[Gretl-users] panel model residuals

A "bug report" has been filed on sourceforge relating to what gretl offers as residuals via its $uhat accessor for the fixed- and random-effects panel-data models. You can find this at http://sourceforge.net/p/gretl/bugs/199/ In my opinion this is not really a bug report, but it can be interpreted as a request for clarification on how gretl's $uhat is calculated for panel-data models (and implicitly, how one might calculate alternative measures using gretl). In that regard it may be of interest to others, and merits a reply. Let's take the fixed-effects model first. It may be represented as y_{it} = a_i + X_{it}\beta + e_{it} Gretl takes the "fitted value" ($yhat) to be a_i + X_{it}\beta, and the residual ($uhat) to be y_{it} minus this fitted value. This makes sense, IMO, because the fixed effects (the a_i terms) are taken as parameters to be estimated. However, it can be argued that the fixed effects are not really "explanatory" and if one defines the residual as the observed y value minus its "explained" component one might prefer to see just y_{it} - X_{it}\beta. In gretl you can get this after fixed-effects estimation as follows: series ue_fe = $uhat + $ahat - $coeff[1] where $ahat gives the unit-specific intercept (as it would be calculated if one included all N unit dummies and omitted a common y-intercept), and $coeff[1] gives the "global" y-intercept. For anyone used to Stata, gretl's fixed-effects $uhat corresponds to what you get from Stata's "predict, e" after xtreg, while the second variant corresponds to Stata's "predict, ue". Now let's consider the random-effects model. This can be represented as y_{it} = \mu + X_{it}\beta + u_i + e_{it} In this case gretl considers the "error term" to be u_i + e_{it} (since u_i is conceived as a random drawing) and the $uhat series is the estimate of this, namely (taking "hats" as implicit, please) y_{it} - \mu - X_{it}\beta which corresponds to Stata's "predict, ue". What if you want an estimate of just e_{it} (or just u_i) in this case? That's more difficult, since random-effects estimation in itself does not require estimation of the u_i in their own right. All that's needed is an estimate of the variance of u, and even that is derived indirectly (and may sometimes be negative, requiring adjustment to zero). Stata offers "predict, e" and "predict, u" but it's not clear how they are calculating these. I'd be interested to know, but I'm pretty sure the calculations are going to be debatable. Allin Cottrell