Hello. I am trying to test which model to use between fixed and random effect by computing Hausman command. And I have a few questions

1. The variables I used are GDP per capita, number of population age 65 and older, fertility rate, mortality rate, education, life expectancy, population growth which I believe that all of them are time variant which FE should apply right?


I run Hausman command and the result said:
"Note: the rank of the differenced variance matrix (6) does not equal the number of coefficients being tested
(7); be sure this is what you expect, or there may be problems computing the test. Examine the output
of your estimators for anything unexpected and possibly consider scaling your variables so that the
coefficients are on a similar scale."

and chi2(6) = (b-B)'[(V_b-V_B)^(-1)](b-B)
= 3.26
Prob>chi2 = 0.7750

2. so in this case Prob>chi2 = 0.7750 is higher than 0.05 then I should choose FE right??
3. And what should I do with the note?

4. Also chi2(6)= 3.26 is higher than critical value of chi2 wtih 6 degree of freedom, then there is no difference between using OLS and instrumental variable estimates right??