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Both models allow for explanatory variables that are time-invariant.

I had thought that the advantage of a random effects model might be related to the fact that random effects models mitigate serial correlation (does it?) whereas pooled OLS regression with cluster–robust standard errors do not, but I then found a post that noted (emphasis added):

Clustered standard errors are robust to heteroskedasticity and serial correlation in the error term. In that sense, clustered standard errors are "appropriate" when you think this is the case in your context, as they still give you valid inference. One likely reason in panel data for (positive) serial correlation in the error term is the presence of time-invariant unobservables. However, if there are such time-invariant unobservables, other estimators might be more appropriate than pooled OLS, e.g. fixed effects if you think the time-invariant unobservables are correlated with your regressors, or random effects if you think there is no such correlation.

A related question is here but the person who asked that question asked about pooled OLS (not pooled OLS regression with cluster–robust standard errors).

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  • $\begingroup$ Related questions: 1. Does the pooled OLS with cluster-robust standard errors automatically handle heteroskedasticity? 2. What about RE models and heteroskedasticity? 3. Does pooled OLS with cluster-robust standard errors automatically manage autocorrelation? 4. Do RE models manage autocorrelation? Or does autocorrelation mean one must build extra bells and whistles (like Arellano-Bond estimators?) into the model? $\endgroup$ – the_scheining Aug 23 '18 at 15:09

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