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blogospheroid comments on Rational Regions? - Less Wrong Discussion
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Not sure if there is a way to do this intra country, but if you are looking for an inter-country comparison, you might check for this criteria.
See how close is their stock market to a random walk, statistically speaking. If you have significant variation from that, then I guess there is a lot of hidden irrationality in that society.
An upwardly biased random walk? Don't we expect stock markets to go up as wealth is created?
That's the crux, isn't it? How do you know if an upward trend line is irrationality or wealth creation?
If you want to measure how close areas are to a competitive market, I would suggest looking at profit margins in non-monopolistic industries. Of course, you'd have to control for regulatory differences and relative concentrations of different industries. But, all else being equal, the place where profits are higher is farther from being a competitive market.