Yet, so far, the connection between job strain and bad health has mostly been correlational — we haven't known whether stressful jobs directly cause our health to deteriorate. Surveys show that people who work more are more likely to suffer from hypertension and more likely to experience a stroke. The plausible biological explanation: Both of these health problems are symptoms of stress and sleep deprivation.

But what if it wasn’t the job’s fault? What if naturally obsessive or anxious people gravitate to occupations where they are forced to work too much? What if the people who volunteer for overtime only do it because they need the money to solve some other crisis in their life? The connection between bad health and overwork, as common sense as it seems, is cloudy.

Recently, economists at Purdue and the University of Copenhagen made a clever attempt to clear up the question. They looked at Danish manufacturing companies where overseas sales increased unexpectedly because of changes in foreign demand or transportation costs between 1996 and 2006. These constituted a set of natural experiments. At firms where exports spiked, there was suddenly a lot more work to do, a lot more things to sell. This put the squeeze on employees, who became measurably more productive — but also started to have more health problems.

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“The medical literature typically finds that people who work longer hours have worse health outcomes — but we try to distinguish between causality and correlation,” said Chong Xiang, an economics professor at Purdue and co-author on the paper, along with David Hummels and Jakob Munch. A draft was released this week by the National Bureau for Economic Research.

This kind of study could only be done in a place such as Denmark, where the single-payer health care system keeps track of everyone’s doctor’s visits and drug purchases. Researchers found that women at companies where there was an export boom were subsequently more likely to be treated for severe depression, and more likely to take prescription medication for heart attack or stroke. For both men and women, there was also an increase in severe on-the-job injuries.

The health effect was related to how much pressure the company faced. If external forces caused a company’s exports to rise by, say, 10 percent, female employees were about 2.5 percent more likely to be treated for severe depression, and 7.7 percent more likely to take heart attack or stroke drugs. For context, about 4 percent of women overall were being treated for severe depression and 1 percent of women were on heart attack or stroke medication. These conditions are not very common, but job strain caused a measurable, statistically significant bump in prevalence. The researchers aren’t sure why men weren’t measurably affected, but it could have something to do with how women are at higher risk in general for stroke or depression in their lifetimes. And the men could have been sicker in other ways that the researchers couldn’t observe.

At companies that experienced the biggest increases in exports, the rate of serious injury also went up. These were on-the-job accidents severe enough to merit an insurance payout from the Danish government. (Such cases are rare, about 4 in 1,000 workers.) If you sorted companies by how big of an export boost they experienced, and focused on the top 25 percent, these exceptionally busy firms saw a 28-percent increase in severe injuries — which translates to about 1 extra-serious injury per 1,000 workers. Most of these injuries seemed to be concentrated in positions involving physical labor, not white-collar work.

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The researchers also found interesting patterns involving sick days. At most firms, employees started taking fewer sick days after business picked up, which indicates that they felt pressured to come in even if they weren’t feeling well.

But at companies that became exceptionally busy — those that enjoyed an export boost ranking in the top 25 percent — the number of sick days per person actually increased, by 14 percent for men and 24 percent for women. At these places, it seems the pressure was too much and the overwork made people too sick to come in. (The researchers focused on sick days that occurred in conjunction with a doctor’s visit or a drug prescription.)

We should always be careful of studies that so neatly confirm our assumptions, but here the conclusion aligns with decades of medical research hinting at similar things. We’ve known for a while that overwork and job stress is associated with poor health; it was just unethical to run an experiment to prove that one causes the other.

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In this case, we can blame (or thank) the invisible hand for doing the dirty work. The more or less random fluctuations in foreign economies provided an opportunity to observe what happens when people suddenly get a lot busier at work. Though this study focused on the Danish manufacturing sector, it covered both blue and white collar workers, so the results seem generalizable enough: Working too hard has health consequences. Our jobs really are killing us.