Political scientists have tried to measure the effectiveness of campaign spending using a variety of methodologies. There is no consensus in the field. One large group of studies finds that spending by incumbents makes no difference whatsoever, but spending by challengers helps them get established. Another group finds that neither incumbent nor challenger spending makes a difference. Another group finds that both kinds of spending have some impact.
I too was pleased by this piece because I agree with Brooks that the role of money in elections is exaggerated. However, I don’t think his description of the political science literature on this issue is correct.
In part of the piece, Brooks looks at how much is spent by each party in any election as a whole, and then at how the election turned out. That’s too high a level of aggregation and it obscures some of the importance of money. In individual congressional races, expenditures by candidates are certainly associated with outcomes. I think a fair description of the actual consensus is this from Gary Jacobson’s The Politics of Congressional Elections (buy it here!):
Challengers (and especially candidates for open seats who face well-financed opponents) rarely win without spending a great deal of money. Even rarer is a losing incumbent who might plausibly blame defeat on a shortage of funds. Moreover, there are solid reasons challengers should get a larger share on their spending than do incumbents. However, there are also good reasons for believing that, under some circumstances, the incumbent’s spending should affect the outcome as well. (p. 49)
In other words, the major debate is not over whether money matters, it’s over the relative impact of incumbent and challenger spending.
There are other questions where political science doesn’t have a solid answer, as far as I know. One is whether independent expenditures matter over and above the (much larger) spending by candidates and parties, so Brooks’s skepticism regarding these expenditures isn’t necessarily contradicted by any evidence.
Nevertheless, the consensus, as I see it, is that money does in fact matter.