Martha said
The model you are trying to apply is generally known as a mixed model. It is possible to use time invariant variables and what would be the equivalent of a fixed effect model in SAS, the procedure is called Proc mixed. The terminology is not the same (random and fixed can mean different things), but it basically allows you to create an intercept for each country, and then "extract" from that intercept the explanatory power of your variables. Concerning your question about random and fixed effects, there is a theory reason and a mathematical one. The theory reason for random effects is that the relationship between the two variables it�s different for each country (basically, a different beta), while the fixed effect assumes just a change in the intercept for each country. The mathematical reason for using random effects is that the independent variables you are using are not correlated with belonging to a particular country (the country you belong to does not change the !
probability of having a particular value in one of your independent variables). This is a strong assumption (called orthogonal). If you use random effects under conditions in which the country determines, even partially, the value of your independent variables, then you will have specification bias and your results will not be thrustworthy. There is also the GLAMM procedure in STata, but I never had good luck with it (it requires too much processing power).
This is quite incorrect. The standard random effects model, xtreg, re, does NOT involve anything beyond a random intercept. She is correct is noting that to use RE there is a maintained assumption of orthogonality between regressors and the random intercept for each unit. As Mark S. said, xthtaylor is a way around the oft-violated orthogonality assumption. Mark is right on in suggesting that you should do the Hausman test.
You do not need Some Alternative Software nor GLLAMM to estimate a mixed model in Stata. These models (which indeed combine random and fixed effects) are available with command xtmixed.
Kit
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