  The relationship between housing costs and homelessness has important
implications for the way that city and county governments respond to increasing
homeless populations. Though many analyses in the public policy literature have
examined inter-community variation in homelessness rates to identify causal
mechanisms of homelessness (Byrne et al., 2013; Lee et al., 2003; Fargo et al.,
2013), few studies have examined time-varying homeless counts within the same
community (McCandless et al., 2016). To examine trends in homeless population
counts in the 25 largest U.S. metropolitan areas, we develop a dynamic Bayesian
hierarchical model for time-varying homeless count data. Particular care is
given to modeling uncertainty in the homeless count generating and measurement
processes, and a critical distinction is made between the counted number of
homeless and the true size of the homeless population. For each metro under
study, we investigate the relationship between increases in the Zillow Rent
Index and increases in the homeless population. Sensitivity of inference to
potential improvements in the accuracy of point-in-time counts is explored, and
evidence is presented that the inferred increase in the rate of homelessness
from 2011-2016 depends on prior beliefs about the accuracy of homeless counts.
A main finding of the study is that the relationship between homelessness and
rental costs is strongest in New York, Los Angeles, Washington, D.C., and
Seattle.
