st: Re: Country and population weights in panel analysis
Sat, 16 Feb 2013 13:42:03 +0000
As I assume that you realise, there is no simple answer to your question.
In purely technical terms, Stata's panel regression procedures all
require that the weighting variable must be constant over all
observations for a particular panel unit, so you have to use, for
example, average population as the weight. Putting this aside there
are two questions that you need to ask.
First, is it really the case that the equation errors vary with
population? This might be true for, say, an unemployment variable
derived from a sample survey but many variables are based on either
complete enumerations or they are derived in ways that their
contribution to the equation error will be very small relative to
other sources of error in the relationship that is being estimated.
Second, what are you actually trying to model? Is it a relationship
in which each country or region, of any size, is a discrete unit? In
this case you want to obtain estimates of conditional means that
apply to countries or regions as distinct units - i.e. the average US
state. Alternatively, you might be interested in conditional means
for the whole US population derived from information measured on a
state by state basis. In such circumstances you would want to give
more weight to observations from large states than to smaller
ones. This is not because the standard errors of the data differ
across states, but because you may believe that the parameters of
interest may differ between small and large states. Of course, you
could try to model this explicitly but this is often difficult
whereas the use of population weights is a simple way of getting
conditional means for the US population rather than for the average state.
As you note, textbooks on panel data econometrics rarely devote much
time to such issues because their archetypal dataset is a
longitudinal survey of individuals. However, there is a literature
on panel data macroeconomics that you can investigate. You will find
references by searching for mean groups methods - for example the
user-written procedure -xtmg- or various papers by Markus Eberhardt,
Hashem Pesaran and Ron Smith.