FEM vs REM

Here are some general guidelines about which of the two models may be suitable in practical applications[1].

1 If T (the number of time observations) is large and N (the number of cross-section units) is small, there is likely to be little difference in the values of the parameters estimated by FEM and REM. The choice then depends on computational convenience, which may favor FEM.

2 In a short panel (N large and T small), the estimates obtained from the two models can differ substantially. Remember that in REM B1i B1 i _ _., where .i is the cross-sectional randomcomponent, whereas in FEMB1i is treated as fixed. In the latter case, statistical inference is conditional on the observed cross-sectional units in the sample. This is valid if we strongly believe that the cross-sectional units in the sample are not random drawings from a larger population. In that case, FEM is appropriate. If that is not the case, then REM is appropriate because in that case statistical inference is unconditional.

3 If N is large and T is small, and if the assumptions underlying REM hold, REM estimators are more efficient than FEM.

4 Unlike FEM, REM can estimate coefficients of time-invariant variables, such as gender and ethnicity. The FEM does control for such time-invariant variables, but it cannot estimate them directly, as is clear from the LSDV or WG estimator models. On the other hand, FEM controls for all time-invariant variables, whereas REM can estimate only those time-invariant variables that are explicitly introduced in the model.

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[1] Source:D.Gujarati-Econometrics by Examples. P-300-302