More bad news for the poor and their allies: New York City is facing a shortfall of at least $55.5 million in federal housing subsidies this year because of a recent regulatory change affecting the government's primary housing program for poor Americans. The change, retroactive to January, stems from an effort by the Bush administration to control spiraling housing costs. In the past, the federal government paid the full cost of the 1.9 million rent vouchers given to poor tenants nationwide to help them pay for housing under the Section 8 program. But on April 22, the Department of Housing and Urban Development told housing agencies that it would pay only the cost of a voucher as of last August, plus an inflation adjustment. The change could affect more than 900 of the nation's 2,500 public housing agencies, particularly those in cities where rent increases outpace inflation, according to the National Association of Housing and Redevelopment Officials. New York City housing officials say that historically, the local cost of providing vouchers has gone up faster than inflation.