Here are some further thoughts on panel data estimation. In the first part I'm "thinking out loud", trying to test my understanding of what's wanted. But the discussion leads up to a specific question on what gretl should do, and I'd appreciate hearing people's thoughts on that.
A common first step with panel data is pooled OLS. This is much the simplest model. Its simplicity is purchased with the assumption of homogeneity, across both time periods and cross-sectional units. This assumption is testable and one generally expects to see it tested. A common step in relaxing the homogeneity assumption is the "fixed effects" model, which allows the intercept (hence, the average value of the dependent variable) to differ across... Ah, to differ across what? In the context of gretl's "hausman" command, I've been assuming that the answer is always, "to differ across cross-sectional units", but I'm not sure that's right. With fixed effects, one can allow the intercept to differ by cross-sectional unit, by time period, or by both. What is the econometrician likely to want? Well, panel datasets can be "long and thin" or "short and fat". For a "long and thin" case consider Panel A, which consists of observations on 4 firms over 25 years. For a "short and fat" case, consider Panel B, which comprises observations on 1000 individuals in each of 4 years. I'm now thinking: the most "natural" version of the fixed effect model, considered as a first step in relaxing the homogeneity assumption of pooled OLS, allows the intercept to differ across the smaller dimension of the panel. Thus with Panel A we'd allow the intercept to differ by firm, but with Panel B we'd allow it to differ by year. As Jack just pointed out, if you're doing fixed effects with intercepts differing by cross-sectional units, it's necessary to screen out variables that are not time-varying. Similarly, if one were doing fixed effects with period-specific intercepts, it would be necessary to screen out variables that do not vary across cross-sectional units. Specific question: for gretl's testing of pooled OLS models, should there be a command option to determine which dimension is used for the fixed effects, e.g. --group-effects versus --time-effects (versus --both-effects ?) Allin Cottrell -- Allin Cottrell Department of Economics Wake Forest University, NC
