The financial outlook for most Washington-area governments has improved greatly in the past year, but the District of Columbia and Prince George's County face severe budget problems over the next five years that may require tax increases and personnel reductions, a new report by the Greater Washington Research Center, a Washington economics and demographics research organization, contends.

This picture contrasts sharply with five-year projections the group made last year, which predicted large budget gaps in all area jurisdictions in fiscal 1987. In the last study, the combined projected budget gap for all jurisdictions in fiscal 1987 was put at $605.3 million. The new study shows a total projected shortfall for all jurisdictions of $311.2 million for fiscal 1989.

Lower inflation rates, an upturn in the local economy, recent spending cuts by the governments and better prospects for state aid to the suburban governments were the main factors that contributed to the generally improved outlook, the new study found.

But the District can be expected to have a $233 million gap between anticipated revenues and expenditures in fiscal 1989, about 75 percent of the total revenue shortfall projected for all area jurisdictions that year, the study indicated.

The study uses the jurisdictions' latest budgets as a base and projects what would happen to future budgets, using current policy trends combined with various assumptions about economic factors, such as inflation and interest rates. Last year's study had to use 1982 as a base and projected to fiscal 1987. This year's uses 1984 as a base and projects to 1989.

The District's budget problems will be exacerbated by revenues that are not expected to match inflation rates, the lack of state aid to bridge the gap, and rapidly increasing outlays for Medicaid, debt service and Metro subsidy, the report concluded.

"The District's projected budget gaps are too large to be easily overcome," the study concluded. "As a result, it may have to increase its tax rates. It also will have to continue to restrain its spending, perhaps through continued employe reductions."

In addition, the study noted, two federal proposals could add $75 million to the District's projected budget gap for fiscal 1989.

President Reagan has proposed that the city's pension contribution to the Civil Service Retirement System for general government employes be raised from 7 percent of payroll to 11 percent. The federal government is also trying to get the District to assume a larger portion of the cost of operating St. Elizabeths Hospital.

Prince George's County is shown to have a $55.3 million gap in fiscal 1989, due mainly to the property tax cap imposed by the county's TRIM charter amendment, the study said. This shortfall will be difficult to manage without laying off additional employes and cutting programs, it added.

"The other four major governments Fairfax, Arlington and Montgomery counties and Alexandria are expected to experience relatively little fiscal stress over the projection period," the report said. Largely because of a stronger local economy and declining school enrollments, Montgomery County could show a surplus of $18.1 million in fiscal 1989, it concluded.

Fairfax County's financial prospects show the most dramatic improvement in the study. Last year the fifth-year gap was projected at $152 million; this year's study put the fifth-year shortfall at $27.2 million.

The study anticipated strong growth in revenues, largely because new construction is expected to push up property tax collections and economic recovery would mean more sales tax revenues.

Arlington County showed an estimated fiscal 1989 gap of $9.3 million and Alexandria of $4.5 million.

Because all local jurisdictions must balance their budgets each year, the projected gaps between estimated revenues and expenditures represent the degree to which each area may have to cut spending or find new sources of revenue.

This presents a particular problem for the District government because increases in federal aid are not expected to match inflation rates, and taxes already are comparatively high.

Despite the study's assertion that tax rates might have to be increased, the research group's vice president, Philip M. Dearborn, acknowledged that "there doesn't seem to be much room to maneuver" on District taxes without putting the city at a competitive disadvantage with surrounding areas.

Mayor Marion Barry has taken this position in his most recent budgeting, opting against any major tax increases that city officials fear would drive out middle-class residents or discourage business. Instead, the city has balanced the budget through sharp spending cuts and increased user fees for services.

D.C. Budget Director Betsy Reveal said the research group's projections are similar to what the city's have been but that this does not mean there will have to be major tax increases or employe layoffs. The city will try to make programs work more efficiently and will concentrate on promotion of economic development to broaden the tax base, she said.

The most important variable in the budget gap equation is inflation, according to the report, and the budget shortfalls change dramatically when different rates of inflation and local government employment growth are used. The study assumed 6 percent-a-year inflation rate and 1 percent-a-year growth in local government employment.

If the inflation rate is changed to 5 percent a year and no growth in employment is forecast, the 1989 total budget gap drops to $21.3 million; at 8 percent inflation and 1 percent employment growth, the figure grows to $726.5 million.

To deal with the last fiscal year's budget problems, most local governments tried to restrain employment levels and all but the District kept pay raises to about 3 percent, the study said. There were no significant tax increases, it added.