Arguably none. It is very plausible that they would have anyway. Other countries also have developed from poverty into highly developed, technologically advanced without US military occupation, e.g. Singapore, Ireland, Hong Kong, France (after the Franco-Prussian war). Japan after all had started industrialising back in the 19th century, as did Germany, Belgium and Switzerland.
The question of why some countries get rich and others don't is hard to answer empirically. Every simple explanation proffered appears to have an exception (frequently Ireland) and complex explanations are inherently more doubtful (if you have a chain of arguments: e.g. A happened because of B and B happened because of C and C because of D, then if any single step is wrong then the overall argument is wrong.)
There is also no particular reason why the most important factors would be measurable. E.g. a relative lack of corruption is arguably very important, but how do you measure corruption objectively? And how do you measure that back in 1946? Let alone 1846?
Somewhat building on the corruption point, there's an issue of something like competent government. Or competentish. One that mostly avoids civil wars, or at least civil wars raging across the entire country and avoids invading Russia/attacking the USA, and one way or another can step back from the brink of policies that are working out really badly. Democracy seems to help with this but it's not sufficient. Arguably the beliefs of the general voting population matter too.
These sort of vague, cultural things are not, on the whole, ones that American occupiers would be good at changing. Which is what the empirics brings out: US intervention is mainly bad for democracy while the US is intervening, but dissipate once the intervention stops.
Sources
My comment above is rather based on broad reading and diffuse knowledge, rather than any particular article. But Bill Easterly was a heavy influence on my views, particularly the following papers, all available at http://www.williameasterly.org/publications
William Easterly, The Mystery of Growth: Shocks, Policies, and Surprises in Old and New Theories of Economic Growth, The Singapore Economic Review, (1995).
Berger, Daniel, Alejandro Corvalan, William Easterly, Shanker Satyanath, Do superpower interventions have long and short term consequences for democracy?, Journal of Comparative Economics, 41, no. 1 (2013): 22-34.
William Easterly, Institutions: Top Down or Bottom Up?, American Economic Review, 98, no. 2, (May 2008): 95-99
And also
Mosk, Carl. “Japan, Industrialization and Economic Growth”. EH.Net Encyclopedia, edited by Robert Whaples. January 18, 2004. URL http://eh.net/encyclopedia/japanese-industrialization-and-economic-growth/ (Note this has a bit more positive assessment of the US military occupation's impact on Japan than I present here.)
Pak Hung Mo, Corruption and Economic Growth, Journal of Comparative Economics 29, 66–79 (2001), https://scholar.google.com/scholar?cluster=8740768150868122304&hl=en&as_sdt=0,5