Countries do well when they reduce barriers to capital investment and trade. I would doubt that the amount spent on a state-run education system has anything positive to do with the economy - in fact public education is a drag on our economy. The US has succeeded since we are still the country with the least number of government interventions - though federal regulations are said to be so voluminous that they would fill my bookshelves.
Capital and entrepreneurial know-how flow to the most open society. That has been the history of the world for eons. No one questioned the quality of the Soviet education system - in fact John Dewey and others cheered it - yet their economy was a basket case.
Causation based on correlation is just as apt to flow the opposite direction as assumed. You see high education spending in the US and other wealthy countries simply because these economies have traditionally been successful. Education spending is the result of successful economies, not the other way around. An example: The education expenditures in Bexley, Ohio, a Columbus suburb, are extremely high simply because the residents have been successful. Bexley residents are not successful due to the amount Bexley City Schools spends on education, since most Bexley residents are not products of their school system.
 Of course, a priori, the Soviet education system had to be a mess since it was a government-run monopoly. Regardless, that didn't stop the socialists over at Columbia Univerity's prestigious Teachers College from trumpeting the success of both the Soviet education system and economy.