Do campaign ads matter? Trump offers a rare chance to find out

I found that Mrs. Clinton’s vote margin decreased, on average, by a third of a point in places where Mr. Trump out-advertised her. But her margin increased, on average, by 2.6 points in places where she out-advertised him. In the forgotten states where neither candidate is advertising very much — those places with fewer than 100 total ads — Mrs. Clinton’s margin is up four points since June.

Maybe you’re thinking the candidates are just good at guessing where they are most likely to pick up votes, and they put their ads in those places. That’s a reasonable concern. To try to get a sense of whether the effect of the ads is actually the effect of selecting the places to advertise (based on where the race is most likely heading), I looked at the same relationship using President Obama’s share of the vote from 2012 in each state and found the opposite relationship. In places where Mr. Trump dominates the airwaves, Mr. Obama won 60 percent of the vote in 2012. In places where Mrs. Clinton is winning the ad war, the president won only 50 percent of the vote.

The ads in 2016 do not predict the 2012 election result, suggesting that the states where Mrs. Clinton both advertised and picked up big gains over the summer were not on their way to some preordained outcome, like the one in the last presidential contest. She is out-advertising Mr. Trump in places where Mr. Obama’s race was quite close, and she is gaining vote share.