MOST OF THE unemployed probably have never heard of him, but economist Milton Friedman has had an extraordinary influence on their lives.

More than anyone else, Friedman popularized a theory that has had a critical impact on economic policy in both the United States and Great Britain, as well as in Chile.

The theory, called "monetarism," holds that government can only have a temporary and shortlived influence on unemployment and should concentrate its efforts instead on fighting inflation. Inflation, the monetarists argue, can only be combatted by controlling the money supply, leaving interest rates to take care of themselves.

Friedman rejects the blame, but many economists contend that the recent deep recessions in the United States and Britain are the result of monetarist policies.

These critics of monetarism also say that the collapse of the economy in Chile, where companies and banks are now going bust and unemployment has risen dramatically, can be blamed primarily on the "Chicago boys" -- Chilean economists who studied under Friedman at the the University of Chicago and ran the Chilean economy after the overthrow of President Salvador Allende in 1973.

Moreover, many economists in the United States and elsewhere now think that the main impetus behind American (and world) recovery came when the Federal Reserve began backing away from Friedmanesque principles last summer, allowing the money supply to grow dramatically and encouraging a decline in interest rates.

Milton Friedman, the man behind the controversy, belongs to a small group of 20th Century thinkers whose ideas truly can be said to have affected the way millions of people view the world.

Now in his seventies, the short, feisty economist waited for years in the academic wilderness before governments embraced his theories. He bided his time during the postwar years when public policy was dominated by the ideas of British economist John Maynard Keynes, who stressed the use of government tax and spending policies to influence employment and economic growth. Then came the high and accelerating inflation of the 1970s. Enter Milton Friedman, a man whose time had come.

Along with a set of fresh ideas in a time when the old orthodoxy no longer seemed to work, Friedman brought personal energy and considerable gifts as an intellectual persuader. These qualities made his name, more than those of other economists, synonymous with monetarism.

He was a tireless and brilliant advocate, an engaging communicator on television, the author of a seminal book, with Anna Schwartz, on the monetary history of the United States, and organizer of a famous workshop at the University of Chicago. Friedman's monetarist ideas were not completely new. They drew on classical theories of 19th-century economics. But it was Friedman who updated and popularized those once discredited concepts.

Since then world recession has robbed monetarism of much of its appeal. But as the leaders of the seven major industrialized nations gather at Williamsburg for this weekend's economic summit, it is also evident that monetarism lives on, at least in Britain and the United States.

Margaret Thatcher in Britain remains a firm believer in Friedman, despite her retreat in the past year from slavish attention to her original monetary targets.

And although the Federal Reserve Board here has moved away from strict monetary control, it has stopped short of pushing interest rates down to the sort of levels that were typical in the past and that would ensure a strong and vigorous recovery, because it does not want the money supply to climb too fast. A number of financiers and ecnomists here, and some administration officials, are now complaining that the Federal Reserve has already moved too far away from monetarism. Recent rapid growth could lead to another bout of inflation, they say. But if the Federal Reserve were to return to the stricter money control that they urge, interest rates would climb again, and the recovery most likely would halt in its tracks, leaving unemployment stuck above 10 percent.

Friedman, a long-shot candidate to succeed Paul Volcker as Federal Reserve Board chairman when his term expires in August, is one of those calling for tighter money. But before Americans climb back on the monetarist bandwagon, it is worth looking at how well this theory has served us so far.

Friedman, perhaps naturally, contends that it has not really been tried, at least in the United States. "In the United States the Federal Reserve has never practiced monetarism," he said flatly earlier this year.

The record suggests otherwise.

In October 1979, the Federal Reserve declared that close and direct control of the money supply would be the guiding principle of monetary policy. Volcker himself may not be a monetarist in the strict sense, but the policy the Fed followed after 1979 was monetarist: it stopped using interest rates as a policy guide and tried to bring down inflation through strict control of the money supply.

President Reagan backed monetarism during the 1980 campaign. He said it would reduce inflation while his "supply side" tax cuts stimulated growth and employment. With Thatcher already busily squeezing inflation out of the British economy through tight money, the monetarists cheered and their opponents watched and waited for the results of the dual experiment.

These are now in. In 1981, the United States followed Britain into the most severe recession since World War II. Interest rates were allowed to climb to unprecedented levels and stay there while unemployment rose and production fell.

The Federal Reserve, along with most outsiders, never agreed with Reagan's "rosy scenario" for the economy. It recognized that even though the central bank can restrict the amount of money circulating in the economy, it has relatively little control over how this policy would play out in actual practice. It would probably hold down prices, but it would also choke off some of the nation's economic activity. The key question was how much would the squeeze affect inflation, and how much would it limit production.

The monetarist argument, as expounded by Friedman in Newsweek last year, is that "after about two years, the main effect is on inflation" and that while there is an initial impact on jobs and production from changes in the money supply, this will "wear off."

Critics make essentially two arguments against Friedman and his colleagues.

The first is that for one reason or another monetarism just does not work the way it is supposed to. For example, both here and in Britain policymakers have found that there is, in fact, no close and reliable relationship between the amount of money that they supply to the economy and the amount of spending and production that results. Last year, the Federal Reserve found that its money grip squeezed the economy much more than it had expected.

The money supply kept expanding rapidly, despite the Fed's efforts to keep to the targets that it had promised Congress, but the economy was dead in the water -- killed by continued high interest rates. The supposedly stable relationship between the money supply and economic activity broke down.

The Bank of England had a similar experience in Britain. There, too, the money supply changes gave the policymakers misleading signals, and the government ended up with higher interest rates and more unemployment than it had bargained for.

The critics of monetarism do not suggest that policymakers ignore the money supply. Countries such as West Germany and Japan, whose governments are not rigid followers of Friedman, also take into consideration what is happening to the money supply as one of their guides to policymaking. But it is not the only criterion.

Monetarists, on the other hand, claim that if policymakers attempt to "fine-tune" the economy and to judge monetary conditions by indicators other than the money supply figures, they will get it wrong. But it seems that monetarism has got it wrong too.

Aside from the question of whether controlling the money supply really enables governments to control the economy, both the Fed and the Bank of England discovered in the last few years that it is much easier to set a monetary target than to hit it.

Since the Fed's October 1979 policy switch, the money supply has been on a roller coaster. In Britain, the money supply grew dramatically in the early years of Thatcher's government, despite her aim of a gradual monetary slowdown.

Eventually the money managers on either side of the Atlantic did succeed in slowing money growth, even if not quite when and how they intended to.

But it turns out there are other problems with the execution of Friedman's theories.

In fact, it's extremely difficult to define what the "money supply" is. The point of controlling the money supply is to control the total amount of money that is spent in the economy -- whether on a machine tool, a candy bar or a haircut. But what kind of money?

Should savings be counted? Probably not, since they are not about to be spent. Should the money in checking accounts be factored in? Yes, since people write checks and spend this money from one day to the next. But what about the new high-interest checking accounts, the "supernow" and money-market accounts, that people have rushed to open?

Such are the puzzles facing the measurers of the money supply. The Fed has found the already slippery concept of the money supply shooting out of its grasp.

Since last summer it has stopped trying so hard to chase after it.

The foreign debt crisis last summer, together with still rising unemployment and recession here, finally made the costs of continued monetarism just too high.

That leads to the second main argument against Friedmanism. It hurts too much.

The cost is obvious now in Chile, although the economic disasters of recent months cannot be attributed solely to its government's policies. World recession and high interest rates have also played a big part.

Since the Chilean experiment has turned sour in the last year, Friedman has disclaimed it. He says that the economic freedom that he believes in apparently cannot work without political freedom, absent from Chile since the 1973 coup. He did not, however, push this view while the Chilean repression was at its height and the economic policy apparently more successful. Moreover, it is hard to see how the government could have implemented its fierce anti-inflation policies without taking away the political freedom of such groups as trade unions to oppose them.

Before monetarism had quite choked the U.S. economy, the Keynesian economist William Nordhaus of Yale predicted that it would take 8 percent unemployment here for "as far as the eye can see" to reduce inflation substantially. Reagan's latest economic forecasts show the jobless rate -- now 10.2 percent -- staying above 8 percent until 1986.

A year ago Friedman argued that the U.S. recession was not unusually severe but was in line with the previous ones since World War II. Now he agrees that times have been very hard, but he still does not attribute this to monetarism. "I don't think people have abandoned monetarism because they never accepted it. . . . How can you abandon something you don't accept?"

Instead, Friedman blames the depth of the U.S. recession on the Fed's implementation of monetary policy. He argues that instead of slowing money growth steadily and gradually, the Fed presided over a series of fits and starts, which have confused and upset people, increased uncertainty and reduced productivity, Friedman said.

One problem with this argument is that Friedman does not say just how much extra unemployment could have been caused by the alleged uncertainty. It is hard to believe, however, that it could have been a substantial part of the 10.8 percent peak rate in December. How often do factories close because of uncertainty about the future, rather than because of falling profits and poor sales?

Another key problem: It is not easy to demonstrate that the Fed could have run a smoother monetary policy. Certainly Volcker and his colleagues sought to avoid sharp changes in the money supply. Their failure may well be evidence that volatility has to be accepted as part and parcel of a policy aimed at slowing and controlling monetary growth.

Finally, if inflation has come down largely because companies and their employes have been pushed by unemployment and falling demand into accepting slower increases in wages and prices, then presumably a less severe recession would have led to a smaller reduction in inflation, regardless of the growth of the money supply.

The political costs of monetarism in the United States are now worrying White House officials. Those who argue against Volcker's reappointment make one central point: if Volcker goes, then the whole nasty recession of 1981-82 can be blamed on him, and on the monetary policy that he carried out. They fear that the political price of responsibility for the recession and its unemployment may be a Republican defeat in 1984.

In Britain, Thatcher remains the favorite to win next month's election, although the monetarist pain has been even greater there than here. Voters who still have their jobs are apparently willing to let Thatcher's policies continue.

After all, monetarism does bring some benefits to some people. Inflation, in both the U.S. and Britain, has been cut dramatically since monetarist policies were adopted by the two governments.

But this success does not vindicate monetarism. Economists have long agreed that inflation can be forced down if times are just made tough enough. Confronted with shrinking markets, firms cut their prices, or at least stop raising them as quickly. Their workers, faced with the threat of unemployment, accept smaller wage increases than otherwise.

What the British and U.S. experience has shown is that there is no special magic about fighting inflation through monetary policy. Contrary to the promises of many monetarists and to the hopes of those who followed their prescriptions, it appears that cutting monetary growth works to reduce inflation in time-honored fashion, by throwing people out of work, closing factories and forcing companies out of business. On a world scale, monetary-induced recessions in the industrialized nations have led to sharp declines in prices for commodities ranging from copper to oil. These have fed through to lower inflation here, but at the cost of cutting demand for U.S. goods from many of the strapped nations that sell commodities.

It would be a supreme irony if, in an attempt to avoid blame for recession and claim credit for recovery, Reagan appointed Milton Friedman, the high priest of monetarism, to fashion the nation's monetary policy in the last 15 months before the 1984 election.