Nearly half a century ago, James P. Warburg, a banker who had taken a job in the early days of the Roosevelt administration, wrote a book called "The Money Muddle." It is a title that could be profitably resurrected today.

Ever since mid-October, obituaries for monetarism have flowed fast and furiously. Monetarism is the notion that government can control the economy only by strictly regulating the money supply. In 1979, the Federal Reserve Board loosely endorsed monetarism. Now many economists declare the marriage ended. Fed Chairman Paul A. Volcker says that it isn't.

Who's right? What makes the answer important is that the economic outlook ultimately depends more on the Federal Reserve than on the president or Congress. Paradoxically, the election was misdirected in this sense. It engaged economic issues, but the agency that most influences the economy -- the Fed -- is deliberately distanced from electoral brawling.

Anyone who doubts the Fed's central role should examine the record. In 1980, the economy didn't grow at all and experienced double-digit inflation. This was supported by roughly a 6.6 percent increase in the money supply. Over the next year, money supply growth dropped to 2.3 percent. The economy collapsed, and inflation declined to about 5 to 6 percent.

Now changes in money markets seem to promise modest recovery. Interest rates on new mortgage commitments have declined from about 17 percent in early July to less than 14 percent now. Michael Sumichrast, chief economist for the National Association of Home Builders, thinks they could decline an additional 1 to 2 percentage points before year's end. He predicts a one-third jump in housing starts in 1983 from this year's estimated depressed rate of a million units.

To say that monetarism failed is to mistake the original dreamy promises of the Reagan administration for the realistic prospects of an economic doctrine. The essential monetarist idea is no more complicated than the old notion of inflation as too much money chasing too few goods. Slow down money and, after a lag of a year or two, inflation will slow.

What monetarism did not promise was a painless slowdown. Indeed, the mechanism by which inflation subsides inevitably hurts. People need money to transact business. With inflation, they need more. If they get less, the economy slows or halts: too many goods chasing too little money. Surplus production capacity, unemployment and depressed profits push prices down.

That process occurred with a vengeance in the past two years. Labor cost increases dropped (from about 10 percent in 1980 to less than 7 percent now) because firms with squeezed profits -- or losses -- couldn't afford to pay more. Oil and food prices moderated primarily because consumers (including overseas buyers) didn't have the dollars to pay higher prices.

This episode's real lesson is that no theory permits a navigated descent from high inflation. In retrospect, the slump was clearly steeper than the Federal Reserve intended. In February, for example, the members of the Fed's key policy-making body -- the Open Market Committee -- gave their estimates of unemployment for the fourth quarter of 1982. They ranged from 8 1/4 to 9 1/2 percent compared with an actual average that surely will exceed 10 percent.

What went wrong? As a practical matter, the Federal Reserve can attempt to control one of two things: the money supply or interest rates (literally: the price of money). Both have their dangers and drawbacks.

Before monetarism, the Fed focused on interest rates. It agreed, in effect, to supply all the funds people wanted at a targeted interest rate. If the Fed judged correctly, this rate would let the economy expand without generating inflation. If the Fed judged incorrectly, then people would borrow cheaply, and the excess supply of money would push up prices.

Precisely that happened. Money growth increased from 4.8 percent in 1974 to 8.2 percent in 1978. Sales of existing homes -- just one sign of the resulting inflationary speculation -- rose by two-thirds, and prices jumped more than 50 percent. This sort of inflation forces the Fed to raise interest rates or risk pumping out so much money that it becomes worthless.

But the current policy of targeting the money supply is also fraught with practical problems. In effect, the Fed agreed to supply a given amount of money and let interest rates take care of themselves. The money the Fed wants to regulate is the stuff people actually use for spending. The monetarist rationale is that there is a historic relationship -- well-established, though neither perfectly smooth nor predictable -- between this kind of money and real economic activity: inflation and expansion.

In the 1950s and early 1960s, defining money seemed relatively simple: cash and interest-free balances. But as inflation rose, people and businesses minimized their cash and checking accounts because holding interest-free balances was expensive. Consequently, devising a workable definition of money becomes progressively more difficult. How much of NOW accounts (negotiable order of withdrawal, or interest-bearing checking accounts) consists of spending money and how much of savings?

This sort of technical problem seems to have turned the Fed's plan for a smooth and gradual decline of money growth -- one with modest pain -- into a sharp plunge that caused economic trauma. Hence, skepticism greeted the Fed's recent announcement that it would de-emphasize its basic money-supply goal (already slightly above its target) temporarily to avoid expected statistical pitfalls. Many economists concluded that Volcker was using technical troubles as a pretext for abandoning monetarism.

That's not clear yet. Weekly money supply changes are inherently erratic, and the Fed typically has tolerated them. Recent declines in interest rates probably stem more from the recession and dropping inflation than a dramatic acceleration of money growth. And the practical difficulties of coming down from high inflation surely have made the Fed wary of repeating the experience.

But the issue remains open because the Federal Reserve -- although unelected -- is inevitably political. The shift toward monetarism reflected the political consensus that inflation was out of hand and something had to be done. Now, the subsequent economic collapse jeopardizes that consensus. The election underlined this uncertainty, but did not dispel it.