Michael Rizzo does New York. He finds no difference in school spending between schools "above the line" (high pass rates relative to their poverty index) and those below the line. However, the regression line appears to do a very poor job of explaining the pass rates, so that being above the line or below the line is almost entirely a matter of being above average or below average in terms of pass rates. I suggested in a comment on his blog that he should group the data by deciles in order to try to extract a better signal.
Reader Jonathan Klick had his undergraduate thesis published by The American Economist. In it, he found no signficant relationship between school spending and test scores in Pennsylvania, controlling for the percent of the student body coming from low-income households.
This type of research is not publishable (The American Economist serves to encourage undergraduate economics research--it's not going to affect anyone's tenure decision). And yet it's interesting. I think society would be better off if more economists were doing simple, interesting work than doing the fancier stuff that gets published.
UPDATE: In an email, Rizzo writes,
n case you were interested, by putting the math performance and the poverty data into deciles and rerunning a simple regression, you get the following result:
Schools that perform better than expected spend $13,843 per student.
Schools that perform worse than expected spend $14,195 per student.