THE AMERICAN standard of living is set chiefly by labor productivity -- the output of each hour that people put into their jobs. Last year the improvement in productivity was minuscule. This country used to be able to take for granted rapid and continuous increases, but no longer. Why?

Nobody really knows -- and since nobody really knows, you would probably be well advised to regard with caution anyone who confidently claims to be able to fix it. The crucial change was in the year 1973. The long boom that had run since World War II came to an end as suddenly as if someone had thrown a switch, here and throughout the industrial world from Japan to western Europe. It's possible to identify some of the events that doubtless contributed to this slowdown, such as the oil crisis of 1973-74. But all of the suspects put together do not begin to add up to an adequate explanation for this sudden and simultaneous loss of momentum among all of the world's most advanced economies. It remains a mystery -- and, in terms of its importance to the way people live, probably the most important mystery in current economics.

The Reagan administration earlier thought that it had the answer. It argued that poor performance in productivity was the result of inadequate capital investment caused by high tax rates. But if lower tax rates were the answer, the productivity growth rate should now be rising instead of falling. Meanwhile the budget deficit is swallowing massive amounts of savings that would otherwise be invested in the private sector. But, again, it's dangerous to attribute the behavior of productivity wholly to American domestic policies and politics, for the same meager progress is visible in other industrial economies that have been following different prescriptions.

Here in the United States last year, productivity gains varied enormously from one kind of business to another. In agriculture -- the highest of American high-tech industries -- productivity rose a phenomenal 11.5 percent in 1985. In the rest of American private business, the average gain in productivity was zero. It rose 2.6 percent in the manufacturing sector, but in the service industries it actually fell. For the whole private economy, productivity last year rose by one-third of one percent.

A country's productivity is the chief determinant of its income. If the trend in productivity is flat, the trend in incomes will also be flat. That's a disquieting prospect for the United States, which relies on a general rise in prosperity to alleviate the want and distress at the bottom end of the income ladder. It's crucial to keep working toward a solution of that central mystery.