Starting Jan. 1, banks and other thrift institutions can offer customers new accounts which will pay interest on deposits, as well as providing checking services. This is just one of several banking innovations over recent years. Some have been a result of Congress changing the banking laws and some of high inflation and high interest rates.

New banking services generally are welcomed by the public, but do they make the Federal Reserve Board's job of controlling the money supply impossible ?

The main task of the Federal Reserve Board is to monitor and control credit conditions -- chiefly, at least in recent times, with the aim of bringing down inflation. But rapid changes in banking laws and practices -- and the fast-growing sophistication of financial markets -- is making the Fed's job harder and harder.

Its money policy is expected in target ranges for the growth of money and credit in the economy. The Fed spells out these targets and then operates in the market to bring the actual growth in the various money aggregates into line with the targets.

But it seems that as fast as the Fed works out which targets would be appropriate -- given the state of the economy and the rate of inflation -- the meaning of the numbers changes.

Earlier this year, the Fed overhauled the various measures of the money supply to take into account changes in the banking laws and to make the measures more reliable guides to credit conditions. But already there are new changes -- chief among them the introduction of NOW [negotiable order of withdrawal] accounts starting next January, which threaten to distort the redesigned measures next year and to lead to considerable comfusion about whether policy is tight or loose, anti-inflationary or not.

A Fed economist remarked recently that it is "unquestionable that it will be difficult for outsiders, and for the Fed, to guess Publicly, the Fed has not tried to hide the problem. Chairman Paul A. Volcker admitted last month in letters to the chairmen of the House and Senate banking committees that there is "substantial doubt" about the likely impact on the money measures of institutional changes next year.

The uncertainty has been compounded by an apparent shift this year in the relationship between the narrow measures of the money supply and the level of eonomic activity. The Fed has to judge whether the shift is here to stay before it can be sure of which targets to pick. All of this made Volcker and the other members of the Fed's Open Market Committee extremely reluctant to chance their arm on any figures for next year's target ranges.

Congressional pressure finally pushed them into giving out some figures July 29, after an initial refusal to announce them a week earlier with the midyear report to Congress on monetary policy.

But the targets are hedged with qualifications and are liable to be changed even if the Fed does not change its view about monetary policy. Volcker said in his letter that the FOMC was "frankly concerned that changes in numerical targets . . . will give rise to confusion even when (perhaps particularly when) such changes are purely in response to a technical, institutional change that has no real significance for monetary policy."

It will be even more confusing if there are changes that do have such significance. These are likely if the Fed finds itself out on a limb as the only policy maker fighting inflation and is then forced to trim its aims.

But it is more likely the FOMC will tinker with the target ranges in an attempt to leave the underlying money policy unchanged as more information comes in on just how the money measures are being doctored.

There are three main areas of uncertainty. The first concerns the likely impact on the two narrowest measures of money, M1-A and M1-B, of the introduction of NOW accounts across the country.

The second is the effect on the next narrowest measure, M2, of continued rapid growth in money market mutural funds.

The third is the possible impact on narrow money growth of the apparent shift in the public's demand for cash balances.

The Fed estimates that NOW accounts could depress the rise in M1-A next year by anything between 1 and 5 percent and swell the growth of M1-B by between 1/2 and 2 1/2 percentage points. Since this year's targets are for growth of only 3 1/2 to 6 percent for M1-A and between 4 percent to 6 1/2 percent for M1-B, the possible confusion is huge. The variation in growth due just to technical change could almost swamp the underliving rate of growth.

The Fed's estmates are based on the experience of New England states, which already have introduced NOW accounts. They found that people shifted money from both demand deposit accounts and savings accounts into the new NOW accounts. These combine some of the advantaged of both by paying interest and providing checking facilities.

The first movement depresses M1-A, as this aggregate includes demand deposits but not NOW accounts. All the other aggregates are unchanged as they include both. The second movement bumps up M1-B as it takes in NOW accounts but not savings accounts.

But one problem with relying on the New England experience is that both consumers and banks are now more used to the idea of NOW accounts and may well build up their use of them more rapidly than was the case in New England. On the other hand, banks already are able to offer a similar service with the Automatic Transfer of Savings (ATS).

This allows customers to write checks knowing that if there is not enough money in their checking accounts to meet the bill, money will be transferred automatically from their savings accounts to pay it.

Banks now have begun to promote this service more actively, perhaps hoping to win customers who might otherwise open NOW accounts at thrift institutions when they become available.

Thus some of the expected bulge in M1-B may occur this year as money moves from ordinary savings accounts to ATS accounts (the latter are in M1-B).

So far, ATS accounts have attracted mostly large-balance customers, but until recently banks have not tried hard to promote these accounts.

Fed economists believe that eventually customers will shift all of their checking balances into NOW accounts, where they will earn interest. But they will be watching closely to see how quickly the shift comes about.

They, along with most other people, were surprised by the speed with which money market mutual funds have boomed. These funds have drawn money from many other sources, including passbook savings, time deposits and holdings of Treasury bills. Many of the alternative investments are in the new M2 -- as are money market mutual funds -- but some are not. To the extent that money is switched out of Treasury bills, for example, into money market mutual funds, M2 growth is boosted artificially.

It adds to the Fed money watchers' problems that they cannot be sure how permanent the latest shift will prove to be.

Although new developments in banking, such as the NOW accounts, may be good for the public, they certainly present headaches for Fed economists. And although the latest areas of uncertainty probably will be ironed out over the next year, more may well take their place after that.

Monetary policy is a major plank of anti-inflation policy, but in the crucial year ahead controlling the money supply could be like steering a ship with faulty navigational instruments.