I am currently working with a balanced time-series cross-section dataset (or a T dominant panel), consisting in 8 units (countries) and 32 observations (quarters) per unit. Thus, the dataset has 8 x 32 = 256 observations. The dependent variable is continuous and there are 5 regressors. I am estimating my model using Fixed Effects (in Stata, "xtreg, fe"), Random Effects (in Stata, "xtreg, re"), Beck and Katz Panel Corrected Standard Errors ("xtpcse") and GLS ("xtgls"). Since my data is not what Greene would called "well-behaved data" -it shows panel heteroskedasticity, serial correlation and contemporaneous correlation-, I am proecting the models against these issues. Thus, my first question is about how to control for time and unit unobserved heterogeneity with PCSE and GLS models. Or, in different words:
(a) Does it make sense to include time and unit dummies with PCSE and GLS models? Any reference supporting your statement will be appreciated. I have found some other people asking this out there, but no proper answer so far.
(b) Does it make sense to include a time trend and time dummies simultaneously in FE/RE/PCSE/GLS? I have found different answers to this question: ones arguing that it makes sense and some others arguing that it does not. Again, explanations with a minimal reference or link are welcome.
Thank you all!