MANY Americans were taken aback when news broke in January that Peter Thiel, an internet billionaire and adviser to Donald Trump, had New Zealand citizenship. For five years this backer of an “America first” president had kept his Kiwi passport quiet. Then the government released details of his $10m-lakeside estate (pictured).

A growing horde of rich foreigners see New Zealand as a safe haven. In 2016 overseas investors bought just 3% of all properties. But their purchases were concentrated at the expensive end of the market, which is growing fast: sales involving homes worth more than NZ$1m ($690,000) increased by 21%. That helped push prices in the country up by 13% over the past year, to lead The Economist’s latest tally of global house-price inflation (see table).

New Zealand is one of several countries where the impact of foreign money on housing is under scrutiny. Prices have also risen rapidly in Australia and Canada. Central bankers fret about the dangers fickle capital flows pose to financial stability. London’s mayor has ordered a study on foreign ownership in the capital after property prices rose by 54% in four years.

Foreign capital also makes itself felt in America, where house prices have recovered to a new nominal high. Canadians once dominated; now they are outnumbered by Chinese citizens spending some of the $1.3trn that has left the country since autumn 2014. The National Association of Realtors estimates that Chinese investors bought 29,000 American homes for a total of $27bn in the year to March 2016. Foreign buyers focus on a handful of cities: San Francisco, Seattle, New York and Miami. In some places, foreign investment has led to a construction boom. In Miami apartments are being built in numbers not seen since the financial crisis, financed in part by Venezuelan money. Australia lets foreigners invest only in new-build properties, and they do: 26,000 new flats are due on the market in Sydney and Melbourne over the next 18 months. In London 45,000 homes have been built since 2014—the highest rate in ten years—but locals grumble many are pads for footloose foreigners. In many of these countries affordability looks stretched. The Economist gauges house prices against two measures: rents and income. If, over the long run, prices rise faster than the revenue a property might generate or the household earnings that service a mortgage, they may be unsustainable. By these measures house prices in Australia, Canada and New Zealand look high. In America as a whole, housing is fairly valued, but in San Francisco and Seattle it is 20% overpriced. Haven investors may disregard affordability measures. Property can either be a bolthole or earn an income; in many supply-constrained cities its value may rise rapidly; even if not, the risks may be lower than at home. Investment from China has gone up as its own property market has become stretched, fears of devaluation have risen and a crackdown on corruption continues. A study* in 2016 found that increased political risk in places such as Greece and Syria explained 8% of the variation in London’s house prices since 1998.

Policymakers may well scratch their heads. It is difficult both to make housing more affordable for a country’s own citizens and to encourage foreigners to buy. Britain has in fact tried to curb foreign enthusiasm with higher taxes, and by publishing a registry of 100,000 British homes owned by foreign companies—a potential embarrassment for some.

But unintended consequences lurk. After a 15% levy on purchases from abroad was introduced in the Canadian city of Vancouver last August, the number of foreign buyers dropped by 80%. That helped dampen house-price inflation there but pushed up demand in nearby Victoria. It also deterred highly skilled immigrants. The levy will soon be amended to exclude foreigners on skilled-work visas.

Explore and compare global housing data over time with our interactive house-price tool

Some foreigners will stump up even if costs rise. More Americans are house-hunting abroad, for example. By one measure, interest in boltholes in New Zealand has tripled since Mr Trump’s election.

*“Home Away from Home? Foreign Demand and London House Prices”, by Cristian Badarinza and Tarun Ramadorai, SSRN, November 2016