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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