WHEN the bottom finally fell out of America’s housing market in 2006, it triggered the worst global recession since the 1930s. But rising house prices need not spell disaster. The Economist’s latest round-up of house prices across the globe shows that prices have risen over the past year in 21 of the 26 economies we track, at a median pace of 4.7% (see table). Not every rise is alike, however.

America is still—just—in the category of countries where the housing market remains in recovery. House prices there increased by 4.7% in the 12 months to July, according to the Case-Shiller national index. Prices have now risen by 25% from their 2011 trough, but still remain 7% from their 2007 peak. The Economist measures national affordability by comparing prices to the long-run average of their relationship with rents and income. On this basis, we reckon house prices in America are broadly at their fair value.

Not for long, perhaps. Activity is buoyant: sales of existing homes increased by 6.2% on the previous year. With 30-year fixed-rate mortgages at record lows, the effect of an interest-rate rise on the housing market is expected to be minimal.

What is more, construction is lagging. The National Association of Realtors, a trade body, has found that new house-building is failing to keep pace with job creation in many cities. For every 12 jobs created builders have historically gained construction permits for ten new homes. Between 2012 and 2014 that number fell to 4.8 permits. Some cities are sizzling again as a result: prices in San Francisco increased by 10% in the year to July, and are up by 75% since 2009.

Other countries’ housing markets are already well above fair value. Taking an average of our two measures, houses are more than 30% overvalued in six markets. Britain is perhaps the most supply-constrained of this group. Although prices have risen by 35% since their trough in January 2009, housebuilding is failing to respond. Just 140,000 homes were completed in the year to March 2014, some 25% below the long-term norm. That puts a firmer floor under prices than in other notably overvalued markets such as Canada and Australia.

Hong Kong is the most extreme example of soaring prices and limited supply. Property prices in the territory appreciated by 21% in the year to June, and have now doubled in five years. Since 2009 the regulator has introduced seven rounds of “macroprudential” measures designed to cork the rises. Its latest, in March this year, reduced the average loan-to-value ratio for new mortgages from 64% to just 52%. In practice, China’s recent stockmarket crash is likely to be a bigger dampener on demand, as wounded mainland investors put off new purchases.

As for China’s own housing market, it is one of only five in our index where prices are falling, joining Singapore and a trio of euro-zone countries—France, Greece and Italy. Prices are falling at a slower rate than before, however. The government has been trying to boost the market over the past ten months, cutting interest rates by 1.4 percentage points and relaxing rules on downpayments. Prices are now rising on a monthly basis in many cities. In Beijing and Shanghai, they look positively frothy again.