Previous studies of congressional spending have typically found a large positive effect of challenger spending but little evidence for effects of incumbent spending. Those studies, however, do not adequately control for inherent differences in vote-getting ability across candidates. "High-quality" challengers are likely to receive a high fraction of the vote and have high campaign expenditures, even if campaign spending has no impact on election outcomes. To avoid that bias, this paper examines elections in which the same two candidates face one another on more than one occasion; differencing eliminates the influence of any fixed candidate or district attributes. Estimates of the effects of challenger spending are an order of magnitude below those of previous studies. Campaign spending has an extremely small impact on election outcomes, regardless of who does the spending. Campaign spending limits appear socially desirable, but public financing of campaigns does not.