Housing First, the approach to chronic homelessness that places people into supportive housing instead of treating them on the streets, has been largely adopted by homeless advocates due to its measurable cost savings. Numerous studies have found that the cost of placing chronically homeless persons in supportive housing is lower than the cost of servicing them on the street.

Housing First’s detractors argue investment in Housing First is crowding out more traditional interventions like homeless shelters, which serve chronic and non-chronic homeless persons alike.

While the research on Housing First has largely focused on the cost of housing versus not housing the chronically homeless, the larger debate is really about how to best allocate the total sum of dollars available for homeless services, chronic and non-chronic.

Ultimately, any social investment is about maximizing or minimizing an outcome given a set of constraints. While cost has largely driven the Housing First rhetoric, another way to think about homeless interventions is to minimize the decrease in life expectancy an individual experiences due to homelessness.

According to Pathways to Housing, chronic homelessness decreases life expectancy by an average of 25 years. Given this assumption, I wondered what the equivalent number of years of life lost for a non-chronic homeless person would need to be indifferent between investing in chronic versus non-chronic homelessness.

In 2011, the estimated national homeless population on a given night was 636,017 people, with 107,148 chronically homeless and 528,869 not chronically homeless. To setup my indifference model, I assumed that the chronically homeless population was a closed population, that is, the same 107,148 people stayed homeless for the year (a knowingly incorrect approximation).

Calculating the number of non-chronically homeless persons is more complicated, the annualized number of non-chronically homeless persons is a function of the average duration of non-chronically homeless persons’ homeless spells (measured in months spent homeless in my model). Mathematically, the approximation of the annual number of unique non-chronically homeless persons is the point in time count divided by the fraction of the year spent homeless.

To get the point of indifference between investing in chronic versus non-chronic homelessness, assuming all we care about is minimizing the total number of years of life lost, we need to find the point where the sum of all years of life lost for chronically homeless persons is equal to the sum of all years lost for non-chronic homeless persons.

The following chart shows the average number of years a non-chronically homeless person would have to lose on account of their homelessness based on the number of months in the year spent homeless. Assuming a twelve-month average duration of homelessness, non-chronic homelessness would have to take an average of five years off of non-chronically homeless persons’ life expectancies to equal the twenty-five years average loss of life for non-chronically homeless persons.

The above calculations make a lot of assumptions, and are better understood as approximations rather than concrete guidelines. Furthermore, the model assumes that we value the total number of lives lost equally, that is, that twenty-five years of life lost for one person is equivalent to one year of life lost for twenty-five people, which might not be how you actually think about the value of life.

I’m not sure what the average duration of non-chronic homelessness is, so I can’t necessarily weigh in on whether this model would suggest a change in the current investment mix in homeless services. Regardless, if the social sector is to be more strategic with its investments, we would do well to carefully consider what outcomes were are maximizing or minimizing over. While the cost savings of Housing First are encouraging, I would hope that our objective has more to do with minimizing harm to humans than to our coffers.