According to a working paper published by UC Berkley’s Institute of Business and Economic Research and the Fisher Center for Real Estate and Urban Economics, the answer is, “Yes.” The paper, by Steven Raphael, is called, “Homelessness and housing market regulation.” From the abstract:

I … present an empirical profile of more and less regulated housing markets in the U.S. This profile demonstrates that more regulated markets experience slower growth in housing, produce less higher quality housing, experience higher housing price appreciation, and experience much larger increases in the budget shares that renters (and particular, low income renters) devote to housing expenditures. Finally, using a new state-level regulatory index …, I explore the direct relationship between housing market regulation and homelessness. The data reveal a striking positive relationship between the degree of homelessness across states and the stringency of local housing market regulation.

H/T: Lyman Stone