US money growth has some economists predicting fresh inflation

''We at the Federal Reserve System recognize that the country paid a very big price to get inflation under control,'' said Frank Morris, president of the Fed's Boston branch. ''We are not going to let that effort go down the drain.''

There's no doubt about the determination of such Fed policymakers as Mr. Morris to prevent a recurrence of rapid inflation. But there is a suspicion among some economists that the genie may already have been let out of the bottle.

''I think they are playing with fire,'' said Michael Hamburger, an economic consultant on Wall Street, who is a former economist with Office of Management and Budget.

What concerns economists of the monetarist school is that the nation's money supply - the fuel for the economy - has grown rapidly over the last two years. M-1, the total of checking deposits plus currency in circulation, grew about 8.5 percent in 1982 and 10 percent last year. This year, Mr. Hamburger guesses, it could grow another 7 percent. That three-year growth is as high as ever, or higher, he says.

Financial innovation, such as the introduction of Super-NOWS, may have added something to the growth of M-1, so that it might be more accurate to put 1982 growth at 7 or 8 percent and 1983 growth at 8 or 9 percent. Nonetheless, such money growth numbers are similar to those of the late 1970s, when the United States moved into double-digit inflation rates.

''If we throw away all past history, maybe we will come out all right on inflation,'' Hamburger says. ''But I find it hard to do that.''

So he is anticipating a rise in inflation to 6 or 7 percent by the fourth quarter of this year, as measured by the broadest measure, the gross national product deflator. Of course, that's not a double-digit rate. But it is above the 5 percent rate forecast by the President's Council of Economic Advisers.

There are, on the other side, some restraints on inflation.

For one thing, the Fed did succeed in bringing down the rate of growth of money in the second half of 1983. The latest revisions of the money numbers show the decline was not so precipitous as originally thought. Money was still growing at a 4.8 percent annual rate in the last quarter, instead of the 2.1 percent originally reported. That erased some fears that economic growth would soon slow dramatically or actually come to a halt.

Further, the major industrial countries of the world are not on a lock-step march to inflation, as most were in the 1970s. Nowadays, inflation is not only a national phenomenon - it can be international. James Lothian, vice-president of Citicorp Global Investment Banking, and Michael Darby, a professor of economics at the University of California, Los Angeles, maintain in a new book that world inflation from 1955 to 1976 was caused by increased money supplies in the US and other countries, not by rising OPEC prices or other special factors.

The US acceleration of money growth in the late 1960s and '70s, they assert, was the primary instigator of inflation both at home and abroad. Other nations, trying to prevent a rise in the value of their currencies, pumped up their supply of money and therefore prompted more inflation.

Oil price increases and other such factors had an impact on prices, but that impact was neither continual nor substantial, they argue.

International Monetary Fund statistics show that the rate of monetary growth in the industrial countries has been edging up again - to an annual rate of 10.4 percent in the third quarter of 1983 from 10.1 percent in the second quarter.

This time, however, some nations have had rapid money growth and others slower growth. Three key countries, West Germany, Japan, and the United Kingdom, have had only moderate growth in their money supply.

Thus Mr. Lothian sees an increase of ''a couple percentage points'' in inflation, but not worldwide double-digit numbers. ''It is a question of how quickly it (more inflation) comes, not in which direction we are going,'' he says.

The Fed's Mr. Morris pointed to another saving feature of the US economy: Productivity has been rising rapidly. This enables management to absorb greater increases in costs without raising prices. Mr. Morris notes how management has become cost control oriented, and labor more flexible in making work rule concessions. These factors, he says, have ''greatly enhanced'' the nation's chances for keeping inflation down in the 1980s.

Making the Fed's anti-inflation job more difficult, Mr. Morris says, is the federal government's budget deficit. He recalls how when he was at the Treasury in charge of debt management in 1963, total outstanding federal debt - built up from George Washington to Jack Kennedy - was about $300 billion. Now there's talk of deficits reaching that level in one year alone later this decade - if nothing is done about trimming the deficit.

The consensus of economists, as reflected in a survey of some 46 forecasters by Blue Chip Economic Indicators, puts the GNP deflator this year at 4.7 percent.

The year did not get off to a good start on inflation. The producer price index jumped 0.6 percent in January, a jump which equaled the increase for all of 1983. Practically all of the increase was accounted for by a bulge in food prices, caused by a combination of last summer's drought and more recent freezing weather.

However, according to monetarist economists, such a surge in inflation cannot last unless it is permitted to by rapid growth in the money supply. The Fed's new target calls for money growth of 4 to 8 percent. That is modest enough to meet the ''guiding principle'' of the Administration's approach to monetary policy as spelled out in the Council of Economic Adviser's annual report - ''. . .the rate of growth of the money stock should be reduced gradually until the rate is consistent with price stability.''