st: Re: Country and population weights in panel analysis

[Gordon Hughes <G.A.Hughes@ed.ac.uk>]

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.

Gordon Hughes
g.a.hughes@ed.ac.uk
 

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