Dear Bill Gates,

We have never met, but your annual letter (coinciding with your Davos speech) seemed to be addressed directly to me. Your aim is to critique books with titles such as “how rich countries got rich and why poor countries stay poor”, and I did write a book with almost exactly that subtitle. You go on to say “thankfully these are not bestsellers because the basic premise is false”. I am afraid you are right to say my book is not a bestseller, but wrong to say its premise is false.

Taking the year 2001, I used two different measures of whether a country was rich: the market value of per capita output (a measure of productivity) and the average consumption of the inhabitants (a measure of material standard of living). The two rankings differ, though not by much; Switzerland had the highest productivity and the US the highest consumption.

Using either measure to order the countries of the world, the distribution was U-shaped. There were about 20 rich countries (with about a billion people in total), many much poorer countries and few states in between. These intermediate states – such as South Korea and the Czech Republic – tended to be on a trajectory to join the rich list, a transition experienced in Japan and Italy a generation earlier. Rich countries operate at, or close to, the frontier of what is achievable with current technology and advanced commercial and political organisation. And when countries reach that frontier they tend to stay there, with Argentina the most significant exception.

You suggest that this claim might have been true 50 years ago but not now. It is 10 years since my book was published and time to update the calculations. So I did, and established that the hypothesis remains true.

There are some significant changes. The dispersion of productivity among already rich countries has increased. Norway and Switzerland have surged ahead – one due to its oil wealth, the other by the growing and seemingly price insensitive demand for its chemical and engineering exports. But laggards such as Italy – and indeed Britain – have struggled to keep up with the pack. More encouragingly, some additional countries, mostly in eastern Europe and Asia, seem on course to join the rich club.

So what about China and India? Their recent growth performance has been exceptional, but both are still desperately poor countries by the standards set by Switzerland and Norway. The gap will take many generations to eradicate.

One effect of globalisation is that the centres of major cities everywhere now appear similar – the offices of KPMG and the branches of HSBC look much the same across the world. But you do not have to venture far from the centre of Nairobi or Shanghai, and only round the corner in Mumbai, to see sights unimaginable in Norway or Switzerland.

Even if incomes are very unequal, every king needs courtiers, every computer billionaire creates a slew of computer millionaires

I was surprised and disappointed that the data you chose to support your case referred not to the distribution of average incomes across states – the subject of your letter – but to the distribution of household incomes across the world. These are very different things.

The information we have on global household income distribution is poor, but there seem to be plenty of middle income people. Even if incomes are very unequal, every king needs courtiers, every computer billionaire creates a slew of computer millionaires. This might change if, as some people argue, the middle of the skill distribution is hollowed out by robots and computers. But no such change is yet evident.

The major part of my book, Bill, (if I may) was devoted to descriptions of the economic and social institutions that enable some countries to operate near the technological frontier. The failure to establish such institutions, or to operate them effectively, condemns most of the world to levels of productivity and living standards far below what is possible with existing knowledge and techniques. That subject should interest you, and I’ll be happy to send you a copy of the book (though I know you can afford the extremely modest price).

Best wishes

John