That graph, though, is just a correlation: that’s not good enough for many economists. But a new paper, by John Pencavel of Stanford University, also shows that reducing working hours can be good for productivity.

Economists have suspected for some time that longer work hours could eat into productivity. John Hicks, a British economist, reckoned that “probably it has never entered the heads of most employers…that hours could be shortened and output maintained.” Hicks reasoned that with longer hours, output per hour would fall. As workers slaved away for longer and longer, they would lose energy, which would make them less productive.

Mr Pencavel looks at an unusual data set: research undertaken by investigators of the British “Health of Munition Workers Committee” (HMWC) during the first world war. Britain was desperate to maximise productivity, given the almost insatiable demand for weapons and ammunition.

HMWC had to provide the government with advice regarding the health and efficiency of workers in munitions plants: how could productivity be maximised? As part of its investigations, the Committee commissioned studies within munitions factories into the link between work hours and work performance.

It concluded, after much investigation, that British munitions workers needed shorter hours. Mr Pencavel analyses of the data collected by the committee and sees if their calculations were up-to-scratch.

The researchers collected a huge amount of data (most of it on women, who dominated the munitions industries). It was easy to measure hours worked. It was also pretty straightforward to measure output, since lots of the workers were paid on a piece-rate basis. Mr Pencavel crunches the data and concludes that there was a “non-linear” relationship between working hours and output.

Below 49 weekly hours, variations in output are proportional to variations in hours. But when people worked more than about 50 hours, output rose at a decreasing rate. In other words, output per hour started to fall (in the jargon, “the marginal product of hours is a constant until the knot at [about 50] hours after which it declines”). To get an idea, look at the raw data in the graph below:

Weekly output and weekly hours: 82 observations on women turning fuze bodies and milling screw threads on fuze bodies

Reducing hours, say, from 55 to 50 hours a week, would have had only small effects on output. The results are even starker when we are talking about very long working hours. Output at 70 hours of work differed little from output at 56 hours. That extra 14 hours was a waste of time.The crucial point that emerges from Mr Percavel’s analysis is that reductions in working hours do not always result in higher output per hour (which is what our initial correlation seemed to suggest). Rather, the initial level of working hours has to be so high. This graph is based on his regression analysis:

Marginal product of hours and average product of hours (as suggested by Mr Percavel’s analysis)

The HMWC also reckoned that the absence of a rest day (like Sunday) damaged hourly output. Mr Pencavel’s regression analysis confirms it. He estimates that output is slightly higher on the 48-hour working week (with no work on Sunday) than on the seven-day work schedule.

Of course, these results say nothing about output in service-sector professions, where most people in advanced economies are employed today. I would bet, though, that the results are even more pronounced. For work that is largely self-directed, and which requires intellectual engagement, you may achieve more in an hour of hard work than in a day’s worth of procrastination.

Mr Pencavel solemnly intones that the “profit-maximising employer will not be indifferent to the length of…working hours over a day or week.” Of course, attempting to tell that that to your boss the next time you attempt to leave the office at half past two may result in unsatisfactory outcomes.

See: The German Way: Few Hours, Great Productivity