The smaller federal budget deficits targeted by the Gramm-Rudman-Hollings deficit reduction bill would improve the U.S. economy's growth prospects in the long term and perhaps in the short run as well, economic analysts said yesterday.

The cuts in federal spending required to meet the bill's deficit targets would tend to slow down the economy at first, but that effect might be more than offset by the stimulus from sharply falling interest rates, the analysts said.

A growing expectation that the bill would become law and reduce future federal borrowing has been one driving force behind a recent strong rally in the bond markets.

Some long-term interest rates have dropped by nearly a full percentage point in the last two months to reach their lowest levels since 1979. For instance, in some parts of the country, rates on 30-year fixed-rate mortgages are nearing 11 percent. Long-term government bond yields are close to 9 1/2 percent.

The prospect of smaller future budget deficits and lower interest rates also has been a major factor in an equally strong rally in the stock market. A rising stock market adds to household wealth and helps encourage consumer spending, the analysts noted.

Lower long-term interest rates would encourage more business investment, adding to the economy's growth potential, they said. Housing construction also would get a boost.

In addition, lower interest rates would tend to reduce the value of the dollar on foreign exchange markets, which in turn would help lower the nation's large trade deficits.

If the Federal Reserve eased monetary policy to offset the restraining effect of the deficit reductions on the economy, as many financial market participants expect it would, then short-term rates also would drop. In that case, bank lending rates would drop and many business borrowers would find their operating costs falling and their profits rising.

Declining rates also would ease the big interest bill owed by developing nations on their foreign debt.

However, all of those positive factors must be weighed against the fact that either federal spending cuts or tax increases would directly reduce economic activity. If spending is cut, the government would be buying fewer goods and services than it otherwise would have and recipients of some types of federal benefits would have less to spend. If taxes are raised, those paying the higher taxes would have less to spend.

Allen Sinai, chief economist of Shearson Lehman Bros., said the prospect of lower deficits has produced a "sea change" in the financial markets. "Gramm-Rudman-Hollings has extraordinary significance for financial markets and the potential longevity of our expansion," he declared.

"Long-term Treasury bonds are headed for 9 percent," Sinai continued. "It's amazing, but it is what one ought to expect with such a reversal of the policy mix" toward a tighter budget and easier money. "It certainly means permanently lower long-term rates, maybe single digits for the rest of the decade."

Sinai said that the lower interest rates and higher stock prices would "give a big boost to the economy" and more than offset the restraining effect of lower government spending. He expects mortgage rates to fall another three-quarters to a full percentage point.

At E. F. Hutton, chief economist Robert J. Barbera also thinks Gramm-Rudman-Hollings would give the economy a boost. "Deficit-cutting measures large enough to change the out year fiscal outlook . . . must be large dollar amounts -- in the tens of billions -- and such reductions, left uncomplemented, will surely contract economic activity," he wrote recently in a weekly commentary.

"Nonetheless, the current level of short-term interest rates remains outrageously above historical levels, providing the Fed with enormous room to lower short rates to prod economic activity ahead," Barbera wrote.

"The simple mathematics are that we have, at present, both very large budget deficits and very high interest rates. Should paring of budget deficits prove to be a sharp negative for U.S. expansion, much lower rates are easy to come by to balance the outcome," he continued.

Barbera added, "A move to reduce budget deficits may contribute to a slowing in the growth in U.S. nonfinancial debt, thereby improving the outlook for durable disinflation."

Other analysts, such as Roger E. Brinner, chief economist of Data Resources Inc., are less certain that the short-term impact of the spending cuts would not depress the economy even if the Fed eases.

For one thing, the economic impact of a spending cut comes about four quarters after the cut occurs. The maximum effect of lower interest rates comes about eight quarters after the rates fall, Brinner said. However, the way in which financial markets are moving in anticipation of the deficit reductions -- which will not begin until March and not in a major way until next fall -- offsets a substantial portion of this difference in the speed with which the two policies work, he acknowledged.

Brinner also pointed to another potential problem with the Gramm-Rudman-Hollings deficit targets. The current Data Resources forecast calls for a particularly weak economy in the first half of 1986, with the gross national product rising at an annual rate of less than 1 percent.

As a result, he said, federal revenues will be about $27 billion lower than the latest official Reagan administration estimates. Even with a resumption of stronger growth later next year, the revenue shortfall in fiscal 1987 will be about $35 billion, he said. To reach the 1987 deficit target of $144 billion would require some combination of spending cuts and revenue increases of around $55 billion.

The DRI forecast specifically shows a decline in real GNP at an 0.3 percent annual rate in the first quarter of 1986 and an increase at a 1.7 percent rate in the second. Together they average a gain of only 0.7 percent.

Under the terms of Gramm-Rudman-Hollings, if real GNP actually grows at less than a 1 percent rate in two consecutive quarters, in the following quarter the director of the Congressional Budget Office is supposed to notify Congress of that fact. The majority leaders of the House and Senate are then required to introduce identical joint resolutions suspending the deficit limitation for that fiscal year and for the following year.