HERE is a riddle. Britain, for now at least, is loved by foreign investors. The stock of inward foreign direct investment (FDI) in Britain’s assets and shares is larger than anywhere except America and Hong Kong. In the past decade overseas investors have splurged some £600bn ($772bn), equivalent to a third of British GDP, to acquire over 2,000 British firms. The textbooks say that foreign investments make a country more productive. The new arrivals should bring with them cutting-edge capital assets and best-practice management. So why over the past decade has Britain’s productivity barely improved?

The question matters for all Britons. If productivity growth is low, then wage growth will be too. Many factors determine Britain’s weak productivity growth, including creaky infrastructure. But new official data suggest that foreign investors are doing a lot less to improve the economy than commonly assumed.

The figures classify FDI flows into around 100 industries. In 2015 financial services accounted for an astonishing 95% of net inflows. This could include, for instance, foreign funding for Britain’s burgeoning financial-technology sector. Finance was unusually dominant in 2015, though even in 2012-14 the industry made up around 60% of the net figure.

Remove financial services, and overall in 2015 a tiny amount of net foreign investment flowed into Britain—a few billion pounds at best. Many industries saw “negative inflows”, suggesting that foreigners were actually disinvesting, selling assets they had acquired back to British firms, for instance. In 2015 they pulled around £20bn from the oil-and-gas sector. Perhaps £1.5bn drained from manufacturing. Finance aside, investors seem to see few profitable opportunities in Britain.

What foreign investment does flow into the “real” economy may make surprisingly little difference. Much of it seems to be about one big company horizontally acquiring another, perhaps with the aim of eliminating overlapping marketing costs (such as in the Kraft-Cadbury deal of 2010) or of acquiring a trophy asset (such as the Tata-Corus steelmaker deal of 2007). A chunk of investment in Britain, meanwhile, is a statistical by-product of big firms moving headquarters for tax purposes rather than anything meaningful.

As Britain begins the process of leaving the EU, interest from foreign investors is only likely to shrink. If so, the prospects for the kind of foreign investment that lifts productivity will start to look even gloomier.