Even before the recent flurry of encouragement, Africa’s turnround was breathtaking. Between 1980 and 2000, the continent had experienced negative economic development: output per person had fallen by a 10th in purchasing power terms. Then, just as the Aids pandemic was thought to represent the final straw for Africa, its fortunes changed dramatically. According to the World Bank’s development indicators, gross domestic product per person has risen every year since 2000, delivering a cumulative gain of more than a third.

Two years ago, Ghana corrected an error in its gross domestic product statistics – and the estimated size of its economy shot up by more than 60 per cent. Its mistake had been to count activity only in well-established sectors, omitting new ones such as mobile telephony. It seems likely that this error exists elsewhere. A forthcoming revision in Nigeria could be as dramatic as Ghana’s, boosting the GDP estimate for the whole of sub-Saharan Africa by as much as 15 per cent.

Alwyn Young of the London School of Economics haspointed to another reason to suspect that standard GDP data underestimate Africa’s progress. Household surveys, which record rates of ownership of consumer durables as well as housing quality, health and education, suggest that consumption in sub-Saharan Africa has been growing by about 3.5 per cent per year over the past two decades – more than three times faster than suggested by the national accounts. Even Professor Young’s critics concede that, in Kenya, for example, real GDP per person rose by just a 10th between 1993 and 2009, while the percentage of people with electricity more than doubled, the percentage with flush toilets more than tripled, and the percentage with a telephone shot up from just about nothing to 60 per cent.

Child mortality statistics tell the most positive story of all. In 1997, in a notably despondent analysis of Africa, William Easterly and Ross Levine reported that the typical African mother had only a 30 per cent chance of seeing all her children survive until age five. But Africa has recently witnessed falls in child mortality faster than any recorded anywhere. In the five years to 2010, Senegal cut its under-five mortality rate from 12.1 per cent to 7.2 per cent. Rwanda and Kenya did almost as well. It took India fully a quarter of a century to achieve a comparable decline.

What accounts for all this progress? Strong commodity prices and the rise of China as a consumer and investor have helped. So have the improving ratio of working age adults to dependants and technological breakthroughs such as mobile phones. But better policy has also made a difference. You can see this in studies of particular advances: the policy of distributing insecticide-treated bed nets to ward off malarial mosquitoes explains a large part of the gains in child survival. You can also see this in the productivity performance of the best-managed nations.

The continent’s advance has not been uniform. A group of dysfunctional laggards, which generate more than their fair share of news headlines, remain as poor as they have ever been. But the flip side is that the success stories have done much better than suggested by Africa-wide averages. Some of the star performers – Angola, Nigeria and Chad – owe their progress to oil. Others are rebounding from civil war. But Mozambique is an example of a country that has been at peace since the early 1990s, does not produce oil, and yet has boosted GDP per person in the labour force by 4.8 per cent annually between 1995 and 2010. Peaceful Ghana has managed a respectable 2.6 per cent per year.

The surest basis for sustained productivity improvement is to move workers from subsistence farming to jobs that involve skills and tools. Between 1995 and 2010, agriculture’s share of Mozambican GDP fell from 42 per cent to 26 per cent as manufacturing, construction and services grew to fill the gap. Between 2000 and 2010, Uganda cut farming’s share from 25 per cent to 16 per cent, while Ethiopia reduced it from 49 per cent to 41 per cent. Again, this shift of economic structure is not a continent-wide story. But the best managed African countries are pulling it off.

Less than 20 years ago, the conventional wisdom was that landlocked, ethnically divided countries battling the burdens of tropical disease might never advance. Today, there is no guarantee of future progress. But the fatalistic talk of an African growth tragedy has been proved wrong.

The writer is a senior fellow at the Council on Foreign Relations and an FT contributing editor