The ending today of the US mission in Iraq concludes a controversial war that lasted nine years, involved at its peak more than 170,000 US troops in 505 bases, and cost 4,487 American lives. The cost in Iraqi lives was, of course, far greater, and remains a subject of controversy.

Regardless of the merits of the war or its equivocal outcome, its ending raises an interesting statistical question. Are wars more or less common than they used to be?

One view, epitomised by Steven Pinker’s recent book, The Better Angels of our Nature, is that the toll of wars and violence has been steadily falling. Those journalists and intellectuals who claim the opposite, he wrote last month in an article in The Guardian, are innumerate. Battle deaths have been steadily falling, as a proportion of the world population, from 300 per 100,000 at the height of the Second World War to teens in the post-war period, to single digits during the Cold War, and less than one in the 21st century.

Choosing the middle of the Second World War as a starting point for this comparison might be considered naughty, but it doesn’t invalidate the general point. Many indicators do support his claims. The number of wars in each year has been declining since 1816, the number of annual military fatalities since 1946, and the probability of bilateral conflicts since 1950.

While 300 US troops were killed per day in the Second World War, 50 a day in Korea, and 20 a day in Vietnam, the toll in Iraq was only two a day. Civilian deaths in conflicts have, of course, increased over the same period but in Pinker’s view not to a sufficient degree to disprove the argument.

But his is not the only way of looking at the issue, as Mark Harrison of the University of Warwick and Nikolaus Wolf of the Centre for Economic Policy Research at Humboldt University point out in the latest issue of the Bulletin of the University of Warwick Economics Research Institute.

They choose instead to count the number of countries at conflict at any one time, and include displays of force as well as its actual use. The result is to show that the number of such pairwise conflicts has been rising steadily since 1870 at 2 per cent per year. The chart illustrates the data, which come from the Military Interstate Dataset.

The trends show some disturbance around the two world wars of the 20th century, which the authors explain by saying that conflicts that would otherwise have occurred later arrived early and were squeezed into the First World  War, or were delayed until the Second, with a lull in between. But post-1945 the trend resumed.

But how, if the number of wars has declined, has the numbers of countries at war or in conflict increased? Partly that’s a function of numbers. In 1870, the world had only 50 states; by 2000 there were more than 180. The break-up of empires and federations multiplied the number of possible pairwise conflicts from around 1,000 to over 17,000.

It is this increase that has driven the rise in the number of countries in conflict in the past half-century. More pairs of countries have clashed because there are more pairs, as the authors put it. In the earlier period after 1870, the number of countries remained much the same but the frequency of conflicts between them increased.

The period since 1870 accounts for 3,168 conflicts between two states. The liberal assumption is that democratic states do not engage in conflict, but the history of the US and the UK suggests otherwise: while the USSR/Russia has been involved in originating the greatest number of conflicts (219) the US is second with 161 and the UK is fourth with 119. China, with 151, splits the two democracies. Germany, charged with originating the First World War and certainly responsible for the Second, is sixth (102) behind Iran (112).

But if the proliferation of countries has contributed to an increase in conflicts, the outlook is not encouraging. Independent states have continued to proliferate, with the break-up of the Soviet Union and Yugoslavia. Both of these have either led to conflicts or have been the result of conflicts. The same process may in future lead to the division of African countries, as it already has in Sudan.

Again, the data do not seem to fit with the conventional wisdom that the growth in prosperity and democracy and the globalisation of trade have made conflicts less likely. These are supposed to have reduced the incentives for war, although the recent history of both the US and the UK suggests otherwise.

The two economists do not deny that greater wealth, trade and democracy have the good effects attributed to them, but suggest they are not the whole story. They suggest that these same factors, while reducing the incentives for conflict, have increased the capacity for it.

Productivity growth has made destructive power cheaper: a suitcase full of plastic explosive can kill hundreds. States can tax and borrow more than they once could, and use the money to support conflicts, and while wars disrupt trade, globalisation has reduced the costs of falling out with a neighbour. There are plenty of other nations to trade with. Globalisation has also reduced the costs of nationhood, creating more nations and more borders.

“In other words” the authors conclude, “the very things that should make politicians less likely to want war – productivity growth, democracy, and trading opportunities – have also made war cheaper. We have more wars not because we want them, but because we can.”