Choosing between OLS, RE and FE

[Huthayfa Nabeel]

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

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

    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.

[Phil Bromiley]

This is a relatively small sample so you don't want to try anything too complicated.

The first question should be is your theory about variation within panels over time or is it about differences across panels, or both. The Hausman analysis normally assumes that the true effect of variation within panel over time is the same as the effect of stable differences across panels. If one is comfortable assuming the within and between effects are identical, then it is quite reasonable to see any difference in the estimated parameters as reflecting inconsistency in the estimates related to the between variance.

Personally, I see many situations where the within and between effects should differ. In some cases, they will even depend on totally different variables, but in others even the same variable may have substantially different meaning over time that it does cross-sectionally.

Whether you are happy assuming within and between effects are the same in your data, or whether it even make sense in your data, depends heavily on the context and your theory and research question.

There are problems with using .05 cut off arbitrarily so when I get significance of .07, .09, and .10 I would not automatically read these as not rejecting the null hypothesis. They suggest there is some evidence against the null hypothesis. That you get significant differences between fixed and random effects likewise suggests at least fixed effects results in different parameters.

I'm sorry I don't have a clear answer for you.

[Huthayfa Nabeel]

Dear Phil,

Sorry for the late reply. Thank you very much for your valuable comment. It really provides me with new insights on how to build up my decision.

Kind regards.