THE GROWTH of the American economy is slowing down this year, after rapid expansion in 1977. In Europe, conversely, the growth rate seems to be rising. Both North America and Europe are now parts of one gigantic trading system that tends to draw its members toward an average level of performance. It pulls the leader down and pushes the laggards up. That is what President Carter was talking about in the press conference on Thursday, when he was trying to explain why he expected the dollar to strengthen during the year. One of the reasons for the dollar's slide is the tremendous American trade deficit, which is partly caused by faster growth here than in Europe. "That difference will be substantially less in 1978," Mr. Carter said.

The question is whether the gap will be narrowed more by a decline in American performance or by an increase in the European rates. The Carter administration has been leaning hard on Germany to crank up its economy harder precisely for that reason - the less Germany does to expand its own economy, the more of a drag it will exert on this country's. Economic growth rates are rather abstract and uninviting statistics. But they are kind of shorthand summary of the processes that generate new jobs, greater security and rising standards of living. Growth rates have a lot to do with the atmosphere in which a country's voters go to the polls, whether in France this months or in the United States in November. Politicians have learned to pay close attention to them.

But for the politicians, the quarrel over the growth rates is turning into a quicksand. Voters in the industrial countries are accustomed to thinking that a competent government. But that seems to be less true than it used to be.

The economic techniques for stabilizing a country's prosperity and employment are one of this century's great triumphs of intellect and public policy. They were worked out in the first half of the century and refined in teh postwar years. The period of their greatest success was the early 1960s. For a time, it looked as though the business cycle might have been eliminated and the threat of periodic recessions abolished. But as time passed, other economies in Europe and Asia became much more powerful relative to that of the United States, and volumes of trade rose tremendously. The international system has now become a major influence over every country's economy, including this one's - but the international system is run by nobody in particular. It does not answer to any government, and it is not under any central authority. It is a loose and cautious consensus, slow in its reactions.

It is not a welcome idea that American policy no longer steers the American economy. It goes against the American character to accept that kind of thinking easily. Last week the eminent economist John Kenneth Galbraith, in a letter to this newspaper, proposed that President Carter's economists give themselves one more year in which to get the unemployment and inflation rates down. If they fail, he argued, they ought to resign and give way to others who are "politically and socially more combative." That's an interesting phrase. Prof. Galbraith is not going to give in without a struggle.

It is less heroic, but also more realistic, to doubt that greater economic combativeness in and around the White House will greatly improve matters. In the present uneasy climate, the effect is a good deal more likely to be the opposite. The trouble is deeper than a mere lack of macho.

There is no longer one nation that dominates the world economy. Economic cause-and-effect now travels farther than political authority can reach. The slogan is cooperation, but the present disagreement is basic. The Americans think that a high growth rate is attainable and necessary.An increasing number of Europeans think that it is hypothetically desirable but impossible. There is a widespread view in Europe that the world has come to the end of a vast cycle of economic growth that began shortly after World War II, and now everybody is going to have to learn to live with much more modest increases. Meanwhile Mr. Carter is getting a lot of complaint form people in his own party who want him to pull the same levers that the Kennedy administration did, and ignite another boom like the one that began in 1961. That is the center of the long debate going on now between the American and German governments over the economic future - theirs and ours.