The problem of managing the U.S. economy now is complicated by the war in the Persian Gulf, coming on top of a recession that is cutting tax revenues, increasing unemployment and swelling the federal debt and the budget deficit.

In his congressional testimony this week, Alan Green-span, the chairman of the Federal Reserve, urged Congress not to raise taxes to finance the war, arguing that since nobody knew what the war would cost, it was better to borrow the money, at least for now.Such borrowing would increase the federal debt but would not add to the deficit for the fiscal year 1991, as defined by the Gramm-Rudman-Hollings budget-balancing law.

In the agreement reached in December between the Bush administration and Congress to cut nearly $500 billion from deficits over the next five years, the costs of the military operations in the gulf were excluded from the deficit.

The hostilities are what Congress calls an "off-budget war."

The administration has joined Greenspan in opposing a tax increase, even as officials watch the budget deficit climb, with the extra costs of the savings and loan bailout taking their toll - Treasury Secretary Nicholas F. Brady has just asked for an extra $30 billion for the bailout.

Indeed, in its budget proposal for the fiscal year 1992, due in two weeks, the administration is expected to seek a cut in the capital gains tax.

Such a cut seems unlikely, given the opposition of congressional Democrats, who see it as a tax break for the rich.

Without other specific plans for fighting either recession or inflation through fiscal policy, the administration is really relying on the budget as an automatic stabilizer of the economy against either inflation or recession.

Michael J. Boskin, President Bush's chief economic adviser, said the new budget legislation adjusts the deficit targets for short-run changes in economic conditions: a forecast of higher growth lowers the deficit target and a forecast of lower growth raises it.

He calls this "good economic policy," adding, "There is widespread consensus among economists that government budget deficits should rise if the economy weakens and should fall if it strengthens."

Tax revenues automatically rise or fall in booms or slumps, and government payments, like unemployment insurance, do the reverse, reinforcing the countercyclical effect of the budget.

By shifting attention from the "cyclical" components of deficits or surpluses, Boskin said in an interview, the deficit targets focus attention on reducing the "structural" deficit.

In the longer run, this should reduce interest rates and stimulate investment, productivity and economic growth.

One concern, however, is whether the war's cost might overwhelm the automatic stabilizers.

Greenspan this week estimated the cost of the air war at "several hundred million dollars a day" but "probably under half a billion a day."

Military planners put the cost of an air-ground war at $1 billion a day, but this is a very rough number.

Much depends on the intensity of the war and whether one uses total costs, including sums already in the military budget, or incremental costs - the extra costs of using reserve troops, fuel, ammunition and so forth - and whether lost equipment is replaced.