As Los Angeles grapples with an escalating homelessness crisis, a new study from RAND Corporation provides support for one of the most obvious solutions: providing more residents with housing.

The study, which was commissioned by LA County in 2014, finds that the county’s Housing for Health program, which launched in 2012 and provides supportive housing and medical services to homeless residents, has reduced the reliance of participants on county medical and mental health services. Once stably housed, people involved in the program made less trips to the emergency room, spent less time in the hospital, and were arrested less frequently.

The financial impact of the program could be dramatic, according to the report, which analyzed the experiences of 890 participants. The cost of services provided to those in the program fell by 60 percent in the year after they found permanent housing (from an average of $38,146 in the year before to $15,358 the next year).

That drop is partially offset by the cost of operating the program (participants receive $825 per month housing vouchers and case management services worth about $450 per month). But, even with those costs factored in, the study found a 20 percent decrease in county expenses related to those residents.

The authors suggest that further research is necessary to properly measure the program’s cost benefit to county taxpayers, but lead author Sarah Hunter said in an announcement Tuesday that the findings “suggest that a permanent supportive housing program that targets people who are both homeless and are frequent users of county health services is feasible and may save local government money overall.”

With close to 43,000 residents sleeping on the street, in parked cars, or elsewhere on a given night, Los Angeles has the highest rate of unsheltered homeless residents in the nation.

Last year, Los Angeles voters approved a $1.2 billion bond to build 10,000 new units of permanent-supportive housing over the next 10 years. Then, in March, county voters signed off on a quarter-cent sales tax bump to pay for an array of supportive services, including some of those offered through the Housing for Health program.