THE HUGE AMERICAN trade deficit is still growing, and imports are still rising fast. In January, according to figures just published, this country imported $16.5 billion worth of goods more than it exported -- another melancholy record. The corrective machinery is already at work: The dollar's exchange rate is falling. But it's a cumbersome process, and the effects probably won't be visible until the end of this year.

Economists call it the J-curve, meaning that the deficit gets worse and the line dips down before it turns around and starts upward toward balance. The reason is that the financial markets that set the exchange rates move much faster than the real economy of boxes and bales of goods delivered on the wharf. In general it takes something over a year for the deliveries to be made, the contracts to come up for renegotiation and the importers to find domestic suppliers to replace their increasingly expensive foreign sources.

The trade statistics for January 1986 reflect the exchange rates as they stood in the last months of 1984. The rate then rose higher to a peak just a year ago and did not drop significantly lower until last summer. That's why the trade accounts are unlikely to show any very great improvement until next fall.

The decline of the dollar is important and necessary, but not painless. Because imported goods will cost more, it means a reduction in the American standard of living -- unless Americans can raise their productivity. For the past year and a half, unfortunately, productivity in this country has been flat.

How much farther does the dollar have to sink to bring the trade accounts back into balance? It will depend on the quality and cost of American products, compared with the foreign goods with which they compete. Abroad, productivity continues to rise.

The Reagan administration has just published its annual trade report, warning that while the United States remains as competitive as ever against Europe, it is losing ground to Japan and the newly industrialized Asian countries. "America's basic deficiency," it observes, "is its inability to save and invest enough to maintain and upgrade its industrial base." The great 1981 tax cut was supposed to launch the country into a great surge of saving and investment. Instead, of course, it has produced an unparalleled wave of consumption resulting in, among other things, the trade deficit.

The very large trade deficits of the past several years have been a signal of things gone wrong deep in the inner workings of the American economy. The falling exchange rate tells you that a remedy is now at work. But it also says that, if Americans want to live as well next year as they are living this year, they are going to have to work a little harder.