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There's a whole mess of fight on methodology here.
As a methodology it's just a dimension reduction technique. On whether you can then run with the factors and make inferences from them, this was thoroughly debunked by Stephen Jay Gould (a self-confessed fan of factor analysis as a data reduction technique) in connection with single-factor models of human intelligence (IQ) in The Mismeasure of Man. Most economists teach a theoretical framework that has been shown to be fundamentally useless. -- James K. Galbraith
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