Dealing with heteroskedasticity, autocorrelation, non-normal residuals in panel data

[Maisa Ali]

Dear Stata experts,
I’m new to stata and I’m working on an assignment with Panel data. I’m using a fixed-effect model after doing a hausman test. I have the following three questions, they are probably basic so please forgive my ignorance:
1.I have a problem of autocorrelation and heteroskedasticity. I used xtserial to test for autocorrelation and xttest3 to detect heteroskedasticity. Is there a command that I can use to correct for both problems? I have used “xtreg depvar varlist, fe vce (cluster id)” but it only correct for heteroskedasticity. I have also read about another command “xtgls depvar varlist, p(h) c(ar1) force” but it yielded totally different results. Which one is the one I should use?
2.I also have a problem of not having normally distributed residuals. I’ve added variables and tried to change the specification of my model but it didn’t work. I’ve read few article that argues normality assumption is sufficient but not necessary for the validity of the t-test and least squares regression for large samples. Is this true?
3.The relationship between my dependent variable (child mortality rate) and few of my control independent variables is not linear (check attached scatter plots), I have transformed the dependent variable and main independent variable (GDP) to natural log and the relationship looks linear. Should I transform the rest of the control dependent variables to log format even if it doesn't result in a linear relationship? if not, what other kind of transformation I could do based on the attached graphs?

Your help and advice would be much appreciated.

Many thanks

[Carlo Lazzaro]

Maisa:
as you should know, doing assigments on someone else's behalf is not among the goals of this list.
That said, you should first consult any decent textbooks on panel data econometrics to answer most part of your queries yourself.
As far as your questions are concerned:
- vce(cluster id) will solve both heteroskedasticity and autocorrelation (please, see Example 3, -xtreg- entry, Stata 14 .pdf manual);
- heteroskedasticity exactly means that you have non-normally distributed residuals;
- natural logging of depvar and indepvars brings about some interpretational issues of your results. It is not mandatory that you log all the variables on both sides of your regression equation.
As a closing-out aside, I would check the literature of your research field to be sure that -xtreg,fe- specification is the right one, given that your depvar is a rate.

[Maisa Ali]

Thank you so much Carlo! this is really helpful. I will check literature re using xtreg fe with a rate dependent variable. Thanks again!