CHINA is proud of its infrastructure: its cavernous airports, snaking bridges, wide roads, speedy railways and great wall. This national backbone (minus the wall) bears the weight of the world’s second-largest economy and its biggest human migration, as hundreds of millions of people move around the country during the lunar new-year holidays—the rush officially begins on January 13th.

Western leaders often shake their heads in disbelief at the sums China spends on its huge projects. And some analysts question how much of it has been wisely spent. In a widely circulated study published last autumn, Atif Ansar of Oxford University’s Saïd Business School and his co-authors say the world’s “awe and envy” is misplaced. More than half of China’s infrastructure projects have “destroyed economic value”, they reckon. Their verdict is based on 65 road and rail projects backed by the Asian Development Bank (ADB) or the World Bank since the mid-1980s. Thanks to the banks’ involvement, these projects are well documented.

One example is a 147-km, four-lane toll road in southern Yunnan province, which was built with the help of an ADB loan approved in 1999. The ADB expected the Yuanjiang-Mohei highway (Yuan-Mo for short) to cut travel times, reduce traffic accidents and lower the costs of fuelling and repairing vehicles, adding up to a compelling economic return of 17.4% a year. By 2004, however, traffic was 49% below projections and costs were more than 20% over budget, thanks to unforgiving terrain prone to landslides.

Were such setbacks enough to damn over half of the projects they examined? As a rule, the ADB and World Bank will approve an undertaking only if they expect its broad benefits (the economic gains from reduced travel times, fewer accidents, etc) to exceed its costs by a large margin, leaving ample room for error. Mr Ansar and his co-authors assume this margin is 40%: they posit a ratio of expected benefits to costs of 1.4 for every project. They scoured the banks’ review documents for examples of cost overruns and traffic shortfalls. Given these assumptions, a project becomes unviable if costs overrun by more than 40%, traffic undershoots by 29%, or some combination of the two. Of the 65 projects, 55% fell into this category. Yuan-Mo was one.

These projects may not be representative of China’s infrastructure-building as a whole. But there is little reason to think they are unusually bad. They are often managed with greater rigour, thanks to the involvement of outside lenders.

The authors’ conclusion, however, rests on their assumption about the margin for error built into the projects they looked at. Take Yuan-Mo, for example. Its projected benefits, over its first 20 years of operation, were several times greater than its costs. But as often with roads, the costs arrive early; the benefits are spread thinly over many years. In the time it takes for an investment to pay off, the resources used could have been earning a return elsewhere. So it is necessary to reduce the future payoffs by some annual percentage, known as a “discount rate”. The higher this is, the lower the value placed today on tomorrow’s gains.

So a lot turns on what rate is chosen. For historical reasons, the ADB adopts a high one of 12%. At that rate, Yuan-Mo’s ratio of expected benefits to costs equals 1.5, roughly in line with the authors’ assumptions. But at a gentler rate of 9%, the ratio improves to about 2. At a rate of 5.3% (more in line with government borrowing costs) the ratio rises to 3. With these higher margins for error, many fewer elephants turn white. At a ratio of 2, the share falls to 28%. If the ratio is assumed to be 3, the proportion of duds falls to just 8%.

The authors also assume that any traffic shortfall persists throughout its life. That is not always the case. Traffic on Yuan-Mo, for example, has rebounded, according to the road’s operator. By 2015 it was 31% higher than the ADB projected back in 1999. Around last year’s lunar new-year holiday the road handled record numbers. Some white elephants turn grey with age.