Eric Hanushek presents testimony against the claims of school districts that are suing the state:
Hanushek analyzed Missouri test scores and spending levels at the state's public school districts. That analysis did find a link between higher spending and higher student performance. But Hanushek said the link was extremely weak.
By his estimate, schools would have to triple, or even quadruple spending to raise average student test scores to levels that meet state standards.
The spending-performance relationship is so weak because most of the variation in Missouri Assessment Program (MAP) scores (about 85-90%, depending on the subject and grade level) is within district, not between districts. So if you compare any two students in Missouri, most of the difference in their test scores is caused by their families, teachers, and personal characteristics--what their districts spend doesn't matter very much.
And as Hanushek points out in his many publications, a weak correlation between spending and achievement at current spending levels won't necessarily translate into any correlation if you triple spending. We don't have enough experience with such high spending levels to know what would happen.