The spending and tax bills signed yesterday by President Reagan won't actually shrink the federal deficit from the 1987 level, budget experts say, but rather will only keep the deficit from widening significantly.

Moreover, some of the savings claimed in the legislation -- such as provisions that simply shift spending into the future -- have minimal effects on the nation's long-run fiscal woes.

Genuine savings were also enacted, however, and the fact that the White House and Congress finally moved forward with their budget agreement will reduce the risk of disaster in financial markets, economists say. In addition, the outcome pleases America's trading partners, making them more likely to cooperate with the United States in keeping the world economy growing, according to administration officials.

That, in short, is the economic impact of the two pieces of budget and tax legislation that lawmakers spent the past eight days drafting and nearly all night Monday approving.

The first thing to understand about the measures, budget experts say, is that they don't cut the deficit, at least not in the way that most people think. Federal red ink totaled $148 billion in the 1987 fiscal year, which ended Sept. 30. If the economy grows sluggishly next year, as many economists expect, the deficit will probably widen to between $160 billion and $170 billion in fiscal 1988, and further the year after, according to budget analysts in the administration, Congress and outside government.

But such an outcome represents a meaningful accomplishment in that the deficit has been cut from the levels that it would otherwise reach. "Without this, we're looking at deficits jumping back to $200 billion a year," said Carol Cox, president of the Committee for a Responsible Federal Budget, a group of prominent citizens and former government officials.

Cox and others agreed that most of the tax increases contained in the package will raise revenue close to the amounts claimed -- about $9 billion in fiscal 1988 and $14 billion in fiscal 1989. Moreover, Congress achieved some restraint in two fast-growing areas of the budget -- farm subsidies and Medicare, the health program for the elderly. One Senate Republican staffer, noting that actual cuts were made in the target prices for commodities used to determine subsidy payments, said, "I'm amazed we pulled that one off."

But there are a number of questionable savings -- especially in domestic spending accounts -- sprinkled throughout the package. The legislation purports to shrink the projected deficit by $33.2 billion in fiscal 1988 and $45.8 billion in fiscal 1989. Of that two-year, $79 billion total in promised savings, about $1.1 billion is achieved by delaying Medicare payments to doctors and hospitals, so that some of the cost is simply deferred. Another $500 million comes from allowing federal retirees to spread benefits over two years -- again, deferring expenses. Another $500 million comes from a tenuous promise by the Postal Service to improve productivity.

Of all the questionable savings, the biggest is a provision promising to cut more than $7 billion in fiscal 1988 spending by allowing certain entities that have borrowed from the government -- including the state of Israel and rural electrification cooperatives -- to prepay their loans. This brings immediate revenue into federal coffers, but means that the government forgoes even more money later.

To Wall Street and financial markets overseas, the legislation, despite its flaws, provides modest comfort. "If they hadn't done it, there would have been a severe reaction," said Stephen Axilrod, vice chairman of Nikko Securities Co. International. That the budget haggling is finally over doesn't necessarily mean markets will rejoice. Said David Resler, chief economist at Nomura Securities International Inc.: "The broad outlines of the package are pretty much as advertised."

One administration official said that the value to the markets and the nation is primarily symbolic, because "it's important to indicate that the executive branch and Congress can work together."

Perhaps even more significant, this official said, is the potential impact on U.S. trading partners, especially Japan and West Germany. Allied governments have cited the U.S. budget deficit as a major cause of world trading imbalances; the United States, in turn, wants Bonn and Tokyo to adopt measures to absorb more imports. "Without this {implementation of the budget agreement}, where's our negotiating stance?" the administration official said. "What do we say to our trading partners?"

Some analysts said that President Reagan's signature on a tax increase could have another sort of symbolic impact -- improving the political climate for a major tax increase when his successor takes office.

But others contended that the tax increase is so modest that the politics of the issue haven't changed. Said William Schneider, political analyst at the American Enterprise Institute: "Serious deficit reduction has been put off until the next administration."