Few ideas have caught the popular and political imagination in the way that the balanced budget has.

President-elect Ronald Reagan, President Carter, a majority in Congress and the chairman of the Fed all apparently agree: A balanced budget is desirable and would help to cure inflation.

At least one important member of Reagan's economic team -- designated director of the Office of Management and Budget David Stockman -- believes that the new administration must immediately curb federal spending and cut the deficit in order to fight inflation. He also promises fairly swift and certain results if this is done.

But most economists would, at the very least, question his faith. Far from being an established truth of the economics profession, the suggested automatic link between a budget deficit and inflation is highly controversial. Although many economists agree that deficits can be inflationary at times, few believe that they always are, or that they are the main cause of today's inflation.

Why is there the popular myth?

Perhaps most importantly, there is an appealing simplicity to the notion that governments should not go into debt and that if they do, they will cause inflation by spending money they don't have. This idea also fits in with the conservative view that big government is bad, although there is no intrinsic reason why the two views should be linked.

The fact that inflation is high, that it has gradually -- and then not so gradually -- accelerated over the past few years and that no effective policy has been found to bring it down, sharpens the appeal of any apparent cure. But unfortunately all the evidence shows that there is no simple or painless one.

Rising oil prices, bad harvests, a weak dollar, can all cause inflation. And the inflation of the last five or six years can more easily be blamed on these factors and other direct influences on costs than on federal budget deficits.

It is true that if the government keeps a large deficit when the economy is already running with a high level of employment and little spare capacity, then it probably adds to inflation because it is increasing demand in the economy when there is little room to increase supply. Employes and businesses react by charging more for their labor or products as they find people willing to pay more.

But this overexpansion in the economy due to excessive deficits would feed through into inflation via general increases in wages and prices, and would occur when unemployment was low. In fact, oil and food prices led the way in the acceleration in inflation earlier this year, while increases in wages remained surprisingly weak, and the numbers out of work grew.

The big jump in underlying inflation in the middle of the 1970s was again triggered largely by massive increases in energy costs. These had nothing to do with the United States government's budget deficit.

Of course there are economists who argue that inflation is caused by the government creating too much money -- rather than, for example, by the Organization of Petroleum Exporting Countries (OPEC) raising oil prices -- and that if there is a deficit in the federal budget, there will be pressure on the Federal Reserve Board to create extra and excessive amounts of money to cover it. This money then will lead straight to higher prices: there will be "too much money chasing too few goods." It is assumed that business cannot or does not respond by increasing its output of goods.

But even in this "monetarist" view of inflation, a federal deficit does not lead automatically to higher prices. The government can always finance its deficit by borrowing money, rather than by creating more. And if it is the creation of money that is thought to be inflationary, then as long as the Fed does not create extra money to cover the deficit, that deficit is not inflationary.

Most monetarists, however, would argue that a balanced budget is likely to encourage monetary restraint, and thus be an indirect curb on inflation. They believe that it is easier for the Fed to control money growth without too high interest rates when the government does not need a lot of extra cash on top of its income from tax revenue. And they imply that the Fed sticks to a higher policy in these easier circumstances.

Federal reserve officials would contest that fervently, and with some reason. Although Chairman Paul Volcker complains that the Fed is having to carry too much of the burden of fighting inflation, his and the Fed's commitment to money targets is no less when there is a big budget deficit.

In 1973 money supply rose by over 14 percent while the budget deficit was only 0.2 percent of the total GNP. Two years later the deficit had risen to more than 5 percent of GNP, but money growth, on the same M2 measure, was only 5 1/2 percent.

This year the budget deficit swelled as a direct result of the recession. As output falls and people are laid off during a recession, tax revenues drop automatically in response, while federal spending on unemployment benefits and some welfare payments just as automatically rises.

This does not give an inflationary boost to demand; it merely helps to cushion some of the fall in the economy. Even Volcker, who is a strong advocate of a balanced or more nearly balanced budget, has said that a recession-induced deficit cannot properly be blamed for causing inflation. Although this year has been characterized by sharp and sudden shifts in the economy, and extremely volatile and now record-high interest rates, the underlying inflation rate has dropped slightly during the year.

Another way of looking at the balanced budget argument is to think of how a lower deficit might affect inflation, assuming that the Fed is sticking to its money targets throughout. A move to cut the federal deficit -- for example by curbing federal spending -- would first of all reduce demand in the economy as the government stopped buying so many goods, paying so many salaries or giving so much money to those on social security or welfare.

This first-round effect -- which constitutes a slowdown in the economy or a recession, depending on the severity of the cuts -- may in time have an effect on inflation. Just as boosting demand can encourage people to increase the price of their labor or goods, so layoffs and recession can encourage workers to accept smaller wage rises, and firms to cut their profit margins to hold onto sales in a shrinking market.

Some advocates of smaller budget deficits admit that they will work as part of an anti-inflation policy that involves business failures and higher unemployment to knock down inflationary expectations and force lower wage and price rises.

But many others imply that there is somehow a painless way of "disinflating" without deflating the economy too. Some Reagan advisers suggest that while federal spending should be cut to reduce inflation, taxes should be cut to boost growth.

But cutting spending on its own does not affect inflation, if taxes are cut by the same amount. There is nothing particularly inflationary about the government giving a pay check, rather than giving a tax rebate. The arguments about inflation center on how the government finances its spending, and whether it adds inflationary pressure to the economy by increasing its deficit. It makes no difference to the argument whether the federal deficit goes up or down because of spending or because of tax changes.

If both spending and taxes are cut, and the deficit remains the same, then whatever the inflationary impact of the deficit also remains the same. There is no evidence that government spending is more inflationary per se than private spending. So if budget cuts are to have an effect on inflation, then they must not be accompanied by tax cuts of the same size. And their somewhat uncertain impact on inflation will come through reducing demand in the economy.

There is a further argument sometimes made against budget deficits that large government borrowings are themselves damaging, even if they do not lead to more money being printed. They therefore do not provide a painless alternative to printing money.

If the Fed resists the pressure to create excessive amounts of money, interests rates will be pushed up, the argument goes. This is because the Treasury will have to sell its bonds cheap -- in other words offering high interest rates on them -- to finance the deficit.

Private firms that cannot afford to borrow at such high rates of interest will be "crowded out" of the credit markets. The government will not succeed in stimulating the economy through its higher deficit because the interest rates that result from the deficit will choke off investment, the argument continues.

There are serious flaws in this view. As the last year has clearly demonstrated, high interest rates can certainly help to choke off economic growth. But soaring interest rates this spring and fall were not caused by a sudden rise in government borrowing nor by an administration attempt to stimulate the economy.

Moreover, the state of demand in the economy almost certainly has more effect on business investment than do changes in the level of interest rates. If the government cuts back on its spending, then it is putting less money into the private sector, whether through direct spending on products and services provided by the private sector, or through transfers to private individuals who then spend their money on private sector goods. If it raises taxes, then it is taking more money out.

If budget deficits were the whole story, there ought to be some clear relationship between large deficits and accelerating inflation both in the United States and elsewhere. But both West Germany and Japan have larger budget deficits in relation to the size of their economies than does the United States, while their inflation rates are usually only a bit higher -- and in the case of West Germany considerably lower -- than here.