st: Problem with proportions as explanatory variables in panel data regression

["F. Javier Sese" <javisese@unizar.es>]

Dear list members,

I am using Stata 10.0 to estimate the following panel data regression  
model (xtreg):

Y = b1*X1 + b2*X2 + b3*X3 + c*Z

I am modeling the dependent variable (Y) as a function of three main  
explanatory variables (X1-X3) and a vector of control variables (Z).

X1-X3 are proportions: they range between zero and one and add up to  
one for each observation (X1 + X2 + X3 = 1). Given the nature of  
X1-X3, there is a high negative correlation between them (an increase  
in one variable leads to a decrease in the other two), which gives  
rise to a potential collinearity problem that may be causing some  
unexpected results in the signs and statistical significance of the  
coefficients. In my dataset, X1 and X2 have a correlation coefficient  
of -0.81; X1 and X3 of -0.42; X2 and X3 of -0.19.

Given that the main focus of my research is on understanding the  
impact of these three variables on Y, I would really appreciate it if  
someone can provide me with some guidance on how to obtain reliable  
parameter estimates for the coefficients b1-b3.

Thank you in advance,
Javier



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