I have a panel data on nonperforming loans from 1990q1 till 2014q4 with 30 banks, 100 units of observation per bank. I would like to estimate the impact of real gdp growth, unemployment, exchange rate, house price index, and equity market index on nonperforming loans (dependent variable in my regression) with fixed effect, random effect and OLS estimation. By using the commands of regress, xtreg ..,fe, xtreg... re, i get almost identical coefficients for fixed effect,random effect and OLS estimation for each independent variable, and even the t statistics are the same across the models with the exception of constant's t statistics (t stat for constant is -85 in random effect, -112 for fixed effect), and the corr(u_i, Xb) = 0.0000 in the fixed effect model, which I did not expect. When I apply the Hausman test, I get (V_b-V_B is not positive definite). I have also problems with R squares. In fixed effect, I do not have any numerical value for R square between groups, and R squares for within and between are 0 in random effect model. Unfortunately I cannot establish another model other than these three. I would really appreciate if you could give some hints where the problem might be.
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