The increase in rents (and median sales price per unit) is credit- driven not population driven. Rents in Lima, Peru, and Quito, Ecuador, are very reasonable compared to the US; this is because Wall Street is a long way away from these places; those who have access to Wall Street credit products are few and far between compared to those in San Francisco and other bubble cities.
Jobs in San Fransisco = speculation w/ borrowed money and Ponzi schemes like Uber- and other product-free tech firms.
The bubble cities list includes Vancouver, BC; Sydney, London, Hong Kong, Singapore; prices in these places go up because they are going up. All of these are seeing multiplier effect: where increased price = increase in collateral for more loans; one sales- or rental transaction sets the price level for the rest. Once price increases disconnect from fundamentals, the multiplier effect goes into reverse, the bubbles pop and housing costs decline (crash).
Ditto when Ponzis unravel which is underway right now.