st: basic panel regression RE FE FEVD

[fenando luiz mistura <f_mistura@hotmail.com>]

Hi,
This is my first time in the forum. Happy to meet you all!
I am running my first panel data regression and would welcome some help on basic things.
I have yet to feel confortable with econometrics, so please excuse me my ignorancies.
 
I want to test the effects of an index of FDI restrictions (range 0 to 1) for years 1997, 2003, 2006, 2010 on the level of FDI stocks in a country (56 countries). 
My panel is unbalanced as for some countries I don't have the FDI Index values. Other explanatory variables include GDP, a measure of Trade, and raw materials, and dummy variable for EU countries. I use the log of all the variables (except the dummy) in the model.
 
The problem is that the Index variables is a rarely-changing variable for some countries (some countries did most of the FDI liberalisation before 1997, those sometimes have only very marginal changes in the index, or no change at all).
So when I regress using OLS and Random Effects (RE), I have a large and significant effect for the variable Index. But when I do it with Fixed Effects (FE) to take into account unoberved country effects, the effects of variable INDEX becomes insignificant and st. erros larger. Hausman test indicates that the FE model is more appropriate (p>chi2 = 0.0005). But under the FE my variable of study is not significant. As I've been told that FE does not work well with data for which the whithin variation is minimum or slowly changes over time, I also regressed using the Fixed Effect Vector Decomposition (FEVD). This is supposed to address the issue of the Index variable right? The st. errors were 2x larger than with OLS and RE and almost 2x than with FE. The coefficient under FEVD was also much larger. Is this normal? Is this model appropriate?
 
Can someone confirm if these basic methodologies make sense for analysing the effects of FDI Restrictions (index) on FDI stocks and which model would be more appropriate to rely on? Does it make sense to rely on the RE model? What kind of tests should I run?
 
Many thanks,
 
Fernando 		 	   		  
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