AMERICAN PRODUCTIVITY has just fallen down the cellar stairs again. Productivity is simply the output per hour of work, and the decline is a bad omen for future inflation rates.

If labor productivity rises 3 percent a year, as it regularly did in the 1960s, everyone who works can have a 3-percent pay increase every year without any inflationary effects. But if productivity does not rise at all and wages go up 8 percent a year, as they have been doing, it will make prices go up 8 percent. That becomes the basic, or underlying, inflation rate that you have been hearing about; other kinds of inflation, like rises in food or oil prices, come on top of it. When productivity drops 1 percent as it has done since last March, it would add 1 percent to the underlying inflation rate even if everyone's wages were unchanged.

The most cheerful and encouraging thing that anyone has been able to say about recent productivity performance is that it always falls at the beginning of recessions. Employers hesitate to lay off workers until the pattern of declining sales and orders becomes firmly established. But the trouble with American productivity isn't merely cyclical. Since the early 1970s, it has at best been rising painfully slowly.

The reasons remain something of a mystery. There are a number of lines of speculation. One is that the American labor force is currently absorbing unusual numbers of young and unskilled workers, the product of the baby boom of the 1950s. Another is that employment is growing most rapidly in the service industries, where productivity is generally much lower than in manufacturing or agriculture. A third is the diversion of investment to pollution control, the products of which - clean air and water - are not added into the conventional accounting of economic output.

But all of that kind of analysis adds up to something less than a persuasive explanation - particularly when you look at the international comparisons. Americans sometimes grow weary of hearing about Japanese success, and discount it on grounds that circumstances there differ enormously from those in the United States. But since the recession five years ago, Japan's annual productivity gains have settled down to a modest rate hardly more than twice the American level.

In the 1970s, it has been Western Europe in which manufacturing productivity has accelerated most spectacularly - and particularly in three small countries - Denmark, the Netherlands and Belgium. The reasons for the emergence of Belgium as the current world champion in raising productivity in manufacturing are no clearer than anything else in this exasperating and complex subject. But it suggests that there is nothing uniquely Asian about the process. You don't necessarily have to speak Japanese to get big productivity gains - and the rapidly rising standard of living that comes with them.