When Countries Go Extinct Thanks To Low Birth Rates

Given the low birth rates of some countries (I'm looking at you, Hong Kong* and Singapore), it's only a matter of time before they simply depopulate themselves out of existence. But how long do they have?
The Economist did the (wild) projection:

In Hong Kong, for example, a cohort of 1,000 women is now expected to give birth to just 547 daughters. If nothing changed, those 547 daughters would be succeeded by 299 daughters of their own, and so on. Extrapolating wildly, it would take only 25 generations for Hong Kong’s female population to shrink from 3.75m to just one. Given that Hong Kong’s average age of childbearing is 31.4 years, the territory would expect to see the birth of its last woman in the year 2798.
By the same unflinching logic, Germany, Italy, Japan, Russia and Spain will not see out the next millennium. Even China has only 1,500 years left.

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*Yes, I know that Hong Kong is not an independent country, but it operates like one.