Centrality of State Capitals Doesn't Matter

The center of population of the United States over time, migrating progressively west from Washington D.C. Does this matter?

Political entities try to locate their capital cities centrally, assuming that this facilitates administration of the entire territory. Consequently, we would expect to see that development indicators would correlate with centrality of capitals. I looked at data from American states, which are more standardized culturally and otherwise than the full set of world capitals would be. Using U.S. state data, the central capital assumption is false.

I compared per capita income, well-being, and Gini data for each U.S. state against the distance between from the geographic center of each state to the capital of each state, both in absolute terms and adjusted for the size of the state (against the square root of the total area including water).

As seen below, the R-squareds for linear correlations are very weak. If not, then what correlations there are, are almost invariably the opposite of what the central capital assumption would predict. (Correlations are shown by + or - in the tables.) That is, the further the capital is from the center of the state, the higher the well-being and per capita income, and the lower the income inequality. I'm not going to take up space with the noisy scatter plots so here's a table of the correlation strengths:

Measure	R squared, Absolute	Adjusted
Well-being	+, 0.0751	+, 0.0651
Per cap income	+, 0.0099	+, 0.0773
Gini	-, 0.066	-, 0.0266

Because geographic center in this case is really a proxy for center of population - does it really matter if the capital is equally near an empty quarter as to an urban area? - I also compared these metrics to capital-to-population center distance, with similar lack of correlation.

Measure	R squared, Absolute	Adjusted
Well-being	+, 0.0311	+, 0.0004
Per cap income	+, 0.0131	+, 0.0738
Gini	-, 0.0126	+, 0.0086

(Data can be provided upon request.)
See here for a map of population centers.

Of course there are outliers on the scatter-plots in terms of distance from capital to population or geographic center (especially Florida and Alaska) but removing them never resulted in significant changes and often actually lowered the already near-zero R-squared. Sometimes taking out the outliers reversed the correlation, but again the R-squared didn’t change much (biggest R-squared improvement with outliers where the correlation reversed was 0.0385 for Gini relating to capital distance from population center as opposed to 0.0126 with outliers, and the correlation went from negative to positive; still no signal.)


What are the implications or explanations here?

- The obvious one: that access to the capital doesn't matter for human development.

- That there are confounding factors; especially since the size of states varies non-randomly with their location and date of entry into the Union, which in turn non-randomly varies with their population density and types of economies.

- That in fact there has been sufficient wealth redistribution by the central national government to erase differences introduced by differing access to the capital (i.e. that having non-central capitals might have indeed hurt some states, but they get support from the Federal government that conceals this.)

- That geographic centrality is only a proxy for proximity to population that's being served, which is rarely distributed exactly evenly throughout a territory; perhaps doing this same analysis and taking into account center of population would give different and/or stronger correlations.


At the national level, I've often wondered what if any harm has been done in leaving the American capital in the original center of the U.S. (along the central East Coast) rather than moving it to Kansas City. Barring scale effects, based on this data, it's more likely that the answer is none at all.