But what exactly accounts for prosperity if not culture?
Excellent question. Unless, as James Fallows notes, we accept an absurdly broad view of culture, institutions are an independent variable. The residents of what would become East Germany woke up in 1945 with a culture virtually indistinguishable from their West German neighbors in work ethic, appreciation for education, commitment to honor and oath, family orientation, devotion to a purpose greater than themselves, and patriotism. Unfortunately, they had an an odious and stupid Marxist puppet government imposed on them by the Soviet Union, and as a result they were much less prosperous than their western cousins when Germany was reunited.
As another example, consider Chinese in Hong Kong, Singapore and Mainland China: similar culture, but very different institutions and outcomes.
Then, of course, there's the factor that Romney calls "the hand of providence" and others call random chance. It may happen that your nation will unexpectedly find itself atop valuable natural resources for reasons unrelated to your cultural virtue, or perhaps other nations will make your ethnic or religious majority and their ethnic or religious minority feel so unwelcome that you get a windfall in well educated immigrants.
Alternatively, your nation may end up with a greedy, powerful and unprincipled neighbor or neighbors that steals your assets and leaves you both poorer and exhausted by the struggle.
Like what happened to Mexico.