When the finance ministers met in London for the economic summit meeting last month, US Treasury Secretary Donald Regan challenged his counterparts from Western Europe to prove that there was a linkage between large federal deficits in the United States and the level of interest rates. They haven't offered proof yet.
The same challenge had been made at the three previous summits, and none of the six other summiteers responded.
This time, noted Beryl Sprinkel, Treasury undersecretary for monetary affairs , one nation immediately got its economists to crank up its computers to run through the statistics to find such a link. When Mr. Sprinkel met the officials of that nation at a more recent meeting in Europe, they told him in astonishment they actually could not find a connection between the deficit and interest rates. They did, however, see some parallel between monetary policy and interest-rate levels.
(Mr. Sprinkel would not identify the nation, saying it was up to it to release the study.)
'Intuitively, it is nonsense,'' said Mr. Sprinkel in a telephone interview. ''You should be able to find it (such a deficit/interest-rate link). But I have yet to see any evidence.''
Indeed, the Treasury claims to have ''at least 20 studies by individual professors, economists, and the like'' indicating there is no connection.
Nonetheless, others disagree. Martin Feldstein, the newly departed chairman of the Council of Economic Advisers, sees such a link, although some of the CEA staff dissent. Much of the financial community believes there is a connection. And the financial press generally goes along with this view.
Yet the fact remains that interest rates - after subtracting inflation - are far above previous levels. For instance, Richard H. Clarida of Yale University and Benjamin M. Friedman of Harvard point out in recent studies that the three-month Treasury-bill rate was 11.60 percent on average during the 15 calendar quarters beginning in the last quarter of 1979 through midyear 1983. During the immediately preceding 15 quarters the average was only 6.55 percent. Similarly, if inflation (measured by the gross national product deflator) is subtracted from these numbers, the Treasury-bill rate averaged 4.6 percent in the latest period, and slightly negative - -0.3 percent - in the earlier period.
Why so high?
Various economists have varying answers.
The Treasury's Mr. Sprinkel figures it is the financial market's disbelief in the dedication of the Reagan administration and the Federal Reserve System to keep down inflation that has been keeping interest rates so high. Lenders want to offset that inflation with higher rates.
He pointed out that in the early 1970s it took the financial markets some years to adjust to higher inflation, with real interest rates negative for a time. The situation may be similar today in reverse, with market expectations not yet taking account of what Sprinkel says is ''the second full year of major evidence that inflation has come down.''
Economists Clarida and Friedman looked at the period from the major change in monetary policy in October of 1979 (when the Fed concentrated on managing the money supply rather than interest rates) to mid-1983. They found that rates were propped up by unexpectedly slow growth in money supply and unexpectedly rapid inflation. Budget deficits were not the problem at that time.
But Dr. Friedman suspects that at the moment that budget deficits are at least one indirect cause of high interest rates. To support this view, he points to two ''unprecedented'' budget-related trends:
* The cyclically adjusted budget deficit - a deficit calculated as if the economy were running at full employment - is much higher at this stage of the recovery than at a similar time in earlier economic expansions. That adjusted deficit was 0.9 percent of gross national product (total output of goods and services) in 1981; 1.8 percent in 1982; and 2.6 percent on average in 1983, but 3.2 percent for the fourth quarter. The maximum level for that adjusted deficit after the 1973-75 recovery was 2 percent of GNP and for earlier recoveries it ranged from a surplus to a deficit of 1.5 percent of GNP.
* Different from earlier postwar years, the deficits are so huge that they are expanding the outstanding federal debt faster than the economy is growing. So that pool of debt, which was 28 percent of GNP a few years ago, amounted to 35 percent of GNP last fall, and will grow to 40 percent in a few years - unless the deficit is checked.
Another economist, Allan H. Meltzer of Carnegie-Mellon University, offers four possible reasons for high interest rates:
1. Large budget deficits worldwide - not only in the US - increase the demand for money in the world capital markets.
(Beryl Sprinkel says another economist, Milton Friedman of the Hoover Institution, tried to find a correlation here but could not.)
2. A demographic change. The number of those in their borrowing years, aged 18-45, and those running down their wealth (the retired) have increased enormously. But those generally in their saving years, aged 45 to 65, have shrunk proportionately.
3. US fiscal and monetary policies have a ''high variability and uncertainty.'' Investors want a premium of 1 or 2 percent interest to cover the risk involved in, say, sudden changes in bond prices.
4. The yield on money invested in plant and equipment in the US is high compared with other nations. This is because of rapid economic growth and tax changes that increase the after-tax yield on such investments. Other investments - such as bonds or shorter-term financial investments - must offer competing yields, that is, high interest rates.
Referring to these tax advantages, Edward Guay, top economist with CIGNA, an insurance company, says: ''There are too many subsidies for using credit.'' They make high interest rates affordable for many investors, forcing them up for others, too.
Michael J. Hamburger, a New York economic consultant, suspects the cause of high rates is a mixture. Large budget deficits fuel inflation expectations, and thus push interest rates higher. The developing-country debt problem adds to uncertainty. Financial deregulation has removed the ceilings on interest rates on various deposits. And the tax cuts raised the after-tax return on real assets. But by itself no one of these is an adequate explanation, he says.
So, like a detective early in a murder mystery, economists have some clues as to the puzzle of high interest rates, but the mystery has not been solved.