This is kind of comparing apple and oranges. First off, almost all of the housing in Singapore is public housing (HDP). If you own one, you cannot own a second one. For private property, there is huge fees for buying a second home, and the market for private property is very small and therefore, tend to be very expensive. There is also a lot more rules (like Minimum Occupancy Period) and taxes to seriously desensitised buying a second home, especially if it is for investment.
This make housing, for most cases, a poor investment in Singapore. You buy a home to live in it. This also mean that the market for rental, especially the one for foreigner, is very small compared to other country.
On the other end, the U.S, at least right now, see housing as a "safe" investment and has a population that is way more mobile than Singapore. People are less likely to invest in a home if they don't expect to stay in the same place for a significant amount of time.