Much like how I approached job vacancies (and hires) using the dynamic equilibrium model, I thought I'd take a look at rental vacancies (where you could imagine a structurally similar relationship imagining rental vacancies as "unemployed" housing). It provides a decent description:
The dynamic equilibrium is -0.0052/year (i.e. vacancies fall by about 0.5% per year in the absence of shocks). The shocks are centered at 1959.1 (positive), 1967.4 (negative), 1985.0 (positive), 2001.6 (positive), and 2013.2 (negative). One could imagine the last two as people leaving rentals for houses in the housing boom, and then returning to rentals after the bust.
According to FRED's release calendar, new data comes out on Thursday, before 2017 Q1 GDP data on Friday. This model expects little change; we'll see if that bears out in the data over the next couple years.