Since 1960, a lot fewer Americans have been dying of tobacco and car accidents, and a lot more have been dying of diseases related to obesity. That is the conclusion of a new study by Harvard economist David Cutler and National Bureau of Economic Research scholar Susan Stewart.

The U.S. obesity problem is staggering. In 1960, 14 percent of the population was obese; in 2010 it was 36 percent. Even though overall life expectancy rose by about seven years in that time, it would have been eight if not for the rise in obesity.

That’s old news by now. But the comparison with smoking is very interesting. It tells us a lot about why these two public health trends have gone in opposite directions, and how the obesity problem might be defeated.

The fight against smoking might be the biggest public- health success story of the past half-century. The percentage of Americans who smoke fell from about 40 percent in the mid-20th century to about 20 percent today.

How did we achieve that victory? One thing that people point to was the increase in taxes on cigarettes. Cigarette taxes rose during the 1980s and 1990s, and then soared after the turn of the millennium. Taxes are about the most basic, Econ 101-style policy intervention there is — when something is more expensive, we expect people to buy less of it.

The problem is, taxes don’t seem to account for most of the decline in smoking. Smoking began a steady decline in the mid-1970s, and there was no obvious acceleration in that decline after the big tax hikes of the 2000s.

Careful economic studies also cast doubt on the importance of taxes. In 2012, economists Kevin Callison and Robert Kaestner looked at the recent big tax hikes and concluded that they had very little effect on cigarette consumption. And in 2006, economists Jerome Adda and Francesca Cornaglia found that smokers were able to partly get around the taxes by smoking each cigarette more completely. Although some papers find a larger effect, most of the literature seems to suggest that taxes weren’t that powerful a weapon against smoking. Sorry, Econ 101.

So what did the trick? Well, surprisingly, mandatory labeling — the good old surgeon general’s warning — might have played a role. When I was young, we made fun of those goofy labels. Comedian Denis Leary declared that forcing cigarettes to rename themselves “tumors” wouldn’t affect consumption. And in fact, some research in the early 1990s suggested a paradoxical effect on young smokers, who viewed the labels as a badge of coolness. But more recent research has shown that a combination of graphic warning labels and antismoking ad campaigns do have the effect of reducing smoking. Warning labels appear to have had an effect in Canada too.

That’s surprising. We’re taught to believe that prices, not behavioral “nudges,” are the most important factor in behavior. Chicago Booth economist and blogger John Cochrane recently declared that “if you want to figure out the effect of prices on tomato demand, the absurdly simplified rational maximizer approach gives a darn good answer. If you want to figure out where to put the signs advertising a tomato sale, or what color to draw them, let me suggest some psychology.”

It appears that the market for cigarettes isn’t quite like Cochrane’s idea of the market for tomatoes.

Another factor in the victory against tobacco might be role modeling. In recent decades, far fewer movie characters smoke. A 2012 surgeon general’s report finds that smoking in the movies has a big effect on teen smoking. In addition, the recent spate of widespread bans on smoking in public places surely had an effect, both by making cigarette consumption less fun, and by establishing a no-tobacco norm.

So how do we use these behavioral solutions to fight the scourge of obesity? You can’t ban being obese in public places (nor would you want to). And Hollywood movie characters are already unrealistically thin. We want to avoid any discrimination against fat people.

Instead, we might want to focus on food consumption habits. Americans are fat because we eat large portions, and because we eat foods that are high in sugar and fat. Perhaps it’s time for the surgeon general to put scary warning labels on sugary and fatty foods. And perhaps it’s time for Hollywood studios to consciously focus on depicting characters eating small portions and healthy meals.

Behavioral economics cut smoking, and Americans are healthier, happier people because of it. We should try the same tactics against unhealthy eating.