Question

Because fixed effects allow arbitrary correlation between a_i and the x_itj, while random effects do not, FE is widely thought to be a more convincing tool for estimating ceteris paribus effects. Let’s say you are concerned about the correlation between a _i and the key explanatory variable that is constant over time. Then what is your modeling strategy? Use FE or RE?

Answer 1

The random effects model assumes that the individual–specific effects are uncorrelated with the independent variables. In case the subjects change little, or not at all, across time, a fixed effects model may not work very well or even at all. There needs to be within-subject variability in the variables if we are to use subjects as their own controls. If there is little variability then the standard errors from fixed effects models may be too
large to tolerate. So random effects models will estimate the effects of time-invariant variables, but the estimates may be biased because we are not controlling for omitted variables.