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