The news that the New York City Housing Authority falsely certified for years that it had inspected apartments for lead paint is a stark sign of how powerless public housing tenants can be and how much the system has eroded.

Franklin Roosevelt’s New Deal established the federal public housing system to provide comfortable apartments with subsidized rents for hundreds of thousands of Americans. But as white working-class families moved out and poorer black and Hispanic families moved in, the federal government’s commitment withered.

Since the mid-1990s, a quarter-million units were demolished or removed nationally because of poor conditions, and the cost of unmet repairs reached tens of billions of dollars.

Public housing fared better in New York than in many other cities, in no small part because of the city’s commitment to providing decent working-class housing. But the federal government has reduced its contribution to the city’s Housing Authority by $2.7 billion since 2001, and the authority now has a repair backlog totaling $18 billion.