THE WHITE HOUSE is making an important mistake in dawdling over the next appointment to the Federal Reserve Board. In June one of its members, Lyle E. Gramley, said that he was going to resign. He has now departed, but despite the ample notice, President Reagan has done nothing visible about a replacement. That encourages speculation that he is waiting until January, when Charles Partee's term expires and another seat opens. Since Mr. Reagan has already appointed two of the board's seven members, the vacant seats would give him, in at least arithmetical terms, a majority. As the delay over the first seat continues, the struggle over this possible majority is becoming increasingly polarized and polemical among the various denominations of conservative economics.

Mr. Reagan does not disguise his opinion that economic doctrine makes little practical difference one way or the other. He appoints people to economic policy jobs the way the mayors of big cities sometimes choose among their ethnic constituencies for seats on the Sanitation Board -- not on the grounds of who's right, but rather who's entitled to recognition. It's one thing for the president to appoint the Council of Economic Advisers that way, but the Federal Reserve Board has actual operating responsibilities of formidable dimensions. It exercises a large day-to-day influence over the national economy -- a larger influence currently than any other part of the federal government.

It is a source of deep annoyance to the White House that most people in the financial markets, here and abroad, credit Paul Volcker, the chairman of the Federal Reserve -- and not the Reagan economic program -- for the drop in the inflation rate. But annoying or not, that opinion exists, and the Reagan administration will endanger its own intrests if it lets people think it is trying to undermine Mr. Volcker by appointing his critics to the board. The first effect would be a ripple of warnings of higher inflation, and the second would be higher interest rates.

The course of the American economy over the next several years is going to depend mainly on international influences -- the flows of capital from one country to another and the exchange rates. The Treasury Department's interest and resources in the international field have declined for some years, and its top command is now focused on a wholly different concern, the president's tax bill. Most of the government's expertise in international finance is now concentrated at the Federal Reserve. It is not a good moment to incite diversionary quarrels there over the fine points of supply-side theory versus monetarist theory. The next appointees to the Federal Reserve need to be named promptly -- people who can contribute to the crucial work that is now being carried on there and nowhere else in this government.