Pop quiz: What percentage of bankruptcies in the United States are caused by medical bills?

If you lived through the debate over passing Obamacare, you probably answered something like “half.” That was the figure in common currency among advocates of health-care reform; then-Sens. Chris Dodd (D-Conn.) and Hillary Clinton (D-N.Y.) were just two of the prominent advocates who used it. Other variants were also popular; Barack Obama, for example, was fond of saying that “the cost of health care now causes a bankruptcy in America every 30 seconds.”

It’s a memorable number. But it’s almost certainly many times the true count.

The figure was based on a series of papers released by a team including Sen. Elizabeth Warren (then a professor at Harvard Law School) and co-authors David Himmelstein and Stephanie Woolhandler of Physicians for a National Health Program. Theirs was hardly the only paper to attempt an estimate of medical bankruptcies, but no one else got eye-popping numbers like that — or nearly so much attention from the media.

Critics at the time, including me, pointed out that there were all sorts of problems with the data, but none of the critiques had the viral charms of the original study. But behind the scenes, the debate has continued. And last week, the New England Journal of Medicine published a new estimate done by a team of health and labor economists.

Their method is considerably more robust than the one adopted by Warren et al., who looked at the presence of medical bills in bankruptcy filings. The problem with doing that is that bankruptcy tends to be multi-causal. If you have a half-million-dollar house, three luxury cars, a boat — and also a heart attack — which of these things “caused” your bankruptcy?

So Carlos Dobkin, Amy Finkelstein, Raymond Kluender and Matthew J. Notowidigdo did what’s called an “event study.” Instead of looking at bankruptcies to see how many involved medical bills, they started with the illness, and asked how much more likely people were to declare bankruptcy after they got sick. That’s a much better way to tease out causation than asking whether someone who just went through a financially ruinous divorce also owed his or her dermatologist thousands of dollars.

The answer they came up with will surprise even critics of Warren et al.: The fraction of bankruptcies caused by medical events is just 4 percent. And even among those bankruptcies, it seems that medical bills may be less of a problem than the other things associated with an illness, such as lost labor income.

In other words: Medical bankruptcy probably wasn’t nearly as big a problem as people thought when we were passing our giant new health-care program. And to the extent that it was a problem, Obamacare probably didn’t do much to fix it.

That jibes with what we’ve seen in the bankruptcy data since Obamacare passed. If medical bills really were driving so many people into bankruptcy, then we would have expected filings to plummet after 2013, when millions of people gained health insurance coverage. Instead we see a smooth decline from the recession-era peak.

That 4 percent figure may be too low. Dobkin et al. looked at hospitalizations, data they matched up with credit reports. And they restricted the study to people who had not had a hospitalization in the three years before the event that put them in the study (though these people might well have been hospitalized after that first illness).

This enabled them to focus on the effects of a discrete health problem, rather than, say, catching someone who lost his job and then had a heart attack from the stress. And since most of the people with high medical spending in a given year had a hospitalization, it’s reasonable to think that they’re capturing the majority of the illness-induced bankruptcies.

But they’re probably missing some people who are quite sick yet don’t require hospitalization. And their method will exclude the longtime chronically ill and people with special-needs children, groups who might be particularly likely to end up in bankruptcy. That 4 percent figure is probably a useful floor, telling us the minimum number of medical bankruptcies we can definitely say occurred; but it’s not appropriate to use it as a ceiling.

Still, double their figure to account for those omissions; triple or quadruple it, even. We’re still not anywhere near half of all bankruptcies. Then consider another finding, which is arguably even more important than the percentage of total bankruptcies: Even among the uninsured, hospitalization accounted for only 6 percent of total bankruptcies.

Why is that important? Because if people with no insurance at all don’t have significantly higher rates of bankruptcy, it suggests that while medical bills are driving some bankruptcies, they’re unlikely to be causing the majority.

The NEJM paper is part of a larger project, which the authors recently wrote up for the American Economic Review. That paper found that the size of the drop in income after an illness was about five times that of the resulting medical bills, suggesting that the financial strain is likely to be much more driven by income loss than health-care costs. And indeed if you talk to bankruptcy practitioners, you’ll hear the stories of plumbers whose heart attacks forced them to cut back on work; surgeons who developed a tremor in their 50s and saw their income plummet too far to make the mortgage; mothers of special-needs kids who had to quit their jobs in order to become full-time case managers. If a family’s debt was pitched right up to the edge of their old income, insolvency quickly looms.

If Dobkin et al. are right, the people who quoted Warren’s inflated statistics, focused around medical bills, didn’t just overstate the problem; they had us focus on a problem we didn’t have, instead of the one we did. And that problem still needs to be solved.

On a personal level, it means that Americans need to plan around potential illnesses by rethinking their debt load. We’d all be much less vulnerable if we kept our debt payments down to a level that would be manageable on a reduced income, instead of buying as much car and home as we can afford. Some of the savings from lower payments could be used to buy short-term and long-term disability insurance, either through our employers or a private broker. And we could put the rest into an emergency fund that would carry us through, say, a three- or six-month illness.

On a policy level, if Americans wanted any sort of social insurance to protect the middle class from the financial effects of illness, they’d have done much better to insure incomes rather than health. That probably would have been just as controversial as Obamacare, to be fair. But at least we wouldn’t have spent hundreds of billions of dollars to fight medical bankruptcies, only to see no improvement.