The Department of Housing and Urban Development's housing voucher program will aid fewer families than expected because HUD underestimated the number of large units needed and overestimated tenant income, according to the Congressional Research Service.

A CRS study says the $87.7 million allocated to the program in 20 cities and counties will provide 11 percent, or 530, fewer housing vouchers than HUD planned. The shortfalls will soar to 44 percent in Dayton, Ohio, 39 percent in Houston and 37 percent in the Buffalo area, according to the survey, which was requested by Sen. Donald W. Riegle Jr. (D-Mich.), ranking minority member of the Senate subcommittee on housing and urban affairs.

HUD told local and state housing agencies in the 20 areas that they would receive enough money to provide vouchers for 4,588 units, but the jurisdictions say the funds will cover only 4,058 units, according to the CRS.

A department spokeswoman acknowledged that HUD overestimated tenant income and underestimated unit-size needs. The public housing authorities' tallies of vouchers that can be provided, however, "are still estimates. . . .They're probably better than our estimates, but we won't know until families actually find units what the vouchers will cost," she said.

The 20 cities and counties are taking part in an experimental program designed to demonstrate the effectiveness of vouchers in providing housing for low-income families. The demonstration, one of several under way to test aspects of voucher use, will compare the experiences of families using vouchers in large urban areas with those of families receiving aid under the Section 8 program. Section 8 has been the major low-income rental-assistance program for the past 10 years.

Congress authorized the demonstration in 1983, and the areas chosen to take part were announced in July 1984. The money was not distributed to the local agencies until this June, however.

Eight of the 20 housing agencies, including the Housing Opportunities Commission in Montgomery County, have issued vouchers to tenants so far, and a small number of the families receiving them have found HUD-approved apartments, according to Morton J. Schussheim, CRS senior specialist in housing. HUD reported that the delays in issuing vouchers are caused by the need to give a Section 8 certificate to a comparable family at the same time.

Under the voucher plan, families spend up to 30 percent of their income for housing, with the vouchers covering the difference between that amount and the fair-market rents established by HUD. Unlike Section 8, families could find more expensive housing and pay the extra amount themselves. The voucher payment is always the difference between 30 percent of family income and the HUD-established fair market rent, so that a tenant who finds housing for less than the HUD payment standard can keep the savings.

HUD Secretary Samuel R. Pierce Jr. has described vouchers as "a dramatic improvement," and said the department wants to channel the majority of its low-income housing aid through vouchers.

Early indications are that vouchers may be more costly than HUD envisioned, however. Officials at four of the demonstration sites, including Montgomery County, said the difference between HUD estimates of the number of vouchers that could be provided and the projections of local authorities ranged from 6 to 11 percent. Six other areas reported the differences between HUD and local counts ranged from 16 to 21 percent, and Boston estimated that the money it received would cover 26 percent fewer units than HUD expected.

In six cities, which account for about half the total budget for the demonstration, HUD and local authorities agreed in their estimates of the number of families that could be assisted with vouchers, the CRS reported. The cities are Los Angeles, San Diego, Minneapolis, New York City, Pittsburgh and Seattle.

The major reason for the shortfall in seven of the areas was an unrealistically low projection of the number of large housing units that would be needed, according to the survey. In framing the demonstration, HUD assumed that two-bedroom units would be the average size needed. Local authorities in the seven areas said, however, that the demonstration program required them to provide vouchers to more families needing three or four bedrooms than HUD assumed, the CRS said.

Overestimation of family income was cited by four jurisdictions, including Montgomery County, as a reason for the shortfalls. Montgomery housing officials told the CRS that families on the waiting list had incomes averaging less than 30 percent of the county median. The Montgomery average is closer to 25 percent of median than 30 percent, Mary Jones of the county Housing Opportunities Commission said this week.

Houston housing authorities reported that most of the tenants on the city's waiting list average $167 a month income for a family with two children, an amount that works out to 10 percent of the Houston median, the CRS report said.

Officials in four other areas said they would not be able to hand out as many vouchers as expected because the HUD estimates were based on fair-market rent levels established by the department at the time agreements were signed with local housing agencies two years ago. The money allocated in those agreements will pay for fewer vouchers now because rent levels have risen in the interim.

Housing agency authorities in several areas commented that federal requirements for administering the voucher demonstration "seem to be extensive and detailed," the study said. " . . . To the PHAs, such close federal surveillance seems inconsistent with an approach that purports to rely primarily on private market forces and local decisions at the grass roots rather than in Washington, D.C."