Hi Guys,

I am running a series of regressions on a panel of 36 countries over a 40 year period to determine the nature of the relationship between democracy (measured by an index - 0-1) and inequality (Gini coefficient). The relationship is being modelled though a 2nd order polynomial function (reverse u-shaped curve).

For a simple linear regression without controls (xtreg), the Breusch Pagan test indicates that POLS is unreliable and the Hausman test indicates that FE are preferred to RE.

For my understanding, I have the following questions:
1). Where heteroskedasticity is detected from BP test and POLS cannot be relied upon, how does RE improve on this? Is the assumption of constant variance relaxed or is the bias in standard errors corrected for? If so then why is it still necessary to deal with the heteroskedasticity, e.g., through use of robust standard errors?
2). Also, in this regression set up, what is the most appropriate way to incorporate robust se's?
3). Where endogenity issues mean that FE is peferred to RE, how should this endogeneity be dealt?
4). Moreover, I have seen it suggested that heteroskedasticity and endogeneity issues be dealt with before rerunning the BP and Hausman tests. Is this the correct order, i.e. run BP and Hausman, then correct for issues, then rerun BP and Hausman to check most appropriate model?


I also have the following general questions:
i). In country, panel data does the FE model have the equivalent effect of adding a full set of country dummies to control for time invariant effects country specific effects?
ii). Is it standard procedure to redo the BP and Hausman test each time a control variable is added to the model, as it is my understanding that adding controls affects the outcome of these tests?

Any and all help is very much appreciated.