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I don't have access to individual data, so I have to rely on aggregate data for a large number of cities in a country.

If my outcome variable is the log of city average earnings and the predictors are dummy variables for n-1 national regions, does it make sense to interpret coefficients in this way: "Average earnings are on average 10.3% higher for Region_B compared to Region_A" ? In other words, does it makes sense to speak of "average advantage in average earnings" , or is that like saying "average of an average" ?

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    $\begingroup$ I can't see any reason this would not make sense. The average earnings (or whatever) of a region is a fact about the city, just like the earnings of a person is a fact about the person. You can compare one to another. $\endgroup$ – Peter Flom Oct 17 '12 at 23:07
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I can't see any reason this would not make sense. The average earnings (or whatever) of a region is a fact about the city, just like the earnings of a person is a fact about the person.

You can compare one to another.

But you are right to allude to a problem with average of a set of averages. You could not add up the averages for each region in the USA, divide by the number of regions and get the overall average, because the denominators would be different

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Yes, this makes perfect sense in your situation. I recognize that it may sound silly, but there's nothing wrong with it.

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