# Model Setup

My dataset is a country-year panel and I ran two estimations:

1. A classical OLS model with country and year fixed effects

$y_{it} = \beta x_{it} + \eta D_i + \mu D_t + u_{it}$

where $x_{it}$ is a vector with my variables of interest and $D_i$ and $D_t$ are country and year dummies.

2. A random effects model that, following Bell and Jones (2015), explicitly controls for the between effects of all explanatory variables:

$y_{it} = \beta (x_{it} - \bar x_i) + \gamma \bar x_i + u_i + u_t + u_{it}$

where $\bar x_i$ contains the country-level means of the variables of interest.

As expected, both specifications produce almost exactly the same coefficients for $\beta$. My question concerns the difference in the resulting standard errors (SE).

I went with clustered SE on the country level for the FE estimation and parametrically bootstrapped SE for the RE model. Naturally, they are not the same. In fact, some of the key coefficients of interest have considerably smaller SE in the RE model.

If it matters: I ran the analysis in R; calculating cluster-robust standard errors with cluster.vcov from multiwayvcov and bootstrapped standard errors with bootMer from lme4.

# Question

How can I interpret the fact that the SE are different in the two models? I don't quite understand (the intuition of) the difference in the assumed error structure. What kind of mistake do I make if I believe the (smaller) SE calculated for the RE model?

# References

Bell, Andrew and Kelvyn Jones (2015). "Explaining Fixed Effects: Random Effects Modeling of Time-Series Cross-Sectional and Panel Data". Political Science Research and Methods 3(1), 133-153.