Gretl Manual: Gnu Regression, Econometrics and Time-series Library
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# Pooled estimation

There is a special purpose estimation command for use with panel data, the "Pooled OLS" option under the Model menu. This command is available only if the data set is recognized as a panel. To take advantage of it, you should specify a model without any dummy variables representing cross-sectional units. The routine presents estimates for straightforward pooled OLS, which treats cross-sectional and time-series variation at par. This model may or may not be appropriate. Under the Tests menu in the model window, you will find an item "panel diagnostics", which tests pooled OLS against the principal alternatives, the fixed effects and random effects models.

The fixed effects model adds a dummy variable for all but one of the cross-sectional units, allowing the intercept of the regression to vary across the units. An F-test for the joint significance of these dummies is presented: if the p-value for this test is small, that counts against the null hypothesis (that the simple pooled model is adequate) and in favor of the fixed effects model.

The random effects model, on the other hand, decomposes the residual variance into two parts, one part specific to the cross-sectional unit or "group" and the other specific to the particular observation. (This estimator can be computed only if the panel is "wide" enough, that is, if the number of cross-sectional units in the data set exceeds the number of parameters to be estimated.) The Breusch–Pagan LM statistic tests the null hypothesis (again, that the pooled OLS estimator is adequate) against the random effects alternative.

It is quite possible that the pooled OLS model is rejected against both of the alternatives, fixed effects and random effects. How, then, to assess the relative merits of the two alternative estimators? The Hausman test (also reported, provided the random effects model can be estimated) addresses this issue. Provided the unit- or group-specific error is uncorrelated with the independent variables, the random effects estimator is more efficient than the fixed effects estimator; otherwise the random effects estimator is inconsistent, in which case the fixed effects estimator is to be preferred. The null hypothesis for the Hausman test is that the group-specific error is not so correlated (and therefore the random effects model is preferable). Thus a low p-value for this tests counts against the random effects model and in favor of fixed effects.

For a rigorous discussion of this topic, see Greene (2000), chapter 14.

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