Dear Statalisters,


I have an unbalanced panel data (N=19 and T=9), I want to choose between running pooled OLS, random effect, and fixed effect. I have run xttest0 command for four different specifications of the main equation to choose between OLS and RE. Following are the Stata output

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Breusch and Pagan Lagrangian multiplier test for random effects

        roae[id,t] = Xb + u[id] + e[id,t]

        Estimated results:
                         |       Var     sd = sqrt(Var)
                ---------+-----------------------------
                    roae |   123.0202       11.09145
                       e |   56.48426       7.515601
                       u |    17.0864        4.13357

        Test:   Var(u) = 0
                             chibar2(01) =     3.34
                          Prob > chibar2 =   0.0338
and for the other three specifications, the Prob > chibar2 are 0.07, 0.09 and 0.10.

In addition, I have also run hausman test to choose between FE and RE. Following are the Stata output
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    Test:  Ho:  difference in coefficients not systematic

                 chi2(13) = (b-B)'[(V_b-V_B)^(-1)](b-B)
                          =       40.88
                Prob>chi2 =      0.0001
and for the other three specifications, the Prob > chibar2 are 0.00, 0.00, and 0.00.

However, some studies in the field did not rely on Hausman test based on the arguments that: (1) the explanatory variables -in my research- are relatively stable over time. As Wooldridge (2013) argued, if the key explanatory variables are constant over time, we cannot use FEs to estimate their effect on independent variables. Thus, it is inappropriate to estimate such explanatory variables with fixed-effect regression, as they would be absorbed into time-demeaning or within transformation processes of the variables in the FEs model. (2) for small T and large N, FE estimation is inconsistent; whereas, RE can estimate such unbalanced panel data (Wooldridge, 2013, p. 475).

Thus, they recommend the use of random effects instead of fixed effects estimation.

Now I am confused about which estimation method to use. since that the null hypothesis of Breusch and Pagan Lagrangian LM test has been accepted for three of the four specifications it looks like I should go four OLS. However, since that the p-value is not that much high for all specifications can I go for RE or FE? if I can, which one looks more accurate in my case?

Thanks in advance.