IT SOUNDS like an inventory for war: 126 tracked armoured vehicles, 138 grenade-launchers, some 1,600 bayonets. That is a sample of items given to police departments by the military as part of America’s “1033” military equipment programme. Since 2001 fully $5bn of surplus army gear has been transferred to cops for nothing.

Military-style kit has long been associated with excessive police force. After riots in Ferguson in 2014, Barack Obama worried that the police resembled an occupying force rather than a crime-fighting one. The president signed an executive order that, by April 2016, requisitioned police stocks of tanks, grenade-launchers and bayonets and provided for closer scrutiny of federal procurement programmes.

On August 28th the White House rescinded that order, giving officers renewed access to the most controversial equipment. Jeff Sessions, the attorney-general, announced the change at a gathering of the Fraternal Order of Police, who had lobbied hard to overturn the restrictions. Is this wise? Two new papers published in the American Economic Journal provide some useful clues. The first one, by Vincenzo Bove of the University of Warwick and Evelina Gavrilova of the Norwegian School of Economics in Bergen, finds that a 10% increase in the value of military equipment transferred to police in one year reduces offending by 5.9 crimes per 100,000 people the next year. A second paper, by Matthew Harris of the University of Tennessee and others, corroborates those results. It also finds that militarisation reduces assaults on officers and complaints against them.

The overall impact on crime seems slight given that there are, on average, 2,500 crimes per 100,000 people. But the effect on property crimes, especially robberies and car theft, seems more dramatic. The first study estimates that these fall by about 1% for every 10% increase in army gear that is deployed. A back-of-the-envelope calculation shows that for every $5,800 of army capital employed by police forces, society saves $112,000 in reduced property crime.

If this conjures up images of tooled-up cops intimidating muggers, however, it should not. Mr Bove and Mrs Gavrilova find that back-office equipment, including such things as air-conditioners, which accounts for about two-fifths of the total value of the 1033 programme, is much more effective than vehicles and tactical gear. They find no evidence that military weapons cut crime. Perhaps office equipment makes cops more efficient, or frees up money for hiring new ones.

Mr Sessions also contends that military equipment keeps officers safe. A Kevlar helmet saved the life of one officer during the Pulse nightclub shootings in Florida last year. But this equipment was not prohibited under Mr Obama’s rules, nor was it procured through the 1033 programme. And despite Mr Sessions’s depiction of police under siege, serving officers have seldom been safer. On average, between 1987 and 1991, 16 out of every 100 officers were assaulted and 18 in every 100,000 died on active duty. Over the past five years those figures have fallen to ten assaults per 100 officers and nine deaths per 100,000.

Other evidence suggests that the 1033 programme could benefit from more oversight. In July the Government Accountability Office reported that investigators were able to acquire restricted military equipment by masquerading as a police agency using a faked website and dodgy credentials. Hopefully no villains noticed.