After Hong Kong, the list continues with Sydney (12.2), Vancouver (11.8), Auckland (10), San Jose/Silicon Valley (9.6), Melbourne (9.5), and Los Angeles (9.3). Next come London and Toronto – at 8.5 and 7.7, respectively – where housing is extremely expensive, but incomes are also high.

Meanwhile, some attractive world cities are quite affordable, relative to incomes. In New York City, the median home price stands at 5.7 times median household income. In Montreal and Singapore, that ratio is 4.8; in Tokyo and Yokohama, it is 4.7; and in Chicago, it is 3.8.

Maybe the figures for these outlier cities aren’t precise. They are hard to check, and there must be inconsistencies across cities, countries, and continents. For example, the geographical boundaries of the areas used to compute median price and median rent may vary. In some cities, higher-priced homes may tend to turn over more rapidly than in others. And some cities may be inhabited by larger families, implying bigger houses than in other cities.

But it seems unlikely that the errors could be so significant that they would change the basic conclusion: home affordability around the world is highly variable. The question, then, is why residents of some cities face extremely – even prohibitively – high prices.

In many cases, the answer appears to be related to barriers to housing construction. Using satellite data for major US cities, the economist Albert Saiz of MIT confirmed that tighter physical constraints – such as surrounding bodies of water or land gradients that make properties unsuitable for extensive building – tend to correlate with higher home prices.

But the barriers may also be political. A huge dose of moderate-income housing construction would have a major impact on affordability. But the existing owners of high-priced homes have little incentive to support such construction, which would diminish the value of their own investment. Indeed, their resistance may be as intractable as a lake’s edge. As a result, municipal governments may be unwilling to grant permits to expand supply.

Insufficient options for construction can be the driving force behind a rising price-to-income ratio, with home prices increasing over the long term even if the city has acquired no new industry, cachet, or talent. Once the city has run out of available building sites, its continued growth must be accommodated by the departure of lower-income people.

The rise in housing prices, relative to income, is unlikely to be sudden, not least because speculators, anticipating the change, may bid up prices in advance. They may even overshoot, temporarily pushing the ratios even higher than necessary, creating a bubble and causing unnecessary angst among residents.