This is worth keeping in mind when you hear the intuitively wrong-sounding empirical results on the lack of campaign effects. What the political science is telling you isn’t that presidential election campaigns couldn’t make a difference to election outcomes, it’s telling you that they don’t seem to make a difference in practice. But if one candidate just refused to fundraise, or did fundraise but did something wildly eccentric with the money, then for all we know that might make a big difference. You could imagine a candidate deliberately trying to tank the race, or just acting plain-out weird. What if John McCain delivered lengthy speeches denouncing his own policy agenda? But in practice we always see two well-funded, well-known candidates run pretty conventional campaigns and within that context the ups-and-downs of the campaign trail don’t seem to make a difference.In practice we see two well-funded, well-known candidates run pretty conventional campaigns in presidential general elections. Therefore, finding campaign effects in those races is going to be pretty hard; my understanding of the latest research (and I'm not a specialist) is that there are real effects, but we're talking around the margins, here.
Since yesterday was primary election day, I'll point out that this means that campaigns should really matter quite a bit in multicandidate primary elections -- they violate perhaps four of Gelman's five conditions for predictability. And that's in fact correct...depending on what you mean by "campaigns." In fact, in primary elections, it's not at all unusual to find one candidate who raises and spends tons of money, while another acts plain-out weird. In fact, that happens in lots of general elections for U.S. House, or state legislature, too.
Now, with general elections for president, we can plug in "fundamentals" including the economy, party identification, and the president's approval rating and, presto! We get pretty good predictions. Primaries don't work like that, especially open primaries (that is, either for open seats or to select a challenger to an incumbent from the other party). Systems that predict winners in presidential nomination fights tend to rest on things that, one might argue, are themselves either part of the campaign (such as endorsements) or an effect of the early campaign (such as standings in the polls). Of course, in nominations party isn't a variable (barring oddities such as open primaries and candidates who do well with nominally independent voters). And where would you plug in the economy? No, the kinds of fundamentals we think of as determining the outcomes of elections generally don't work or exist for nominating primaries. Campaigns must matter.*
However, as I said, it depends on what you think of as "campaigns." I'm confident that the ability of a candidate to earn support from party leaders -- by which I mean not only people from formal party organizations, but also from informal party networks -- is an important part of winning primary elections. See Seth Masket's great book, No Middle Ground, which talks about how local organizations outside of the formal party control nominations in California. The idea is that once party elites settle on a candidate, most primary voters -- who after all, tend to be both relatively well-informed and relatively partisan, and therefore generally willing to know about and respect the opinions of party leaders -- will ratify that choice. So a candidate who locks up party leaders has run a good campaign and will usually win, regardless of the quality of her stump speeches and TV ads.
Sometimes, however, party elites are split, say between the current and former president against the labor unions (as in the Arkansas Senate race) or the local formal party against insurgent Tea Partiers and outside elites (as in the South Carolina contest for governor, if I'm reading the coverage correctly). What will voters do in those cases? Hard to tell! Perhaps the election will demonstrate whether voters are loyal to one particular party faction. Perhaps, with no clear signals, people will pay a lot of attention to gaffes, ads, and debates -- although again, be careful. The number of ads that voters see is going to be an effect of how much money a candidate has to spend, which in turn may be an indication of how successful he is in tapping into party money. The coverage a gaffe receives may be in indication of the attitude of partisan media (blogs, Fox News or the partisan shows on MSNBC) towards the candidate. So even there, a "gaffe" may well be constructed by the success or failure of a candidate to win the support of party leaders. Or, we know that in some cases a good field operation can make a difference in voter turnout, but again one cannot (with the possible exception of self-funders) will an organization into existence; it takes either money or enthusiasm or both, and both of these resources are more readily available to candidates who have support from formal or informal party leaders.
In other words, yes, campaigns matter in primary elections -- but the things within the campaigns that matter are, even in these elections, less likely to be the quality of a particular ad, or a successful bit of opposition research, or a gaffe by a candidate, than the work a candidate does to win support from party leaders. But, yes, all those other things, the stuff that we political junkies thrive on...even with all of this context in mind, they're more apt to matter more in primary elections than in general elections. After all, voters are far more free to shift their vote. Multicandidate races can yield goofy results. And plenty of primary election voters are still going to be woefully ill-informed in many cases, especially in low-information contests (such as, for example, the Democratic primary for Senate in South Carolina yesterday, which presumably had very little local coverage because everyone knows that the Democrat will have no chance in the fall, and because the Republican primary for governor did such a good job of sucking up all available political space). Bottom line: primaries tend to be complex political events, difficult to predict and difficult to correctly analyze even after the fact, and therefore beware any conclusions that are strictly limited to the most visible actions from the campaign trail.
*I have to admit to being pretty out of date on the literature on Congressional primaries outside of the party network literature (see above)...I did a paper on House primaries long ago, and there wasn't much out there at the time, and it's just about completely ignored in the edition of Gary Jacobson's Politics of Congressional Elections I have close at hand, so perhaps there's still not much there.