Boston — There's a huge gap between scientific economics and Washington economics. That was shown clearly by the storm created when a member of the President's Council of Economic Advisers, William A. Niskanen, told a conference of mostly conservative economists that ''there is no direct or indirect connection between deficits and inflation.''
It was an offense to long-standing Republican doctrine, which holds that federal deficits are evil and inflationary. Moreover, Congress had just gone through the trauma of restraining federal spending, mostly on the basis of fighting a war on inflation.
In a Senate debate, Budget Committee chairman Pete V. Domenici (R) of New Mexico, called it ''a most incredible statement.'' Colorado Sen. William L. Armstrong (R) termed the Niskanen statement ''a malevolent metamorphosis.''
All the fuss and feathers showed was that Washington politicians rarely have time or inclination to learn genuine economics - the results of modern, scientific economic analysis. Within such analysis there remains plenty of room for dispute and choice. But it is difficult to quarrel with some of the findings of econometric (a combination of mathematics and economics) research.
Here are some of the ''facts'' about federal deficits, noted by Benjamin M. Friedman, a Harvard University economist and head of the National Bureau of Economic Research's program in the financial area:
* There is no tie between inflation and federal deficits unless the deficits are ''monetized,'' that is, they are financed by the Federal Reserve System. If the public buys Treasury bills and bonds, no new money is created. The public gives up some of its money, which is then spent by the government and thus returns to the public. If the Fed buys federal debt, it merely writes a check and the government spends it. This creates money out of nothing.
If the Fed keeps the growth of money slow, then inflation would probably decline even if the federal deficit was increasing. Or, vice versa.
* An increase in the federal deficit, if prompted by either a boost in government spending or a drop in taxes, would likely give the economy a boost. But this rise in business activity will be short-lived if the Fed does not pump up the money supply at the same time. Indeed, the expansion could slow down or be reversed after several months.
* Over the longer term, federal deficits can damage the economy by making money more expensive or less available for private enterprise.
Mr. Friedman has done some recent research which shows that when government debt rises in proportion to GNP, private debt goes down relatively. Or see-saw-like, private debt can rise more when government debt drops in proportion to GNP. In other words, Mr. Friedman finds some merit in the ''crowding out'' theory - that government debt can crowd private debt out of the money markets.
In practical terms, this means that if the federal deficit becomes large, private investors will have less money to spend on modern new plant and equipment. So the nation's productivity will rise more slowly. Gains in the standard-of-living will slow down. The US will be less competitive in international markets.
After the Niskanen remarks stirred up Washington, his boss, Council of Economic Advisers Murray L. Weidenbaum asked another audience to rise, raise their right hands, and say with him: ''Deficits do matter, do matter, do matter.''
Mr. Friedman agrees. He described the Niskanen statement as ''limited'' in that it did not point out the long-term danger from huge and continuing federal deficits. He found it ''ironic'' that the importance of deficits should be in any way played down by the Reagan administration, since it is pledged to ''supply-side economics'' and the stimulation of capital formation.
There are a few other clarifying points that should be made about the budget and the deficit:
1. President Reagan has not reduced government spending, despite impressions to the contrary.
H. Erich Heinemann, an economist with the investment banking firm of Morgan Stanley & Co., notes that since the Reagan administration took office last January, government expenditures have increased at a compound annual rate of 10. 9 percent. Nondefense outlays have risen at a rate of 10.7 percent, while defense spending is up at a rate of 11.6 percent. But this rate of gain is far below the 19 percent surge in government spending during President Carter's final year in office.
2. A major reason for the increase in the deficit is the slide in the economy. Revenues decline and spending for unemployment benefits and welfare increases.
3. The projected deficits are not unusually large in relation to nominal GNP. A deficit of $100 billion, for instance, would come to about 3.2 percent of GNP in 1982. That is far below the postwar peak of almost 7 percent in 1975.
4. Measured by what economists term the ''high-employment'' budget, which assumes full employment, the budget was in surplus by $17.2 billion in fiscal year 1981. In summary, deficits do matter to the economy. But mostly in the long run.