Out. Everywhere. Yesterday. Those three words sum up the mood here at home when it comes to American military presence outside US borders.

President Barack Obama is signalling he wants to get out of Afghanistan so badly he’s even taking a few political gambles to accelerate a pull-out. There’s also a more general sense that putting soldiers in other countries has proved a bad investment for everyone involved, rendering those nations sadder, rougher and poorer.

Given the parlous budgetary conditions in the US, the thinking goes it would be better to slash US defence spending. America needs money at home. This week, Obama proposed reductions in military spending, saying a cut suited America’s “strategic priorities”.

Yet the opposite may be true, at least when it comes to the most obvious form of investment – in economic growth abroad. That is the finding of a study published in recent weeks by Garett Jones of George Mason University in Virginia and Tim Kane of the Kansas City, Missouri-based Ewing Marion Kauffman Foundation.

The more troops, the more growth, the scholars found.

Looking at navy, army, marine and air force presence in 94 countries over 50 years – 1950 to 2000 – the authors found putting US troops in a country, starting from 0 to a presence of 100 000, about the number the US had in Germany during the period studied, was over time associated with an increase in the per-capita growth rate of that country by an extra 1.8 percentage points a year. Even an increase from 10 to 100 troops corresponded with a rise in growth of a third of a percentage point on average.

“This study suggests Africa is poorer than it would have been with more active alliances between the US and its many countries, particularly because of the absence of US bases there,” Kane said. Right now the concept of nation-building is unpopular. But the study suggests “nation-building has a half-century track record worth remembering”.

It’s worth noting that such sweeping conclusions are only possible because of something many young Americans never knew or have forgotten – the US was everywhere once, and for a long time. The Pentagon had an average of 730 000 soldiers stationed abroad in the 1950s and 762 000 during the 1960s. Then the numbers dropped to 502 000 in the 1970s, 447 000 in the 1980s and 269 000 in the 1990s. In any given decade, between 26 and 49 countries hosted American troops, according to data assembled by the authors, using Pentagon figures.

But is the experience of the previous century – when troops were heavily concentrated in European countries with courts and diverse economies – applicable in places such as Afghanistan or Iraq? In one encouraging sign, Jones and Kane found growth in places with fewer such institutions still accelerated when GIs were present. A prime example is Turkey.

What about military, economic or social aid instead of troops? Today it seems an easy substitute to the US voter, battle-fatigued as he is more than a decade after September 11 and two decades after Operation Desert Storm. But the authors found “more troops predict growth, but more aid does not”, Jones said. “Aid is not a good substitute for growth, even military aid.”

Conversely, the absence of soldiers seemed to hurt. Countries that asked the US to withdraw, like France in the 1960s and Thailand in the 1970s, afterwards paid a growth penalty.

The amount of growth forgone in Africa due to the absence of longstanding troops was tragic, Kane said. The 7 percent annual growth World Bank types once predicted for Ghana would have been more easily realised with troops than with all the aid it received, he said.

Interestingly, the troop growth effects prevail even after the US leaves a place where it has been for a long time. Sometimes there is an initial collapse caused by command economics. But when such countries open up, they tend to grow faster than countries that never had a US military presence. The troops’ presence also tended to bring in foreign direct investment from the US, supplying capital to locals.

Current thinking may be backwards. Defence spending, said to be part of America’s growth problem, might instead be part of its growth solution, Kane said.

Amity Shlaes is a Bloomberg View columnist. The opinions expressed are her own.