Over the weekend, Democratic Senate candidate Alison Lundergan Grimes picked up endorsements from two major Kentucky newspapers. In Iowa, Democrat Bruce Braley gained the nod from the Des Moines Register. Earlier in the month, Colorado Republican Cory Gardner won the confidence of the Colorado Springs Gazette.

The races in all of these states are tight, but will newspaper endorsements — what might seem to be relics of a seemingly bygone media age — have any bearing on what happens next Tuesday?

On the one hand, there are good reasons to be dubious of claims that endorsements matter much. Even in a campaign season about nothing, voters in competitive Senate states have for months been bombarded with debates and ads about abortion, the Islamic State, hog castration, and the like. Most have made up their minds. The Lexington Herald-Leader’s endorsement of Grimes, for instance, will do absolutely nothing to undermine the loyalties of Senate Minority Leader Mitch McConnell’s staunchest supporters.

And as The Washington Post’s Chris Cillizza pointed out last week in the wake of Iowa Republican Joni Ernst canceling a meeting with the Register’s editorial board, the fragmented media environment may diminish any influence that newspapers once had. The Huffington Post also noted that claims about endorsement effects are probably exaggerated.

But political science research suggests caution in dismissing endorsements’ relevance. A number of studies report small effects. And especially in races where the outcomes are razor close — as could be the case in several Senate contests this year — endorsements might in some circumstances prove consequential.

In a study of 60 Senate races in 1988, 1990, and 1992, political scientists Kim Fridkin Kahn and Patrick Kenney collected data on endorsements by each state’s largest-circulating newspaper. When they matched that information with survey data, they found that an endorsement in a heavily covered race produced a small bump in the polls for the endorsed candidate.

Even accounting for voters’ party loyalties, ideology, and issue positions, the effect was about 9 percent on a scale that compared the two candidates’ favorability ratings. For voters without strongly held views — a rare, but not extinct, species — such an effect could be enough to move them out of one candidate’s column and into another.

A study of presidential endorsements in the 2000 and 2004 elections also found measurable effects. Economists Chun-Fang Chiang and Brian Knight reported that endorsements mattered most when they were surprising. For example, a left-leaning editorial page’s endorsement of Republican George W. Bush was more influential than one by a conservative paper. Like Kahn and Kenney, Chiang and Knight found the strongest effects among voters with relatively moderate — and thus perhaps more malleable — political attitudes.

This isn’t a distinctly American phenomenon. Political scientists Jonathan Ladd and Gabriel Lenz found that the switch by several British newspapers to the Labour Party in 1997 had a significant effect on voter attitudes. Their analysis doesn’t try to distinguish the influence of an endorsement from other news content, but the findings clearly demonstrate that the media can lead public opinion.

Of course, these studies were all conducted at least 10 years ago. And maybe the subsequent explosion of media options means that there are so few readers of these old dinosaurs now that newspapers simply don’t matter any more. After all, the Pew Center just last week released a report showing that “consistent” conservatives and liberals have starkly different news diets, choices that reflect their political views.

But as Brendan Nyhan notes, there is other evidence suggesting people’s consumption patterns aren’t quite so “cocooned.” For instance, when you ask people about their TV viewing habits, large percentages of Americans say they watch Fox and MSNBC. But as Markus Prior shows, Nielsen data reveal the regular audiences for cable news to be very small indeed (see Prior’s Figure 1).

At the same time, while the audiences for local newspapers, such as the Des Moines Register, have fallen in recent years, they are still immensely larger that those for political blogs or cable news. Survey data show that newspapers, in both their print and online forms, remain a critical source of local news for most citizens.

None of this is to say that the odds of a newspaper endorsement flipping a Senate race are high. But the research does suggest that even in a cacophonous media environment, such signals could break through the noise, whether from squealing hogs or runaway chickens.