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.

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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

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