IT'S MYSTERIOUS, is it not? Economics says that a large budget deficit makes the economy grow faster, and the country is now running a tremendous deficit. So why is the economy slowing down?

This time the mystery has a clear and precise explanation. It's true that a budget deficit pushes toward growth -- but it's also true that a foreign trade deficit pulls the other way. The American budget deficit is a powerful stimulus, but its effects are not confined to the United States. The trade deficit reflects the amount of the stimulus that is going abroad -- currently, most of it. The budget deficit is very effective in lifting industrial protion, but this year it's lifting production principally in Japan, Western Europe and Latin America.

The budget deficit soare to its present magnitude in the second half of 1982, with powerful effects on the whole economy. The recession ended and a rapid recovery began. In mid-1982 the trade deficit, as measured in the broad definition known as the current account, was zero. It grew through 1983 and early 1984, hitting a peak last summer. That is the point at which the rapid recovery ended. That is also the point at which unemployment in the United States stopped falling.

This country is now running a strange split-level economy in which demand is expanding rapidly while supply and industrial production sputter and stumble along. From the first quarter of this year to the second, the Commerce Department said last week, gross national product rose at the very modest annual rate of 1.7 percent. But demand, measmestic sales, was rising at a rate of over 6 percent. That's extremely fast, and not sustainable.

The central idea of the Reagan administration's original economic strategy was to rely on steadily expanding production to create jobs and raise incomes. But as it is working out, the supply side of the economy languishes while the country is off on a binge of borrowing and overconsumption that has no parallel in its history.

It's happening because no one -- neither the administration nor its critics -- foresaw the enormous importance that international trade and finance would assume as the American budget swung farther and farther out of balance. No one foresaw the way the deficit, and the flow of foreign loans to finance it, would raise the exchange rate of the dollar. For most of the years from World War II to the 1970s, the rest of the world had little effect on the American economy, and Americans are still not accustomed to taking it into account when they make policy. That's turning out to be an expensive error, with the costs reflected in slow economic growth and rapidly rising foreign debt.