The Reagan administration's estimate last year that it could save $1.6 billion by reducing the federal work force by 43,000 people was up to $1 billion too high, the General Accounting Office says.

In a report released yesterday by Rep. Geraldine A. Ferraro (D-N.Y.), the GAO said, "OMB officials could not provide any documentation to support their projected savings or the extent to which they considered offsetting costs."

The administration made "a public show of announcing public savings," Ferraro said, but declined to testify on the issue Jan. 20 before a House subcommittee. Ferraro said the projected savings "were unrealistic and undocumented from the beginning."

"If the Congress and the public are to rely on OMB's budgetary cost and savings estimates, it is imperative that OMB document these estimates," the report said. "For OMB to do otherwise diminishes the credibility of the budget proposals and makes it difficult for Congress to make informed decisions on the president's proposed budget."

The GAO said it used the Office of Management and Budget's method of calculation to show a $572 million mathematical error.

It also said that the OMB did not consider an estimated $94 million in severance pay, unemployment compensation and lump-sum annual leave payments that would have to be paid because of the reduction in force, nor did the OMB consider $70 million in early retirement costs or about $148 million in refunding employes' retirement contributions.

Further, the Internal Revenue Service told the GAO last year that its personnel cuts would cost the government an estimated $182 million in tax revenues that would escape audits and collection efforts. (The IRS, however, is now trying to add 5,000 auditors.) The GAO said the cuts also could hurt debt collection efforts at the Veterans' Administration and the Small Business Administration.

George H. Strauss, who heads the OMB division that prepared the numbers, said, "Whether one or the other is right is beside the point.

"I will readily admit that our calculations did not take into account those elements that GAO said were missing ," Strauss said, noting that OMB staffers simply multiplied the number of people that were to be dropped in fiscal 1981 and the number in 1982 by the average estimated salary of a federal employe in those years ($24,500 and $25,676) when they compiled the data last April. Certain other minor adjustments were made.

"The question is: what would be saved if a particular job is abolished?" Strauss said. "Suppose we figured this with GAO numbers? It wouldn't make any difference. Program managers would not have decided not to fire people. It's not that anyone was cheated in any way."

In the fiscal 1983 budget released last Saturday, Strauss said, "We tried to be somewhat more careful . . . this time. Once the entire 75,000 proposed work-force reduction is off the rolls, that's when we save $2.1 billion. It will avoid all of this confusing separation pay, and so forth."

But even the OMB's figures in the fiscal 1983 budget are somewhat confusing. The budget says the administration will reduce the number of federal workers by the equivalent of 75,000 full-time work years, from 1,162,100 in fiscal 1982 to 1,087,100 by fiscal 1984. But Strauss admits that the fiscal 1982 number, issued last spring, is no longer real.

For instance, the Veterans' Administration, which is supposed to grow by 9,300 work years from a base of 209,600 employes in fiscal 1982, has never had that few employes in recent years, according to VA officials. Strauss said the figure "must be used as a comparison, because it's the last figure we announced."

Ferraro disputed Strauss' contention that "no one was hurt by the numbers." "What is particularly annoying," she said, "is the fact that the cuts are hurting the American people."