Office of Management and Budget director David A. Stockman has cleared a regulation designed to break the logjam in federally subsidized housing construction by compensating developers for the high cost of money.

The announcement was made at a press conference yesterday by Housing and Urban Development Secretary Samuel R. Pierce Jr. and Rep. Marge Roukema (R-N.J.). More than 50,000 housing units that had been authorized but stalled "in the pipeline" can now be built, they said.

Pierce gave Roukema most of the credit for pushing OMB to clear the regulation, which had been sent up by HUD, but sent back to the department for more review.

For two weeks she had tried to mobilize bipartisan congressional support and pressure Stockman to give in, calling his opposition to the regualtion "penny wise and pound foolish" and "extremely shortsighted" in view of the continuing housing shortage.

Roukema acknowledged she recently had voted for a bill that would cut low-income housing severely. She said she shaes a widespread concern that "Section 8 [subsidized housing] has grown too fast, become too costly and will need some restructuring." But money for the housing affected in yesterday's agreement, she said, had already been authorized in previous years' budgets.

The new agreement permits HUD to adjust the subsidized rents for housing units to reflect higher interests rat es developers now must pay to finance the projects.

The interest rate on development loans, usually made through tax-exempt financing by state housing agencies, was 7 1/2 percent when the old rent subsidies were established. The new finance adjustment can accommodate up to 12 percent. Work on HUD-sponsored housing projects had virtually ceased in the absence of this accommodation.

The adjustment will require no increase in the HUD budget, Pierce said. While more money will be spent per housing unit, fewer projects will be built than originally authorized.