There might be evidence, but I could not find it in a cursory search. Let us assume constant demand for houses. Suppose a housing shortage is going to happen

There might be evidence, but I could not find it in a cursory search. Let us assume constant demand for houses. Suppose a housing shortage is going to happen in 1 year. Speculators will buy houses thus incentivizing construction and lowering prices in the future. The more adverse the shortage (consider supply and demand) the greater the difference in prices between now and 1 year from now and thus the greater the gains of the speculators. Speculators are essentially arbitraging over time. If the speculators incorrectly buy houses when there is excess housing, they will lose money proportional to their mistake.