pooled OLS model with binary indicators (fixed effects) assigned to year and EU, with robust (heteroskedasticity-consistent) standard errors clustered by country. Country FEs were not included in this model as the time-invariant EU FE would drop out of the model.

Someone suggested that I should estimate a mixed model instead, with random effects assigned to country in addition to the original FEs. I was unable to ask for more details.

Could you help me by explaining to me what the purpose of adding country random effects is? I read up a bit about it, and I understand that it could account for random variation on the country level. Is this correct? Does adding it risk introducing bias in my model or is it always better than not controlling for any effects on the country level?

Answer 1

I would perhaps consider what the purpose of your countries in the model would be. I'm guessing you are not interested in every individual country's GDP. However, it seems you have some critical grouping variables (e.g. EU vs non-EU) as important to your research question. My suggestion would be to model this with a mixed model, using this grouping variable (e.g. region) and year as predictors, GDP as the outcome, and country as random effects.

The reason this would be more ideal is that fitting a model with country would just produce a ton of coefficients and wouldn't be very interpretable on its own. Random effects models also take advantage of shrinkage via pooling so that one gets a sense of the average effect as well as by-country variations around that average.

With respect to your question about potential bias, a mixed model would actually do the opposite, in that it weights the average effect based on this heterogeneity of groups (which inclusion as fixed effects doesn't do). The only real problem there is if there is essentially no variation among the countries, which would cause the model to crash. But that would be obvious and I don't believe that would be the case for your specific data anyway.