After an enjoyable blog post about New Zealand at Crooked Timbers, a commenter pointed out how unusual it is for a country's capital not to be the biggest city. (Wellington is New Zealand's third largest.)
I previously investigated another assumption, namely whether it is better for a capital to be located centrally in its district. Using capitals of U.S. states and those states' per capita income as a snapshot indicator of "better", this doesn't matter.
So does it matter if there's life outside the capital in your country? It's easy to make just-so arguments in both directions. Having a smaller capital that is (presumably) separate from the financial life of the country keeps legislators and businesspeople separate, preventing corruption (right?) as well as providing multiple paths to success. But at the same time, it would seem obvious that this creates inefficiencies in allocating human capital (how many petrodollars and attention-minutes have been wasted in airports and train stations between New York and Washington?) So what do the data say?
Only about 18% of world capitals are not also the largest city (I'll call these "smaller-capital" countries).
The New World-Old World distribution is not that different (higher in the New World, 24% are smaller-capital). In fact the smaller-capital countries really seem to be the Anglosphere - about half of them (more than random chance since the Commonwealth makes up about a quarter of the world's countries). The other half of the smaller-capital countries are ones that have had revolutions or otherwise gotten their act together enough to deliberately relocate the capital (e.g. Vietnam, Brazil).
And (drumroll), smaller-capital countries do have a median per capita income advantage of about US$800, or almost 10% more than large capital countries. But, we may lose resolution here because the data are broken into categories. That is to say, if we're looking for some effect of capital dominance, we should expect it to be weaker if the population of the capital only barely edges out another city, vs if the capital is obviously the only significant city in the country. Consequently, it might be more informative if we look at the relationship between % of country's population living in the capital, and the per capita income of that country. So I did, and there wasn't one.
So again I turn back to the my homeland, and use data for U.S. states, which are much more homogenous and don't suffer from having been colonized by different countries and have different mixtures of aboriginal vs colonist, recent wars, etc. The majority of U.S. states (33 out of 50) are smaller-capital states. (Why the capitals have not become the largest city is an interesting question for another post.) There didn't seem to be a clear weighting of one area of the country or the other - the big capital states are pretty much scattered around the country. And again, the smaller-capital states had an advantage in median per capita income, $26,929 vs $25,182, a 7% gain relative to large-capital. So again I looked for a relationship between % population in capital, and PCI. Again there was effectively none (very poorly fitting, very slight decrease with increasing % population in the capital). Out of curiosity I looked at effect of % population in the largest city; again, no dice (very poorly fitting, very slight increase with increasing population in the largest city).
So yes, there's a repeated categorical relationship (smaller-capital, lower PCI) that evaporates when looking at it more closely. It probably doesn't matter whether the capital of your state or country is also the largest city. Whether this means political life integrates itself effectively into the economy of a country regardless of human geography, or that government doesn't matter all that much, is difficult to say.
Data notes: I used Wiki tables, and CIA income information. I did not include overseas dependencies (sorry Greenland and Puerto Rico). For countries that divide their branches of government between cities, I added up the branches as one city; the only place this made a difference in whether they counted as smaller-capital was South Africa.