st: Panel model specification

[Federica Di Marcantonio <dmfederica@yahoo.it>]

Dear Statalisters, 

I have a balanced panel (41 SSA countries  from 1968 to 2008). 

In order to check all the issues relate to panel data I proceded as follow:
run ols with id and year dummies and then check if they are significant
noi xi: reg logfood_pin2004 logland logirrigation logfertilizer_fao loganimtrans logtractors logurb loglabour logexp logcereal_aid logbatt landl raindu p1 p3 i.id i.year
noi testparm _Iid*
noi testparm _Iyear* (significant so I include them in the FE)

Then I generate a time trend ( I don't remember where, but I read that time trend has to be retained if significant but I am not sure why it is so, can you explain and tell me if I have to retain it?)
g t=year-1968
noi tab id, g(ctry)

it is significant 
but then I have also generate COUNTRIES TREND

forvalues i=1(1)40{
gen tr`i'=t*ctry`i'
}
I remember to read that if the trends are significantly different across states and cannot be combined into a single overall keep the country trend. In my case considering that the trend is significant I have to keep only t

So with this model I have runned the FE and RE model 
xi: xtreg logfood_pin2004 logland logirrigation logfertilizer_fao loganimtrans logtractors logurb loglabour logexp logcereal_aid logbatt landl raindu p1 p3 t i.year, fe
then I tested for cross-sectional dependence - Pasaran CD (xtcsd, pesaran abs), for heteroskedasticity (xttest3), and serial correlation...all the problems are present in my model so I corrected them by using xtpcse, corr(ar1)
I also tested for unit root and variables are stationary (some with drift some with trend). However, I also did a second checking for unit root by calculating the residual of my final model (pcse) and test the residual for unit root (predict e, resid; xtfisher e ). Here the results
Fisher Test for panel unit root using an augmented Dickey-Fuller test (0 lags)

Ho: unit root

      chi2(74)     =  219.5621
      Prob > chi2  =      0.0000

Nevertheless, since I wanted to include time invariant var i did a Three stages FEVD and in the last stage i used pcse 
My questions are:
1) do I have to retain the trend? 
2) Is my procedure correct? 
3) what can I do in order of understanding if my estimator fit well the model?

Thanks

Federica Di Marcantonio
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