The chairman of the Federal Reserve Board said yesterday that the regulation limiting the amount of interest banks and thrift institutions can pay small investors -- Regulation Q -- "has outlived its usefullness" and ought to be changed.

G. William Miller told the Joint Economic Committee that "a change right now would cause distortions" but that when interest rates came down, the Fed "ought to find an occasion to allow small savers to have high yields on savings" now available only to those with at least $10,000 to invest.

Administraion officials said yesterday a study of Regulation Q and other housing finance issues is under way within the administration. Officials said recommendations for change were not imminent, however.

In his testimoney before Congress, Miller said the problem with the regulation was timing."This is a timing problem," he said, Right now, he said, any major change in the regulation, with interest rates as high as they are, would substantially increase the cost of lendable funds to housing mortgage lenders.

Reg Q is strongly supported by savings and loan associations and other thrift institutions because it allows them to pay a one-fourth of a percentage point higher interest rate on a given type of deposit. For instance, commercial banks cannot pay more than 5 percent on deposits in ordinary passbook accounts, while the thrifts can pay 5 1/4 percent.

In most periods of high interest rates, Reg Q limits have caused many savers to withdraw their money to invest it elsewhere, such as in Treasury securities, where rates were higher. As a result, mortgage money has dried up and housing sales and construction fallen sharply.

Last year, the Federal Reserve, with the agreement of the Federal Home Loan Bank Board, decided to allow the thrifts to issue six-month money market ceritficates in a minimum denomination of $10,000 carrying an interest rate tied to that of Treasury bills. Currently, the certificates are paying nearly 10 percent.

Spokesmen for groups of small savers -- those with less than $10,000 to invest -- are complaining that they are being discriminated against. Sen. William Proxmire (D-Wis.) raised this point, and Miller said, "I agree completely" they Reg. Q should be changed to give such savers a break.

"Reg Q came into being for other reasons" and it "has outlived its usefullness," he said. In the meantime, Miller said, some savers were turning to so-called money market funds, which are similar to mutual funds but whose assets are pleaced in financial market instruments, such as certificates or deposit at commercial banks, instead of stocks. An investor can place as little as $1,000 with many money market funds.

Miller said the high cost of lendable funds associated with the six-month money market certificates is causing some institutions to reinvest their proceeds in such things as bank CD's rather than lending the money for mortgages.

"There is some tendency not to flow that money through to housing," Miller said. That means the cost situation os "correcting itself" and it is unlikely that the Fed will have to take any specific action to limit the use of the certificates -- such as lowering the allowable interest rate, which is set under Reg Q.

The administration study began more than a year ago but the various agencies involved, including the Treasury Department, the Department of Housing and Urgan Development and all regulators of financial institutions, have reached no agreement on what to do about Reg Q.