Belligerati

Unfortunately, I didn't have access to time series data on homogeneity, so I had to look at current per-capita income versus homogeneity coefficients (measured with herfendal index). I didn't find any association.

A new paper at the NBER has found what I could not.They tackled the problem in a different way. They measure the extent to which a state is artificial. A state is artificial if political boundires don't coincide with the actual distribution of ethnic borders. They use two measures of this:

One is relatively simple and captures whether or not an ethnic group is "cut" by a political border line...

...a second measure, based upon the assumption that if a land
border is close to a straight line it is more likely to be drawn arti…ficially i.e. by former colonizers; if it is relatively squiggly it is more likely to represent either geographic features (rivers, mountains etc.) and/or represent divisions carved out in time to separate different people. This second measure probably come closer to capturing instances in which lines drawn at former colonizers’tables
have stuck to the ground.

They talk about looking at island nations as a control, which is interesting. This allows them to calculate a baseline of natural with which to measure the artificiality of drawn borders. They could have also used water borders to further calibrate what is a natural level of disorder in a boundary, and what was likely drawn by a dead white guy with a ruler. They don't just try to use economic variables.

We consider three groups of variables as left hand side variables. (See Table 3 for variable definitions and sources). First, the variables that measures economic or economic policy success: (log of) per capita income in 2002; an index of economic freedom in 2005 that measures adherence to a free market economic system; and an alternative index of economic freedom averaged over 1970-2002.12 Second, we look at politico-institutional variables: voice and accountability (which measure checks on power), political stability and violence, government effectiveness, regulatory quality, rule of law, and corruption. Third, we use quality of life and public goods delivery-related measures: infant mortality in 2001, literacy rate averaged over the period 1995 2002; measles immunization rate in 2002; immunization rate against DPT in 2002, percent of population with access to clean water, in 2000.

They find that for just about every variable of interest they have a significant impact:

Of the 28 coefficients in the …first two columns, 20 are
statistically signi…fficant (5 per cent or better) and there are borderline (p value 0.10 or better). Our two measures are not highly correlated with each other and in fact as discussed above, they capture different aspects of the nature of borders. For this reason there is no reason why they could not be used in the same regressions. In the third column, we use them both. IN all regressions at least one is signi…cant at the 5 per cent level or better and in almost all regressions they are either both statistically signiffi…cant at the …5% level or one is and the other is borderline.