The New York City Housing Authority complains that the federal government is providing "$50 million less than what the agency needs." NY Times.
(1) Housing should be a local issue and not a federal issue. Eliminating the entire federal Department of Housing and Urban Development would help reduce the budget deficit by $31.3 billion.
(2) Housing can only be made more affordable by increasing supply or by reducing demand. Basic economics.
(3) Housing vouchers make housing less affordable because they increase demand by increasing the amount of rent that voucher recipients can afford to pay. Voucher recipients wind up bidding against each other for a fixed supply of housing resulting in higher prices.
(4) The economically sensible way to help poor people is to increase supply, which can easily be done by changing zoning laws and reducing other regulatory impediments to residential construction. And the best part of this solution is that it doesn't cost the taxpayer any money at all.