Economics of Homelessness: Are housing prices to blame? Lots has been written in terms of the social context of homelessness. Often attributing the causes due to mental illness, previous criminal activity and addiction.

I've been wondering, how much of a role (if any) does home price or rent play into the phenomenon of homelessness?

Im guessing estimates will be different depending region, but I'd like to know if the relationship is consistent across the board.
This paper is close to what you want. 


  It is generally believed that the increased incidence of homelessness
  in the United States has arisen from broad societal factors, such as
  changes in the institutionalization of the mentally ill, increases in
  drug addiction and alcohol usage, and so forth. This paper presents a
  comprehensive test of the alternate hypothesis that variations in
  homelessness arise from changed circumstances in the housing market
  and in the income distribution. We assemble essentially all the
  systematic information available on homelessness in U.S. urban areas:
  census counts, shelter bed counts, records of transfer payments, and
  administrative agency estimates. We estimate similar statistical
  models using four different samples of data on the incidence of
  homelessness, defined according to very different criteria. Our
  results suggest that simple economic principles governing the
  availability and pricing of housing and the growth in demand for the
  lowest-quality housing explain a large portion of the variation in
  homelessness among U.S. metropolitan housing markets. Furthermore,
  rather modest improvements in the affordability of rental housing or
  its availability can substantially reduce the incidence of
  homelessness in the United States.


Quigley, John M., Steven Raphael, and Eugene Smolensky. "Homeless in America, homeless in California." Review of Economics and Statistics 83.1 (2001): 37-51.


  The results in table 5 provide the strongest evidence that housing
  market tightness is an  important determinant of homeless. For
  permanent caseloads, vacancy rates have a strong negative and
  statistically significant  effect (at the 1% level) on the incidence
  of homelessness. Moreover, these elasticity estimates are quite
  similar across specifications. In the two specifications including
  fair market rents (specifications (1) and (3)), rents exhibit a
  significant  positive effect on the incidence of homelessness as
  predicted by theory. In addition, the specification including the
  ratio of rents to income indicates a strong positive effect. Hence,
  for homelessness, as measured by the incidence of  homeless
  house-holds seeking permanent assistance, measures of housing market
  tightness consistently exhibit strong and statistically significant
  effects, which is consistent with the predictions of theory. We also
  find a negative and significant effect of per capita income. There are
  no important effects of county unemployment rate  s and no consistent
  and significant effect  of the SSI populations across specifications.
  Similar to the results from the S-night and continuum-of-care data
  sets, the results in table 5 also indicate that warmer weather is
  positively associated with homelessness


The key results table:



Open access version?