WITH THE DOLLAR'S latest lurch downward, the White House has broken its silence on the subject and declared that it wants to see stability. It's the kind of statement that does more harm than good -- like the very similar joint statement last week by the seven big industrial countries. While they express a desire to maintain the present exchange rates with no further slides or swoops, these declarations conspicuously avoid any mention of the steps by which -- if they were entirely serious -- it might be accomplished.

Someone asked at the White House for an explanation of the fall of the dollar and the stock market. "We don't do psychoanalysis," replied the spokesman. But you don't need an analyst to see what's happening. A calculator will suffice. Suppose you were an Asian or European investor wondering where to put your money. Perhaps you think, as some money managers seem to think, that the dollar might fall another 10 percent over the coming year. Interest rates in the United States are higher than in Japan or Germany, but not anywhere near 10 percentage points higher. The exchange risk outweighs any additional interest that you might gain by investing your money here, and you decide instead to put it into a country with a rising currency. The dollar is falling because foreigners don't want to buy it.

As foreigners reduce the amounts of capital they send here, competition rises among American borrowers for a diminishing pool of credit. That pushes interest rates up. Higher interest rates are bad for stock prices; it was a sharp rise in interest rates that led to the great stock market crash last October. When investors and speculators think that they see further trouble with interest rates ahead, they sell.

That's the dilemma. If the administration and the Federal Reserve wanted to defend the dollar's exchange rate, they would have to raise interest rates. But if they did that, stock prices would fall further -- and not only stock prices. It would hurt all the industries that depend on credit, and the country would probably go into a recession.

The Reagan administration has talked a lot about the great desirability of leaving prices to the invisible hand of the market. Now the price of the dollar is in the grip of the foreign exchange market, which is dragging it down to depths that are dangerous both to this country and to its trading partners. The White House would like to break the market's grip on the dollar, but it hasn't been able to find a painless way to do it.