In 2012, Bruce Baker released a report that surveyed all the literature on the effects of school funding.  It was the first significant survey of the literature since Greenwald, Hedges and Laine's study from the mid-1990s.  Baker has now released a new update to his prior work.  The report finds:

• On average, aggregate measures of per-pupil spending are positively associated with improved or higher student outcomes. The size of this effect is larger in some studies than in others, and, in some cases, additional funding appears to matter more for some students than for others. Clearly, there are other factors that may moderate the influence of funding on student outcomes, such as how that money is spent. In other words, money must be spent wisely to yield benefits. But, on balance, in direct tests of the relationship between financial resources and student outcomes, money matters.
• Schooling resources that cost money, including smaller class sizes, additional supports, early childhood programs and more competitive teacher compensation (permitting schools and districts to recruit and retain a higher-quality teacher workforce), are positively associated with student outcomes. Again, in some cases, those effects are larger than in others, and there is also variation by student population and other contextual variables. On the whole, however, the things that cost money benefit students, and there is scarce evidence that there are more cost-effective alternatives.
• Sustained improvements to the level and distribution of funding across local public school districts can lead to improvements in the level and distribution of student outcomes. While money alone may not be the answer, more equitable and adequate allocation of financial inputs to schooling provide a necessary underlying condition for improving the equity and adequacy of outcomes. The available evidence suggests that appropriate combinations of more adequate funding with more accountability for its use may be most promising.

He boils the research on those points down to this:

While there may in fact be better and more efficient ways to leverage the education dollar toward improved student outcomes, we do know the following:

• Many of the ways in which schools currently spend money do improve student outcomes.
• When schools have more money, they have greater opportunity to spend productively. When they don’t, they can’t.
• Arguments that across-the-board budget cuts will not hurt outcomes are completely unfounded.

In short, money matters, resources that cost money matter, and a more equitable distribution of school funding can improve outcomes. Policymakers would be well-advised to rely on high-quality research to guide the critical choices they make regarding school finance.

Get the full report here.