Affordable housing is in short supply in many US cities, perhaps nowhere more chronically than in New York City.  Even though New York has more public housing than any other US city, the demand for subsidized units is far greater than supply. As a result, the city regularly conducts lotteries to allocate available units to eligible applicants.

A recent article in DNAInfo describes the demographics of recent lottery winners.  They tend to be younger than the overall population (those aged 25 to 34 accounted for 45 percent of the total), and a majority of winners were Hispanic or African-American, according to the article.  The article implies that somehow the lottery system is excessively favorable to young adults, but is this the case.  Apparently the Housing Authority declined to provide details on the demographics of the applicant pool, so its was difficult for DNAInfo to tell whether the applicants skewed younger because of some bias in the selection process, or whether because younger people are more likely to apply.

When we compare the demographics of lottery winners with those who are currently in the market for an apartment in New York, there’s little evidence of age-related bias. To see why, take a look at data from the American Community Survey on the age of persons who moved into rental apartments in New York City in 2015.  We downloaded this Census data, tabulated by the age of household heads, from the University of Minnesota’s invaluable Integrated Public Use Microdata System (IPUMS).    The age distribution of lottery winners closely mirrors the demographics of people who’ve moved into an apartment in the past year.  (The DNAInfo article reported applicant age for 1,351 of the 1,470 total winners; our table compares the share of movers in each age group with the share of lottery winners.  While 25 to 34 year olds make up 44.8 percent of lottery winners, they make up virtually the same share of persons moving into apartments (45.5 percent).  Their are slightly more 35 to 44 year olds winning the lottery than their share of recent movers would suggest (19.4 percent vs. 17.1 percent).  Older persons were also somewhat less likely to be lottery winners (making up 5 percent of winners, but 8.5 percent of the recent mover population.  The final column of our table shows the odds (computed over three years), that a person in each age group moving into a new apartment was a lottery winner.  While there’s some variation by age group, overall, lottery winners accounted for about two-tenths of one percent of all renters moving into an apartment in New York City.

Contrary to the headline claim in the DNAInfo article–“City’s Affordable Housing Lotteries Favor Young Single People, Stats Show”–there’s little evidence that the New York City Housing Authority’s lottery unfairly favors 25 to 34 year olds.  The people who are in the market for apartments in New York in any given year tend to fall disproportionately into this age group, so its hardly surprising that they would make up a plurality of lottery winners.

While the article focuses on the demographics of winners, and offers tips from those who have successfully navigated the lottery system, the real headline here is the extraordinarily long odds of getting any housing from one of these lotteries.  For the period 2013 to 2015 covered in these data, New York City awarded housing to a total of 1,470 lucky households; 99.8 percent of new renters got their housing with no help from the lottery.  The housing authority didn’t report the number of applicants, so we don’t know the precise odds.  But we know the demand for some apartments was overwhelming:  Nearly 200,000 households applied for 14 apartments in Bushwick, for example.

The long odds associated with these lotteries is a reminder that our housing problem is fundamentally one of scale:  we have much more demand for housing than supply. Lotteries for affordable housing, like the one’s in New York, and a similar program we profiled that provides discounted condominiums in San Francisco are so small relative to the problem that they really amount to nothing more than token efforts. No one would seriously suggest that we try to redress the nation’s income inequality problems by encouraging people to buy lottery tickets. But given the trivial scale and long odds, that’s effectively what we’re doing with these kinds of housing programs.