The number one correlation of underachievement in schools is if you are in a non-intact family. (Remember this is a bell-shaped curve with overlap to intact families) Anyway, you'll never find a study risk adjusting to give the same percentage of intact families for good schools and bad, country vs country, etc.
The U.S. has 15-30% fewer intact families than most developed countries. And within the U.S. different school districts have different rates of intact families. If you'd risk adjust, the U.S. is probably at the top educationally and the educational product available is probably very much the same between good and bad schools. Unfortunately, this is a cultural problem and not easily solved with money ... when money is thrown at the problem it just bounces off the kids. You'll never find a study ... the solution doesn't involve money.
Even Sweden with a low rate of marriage still have rates of intact families in the 70-80% range vs the low 50% range for the U.S.