Fixed Effects Model - Testing FE Vs. RE

Testing FE Vs. RE

We can test whether a fixed or random effects model is appropriate using a Hausman test.

:
:

If is true, both and are consistent, but only is efficient. If is true, is consistent and is not.

\widehat{HT}=T\widehat{Q}^{\prime}[Var(\widehat{\beta}_{FE})-Var(\widehat {\beta}_{RE})]\widehat{Q}\sim\chi_{K}^{2} where

The Hausman test is a specification test so a large test statistic might be indication that there might be Errors in Variables (EIV) or our model is misspecified. If the FE assumption is true, we should find that \widehat {\beta}_{LD}\approx\widehat{\beta}_{FD}\approx\widehat{\beta}_{FE}.

A simple heuristic is that if \left\vert \widehat{\beta}_{LD}\right\vert >\left\vert \widehat{\beta}_{FE}\right\vert >\left\vert \widehat{\beta} _{FD}\right\vert there could be EIV.

Read more about this topic:  Fixed Effects Model

Famous quotes containing the word testing:

    “Bourbon’s the only drink. You can take all that champagne stuff and pour it down the English Channel. Well, why wait 80 years before you can drink the stuff? Great vineyards, huge barrels aging forever, poor little old monks running around testing it, just so some woman in Tulsa, Oklahoma can say it tickles her nose.”
    —John Michael Hayes (b.1919)