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st: Re: Country and population weights in panel analysis


From   Gordon Hughes <G.A.Hughes@ed.ac.uk>
To   statalist@hsphsun2.harvard.edu
Subject   st: Re: Country and population weights in panel analysis
Date   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.

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