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Will slack economy check inflation, or money growth heat it up?

Martin Feldstein apparently belongs to the ''economic slack'' school of inflation forecasters. During a recent visit to Boston, the chairman of the President's Council of Economic Advisers admitted that the recovery was continuing at a rapid rate in the first quarter of this year. But, he said, ''there is just no evidence the pace of the recovery is putting upward pressure on inflation.''

In fact, he counts on slack in the economy to keep the inflation rate to about 5 percent this year.

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Lawrence A. Kudlow, a Washington economic consultant, adheres more to the ''monetarist model'' of inflation. He figures that the rapid growth rate of the nation's money supply since mid-1982 suggests a new surge of inflation this year and in future years - perhaps 7 to 10 percent.

Who's right?

Well, time will tell for sure. So far this year, the consumer price index has been rising at a 6.1 percent annual rate, somewhere in between the two forecasts. Now a Federal Reserve Bank of San Francisco economist, Adrian W. Throop, has carried out an economic exercise to test the two views. He uses two econometric equations to model the two views.

One incorporates the impact of unemployment levels on inflation - that is, slack in the economy. It assumes that prices are primarily determined by a markup over labor costs per unit produced of a product or service. When labor markets are tight, wages will rise faster, and thus costs, and finally prices.

The other equation assumes that inflation is primarily a monetary phenomenon. It assumes that inflation tends to follow the path of narrowly defined money (M- 1), with an average lag of two to three years. So, with M-1 expanding by 13.4 percent from July 1982 to July 1983 - the highest sustained monetary expansion since World War II - inflation should be picking up pretty soon.

Economist Throop uses as his measure for the inflation the ''implicit price deflator for personal consumption expenditures, excluding food and energy.'' This special measure is used in an attempt to exclude so-called price ''shocks, '' such as OPEC oil price boosts, that could distort the test.

His two equations are ''estimated'' or based on the years 1964 through 1980. Both equations work well in that period. To the extent economic slack affects inflation, its influence appears to have been captured already by past monetary growth for that test period.

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But after 1980, the forecasts of the two models differ considerably. The economic slack model tracks the decline in the inflation rate during 1982 and 1983 quite well. It makes an average absolute error of only 0.9 percent.

By contrast, Mr. Throop notes, the monetary model overpredicts inflation ''quite badly'' in 1982. The average absolute error (inflation is looked at quarterly) amounts to 1.7 percentage points. It does even worse at 4 percentage points in 1983.

For 1984, the monetary model forecasts a 9.2 percent inflation rate from the fourth quarter of 1983 to the fourth quarter of 1984. The slack model predicts 6 .1 percent, which is probably about where that particular measure of inflation ran in the first quarter. It is, incidentally, precisely the figure for the first two months at an annual rate for the consumer price index.

The monetary model assumes M-1 growth of 6 percent this year. That is what Dr. Feldstein recommends for monetary growth (as long as national economic output remains on target). The slack model is based on a reduction of unemployment of 0.8 percent this year, which is what one sample of economic forecasters has predicted on average.

This same sample, compiled by the American Statistical Association and the National Bureau of Economic Research, forecasts a 5.4 percent inflation rate this year (as measured by the gross national product deflator, a broad measure of inflation).

Throop figures the slack model will provide a better inflation forecast for 1984 than the monetary model, because it was more accurate in 1982 and '83, and because it is closer to the consensus forecast of economists.

Feldstein notes how the economic recovery started from ''a deep hole.'' He added: ''So we are still a long way from a capacity ceiling.''

On the other hand, he is concerned that the need for financing the huge federal budget deficits will put pressures on the Federal Reserve System to expand the nation's money supply too rapidly. ''Experience does not give us much confidence for complacency,'' he says.

Mr. Kudlow, former chief economist at the Office of Management and Budget, mentions an economic study showing that the Fed tends to monetize (finance) 20 to 25 percent of the yearly increase in federal debt held by the public. With large deficits, that would be inflationary.

He also refers to a leading index of inflation created by Dr. Geoffrey Moore of the Center for International Business Cycle Research. It predicts faster inflation.

On balance, where will inflation fall? A compromise between the two inflation theories would put the rate around 6 percent.