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We had some discussion about the usefullness of Pooled-OLS and RE Estimators compared to FE.

So as far as I can tell, the Pooled OLS estimation is simply an OLS technique run on Panel data. Therefore all indivudually specific effects are completely ignored. Due to that a lot of basic assumptions like orthogonality of the error term are violated.

RE solves this problem by implementing a individual specif intercept in your model, which is assumed to be random. This implies full exogenity of your model. This can be tested with the Hausmann-Test.

Since almost every model has some endogenity issues, the FE-Estimation is the best choice and gives you the best consistent estimates but the individual specific parameters will vanish.

The question I'm asking myself is when does it actually make sense to use Pooled OLS or Random-Effects? Pooled OLS violates so many assumptions and is therefore complete nonesense. Also the strong exogenity of the RE-Estimator is basically never given, so when can it actually be usefull?

Besides this, in all models, autocorrelation can not be considered?

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  • $\begingroup$ Try to have a look at the Mundlak-Chamberlain approach to this. Google correlated random effects or Mundlak approach. They allow you to relax the assumption of non-correlated random effects. I'll expand in this comment as a proper answer when I have time (Friday night here, you know). $\endgroup$ – Kenji May 19 '17 at 18:46
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    $\begingroup$ To follow up on the comment by Kenji: Random effects models are more flexible and the problem of endogeneity can be solved by including the mean of the time-varying covariate as a predictor in the model. See: Bell, A., & Jones, K. (2015). Explaining fixed effects: Random effects modeling of time-series cross-sectional and panel data. Political Science Research and Methods, 3(1), 133-153. $\endgroup$ – Wolfgang May 19 '17 at 19:35
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First, you are right, Pooled OLS estimation is simply an OLS technique run on Panel data.

Second, know that to check how such your data are poolable, you can use the Breusch-Pagan Lagrange multiplier test -- whose null hypothesis $H_0$ is that the variance of the unobserved fixed effects is zero $\iff$ pooled OLS might be the appropriate model. Thus, if you keep $H_0$ and suspect endogeneity issues, you may want to leave the panel-data world, and use other estimation technics to deal with those, e.g. IV (multiple-SLS), GMM.

Third, in a FE specification, individual specific parameters do not vanish and can be added back in (which identical coefficients but standard errors which need to be adjusted). This is actually all what LSDV model is about (with added-back grand-average and within averages).

Fourth, to deal with autocorrelation (of errors), GLS-like transformations may help you theoretically, but in practice, it only deals with heteroscedasticity (WLS, FGLS). However, note that depending on the space (temporal, geographical, sociological, etc...) in which you assume the autocorrelation works through, you can proxy its structure and finally perform a GLS-like transformation, e.g. spatial panel.

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