AMERICAN PRODUCTIVITY dropped like a stone last year -- and no one has yet been entirely able to explain it. Only twice in the past generation has productivity dropped steadily through a full year. The first time was in the dire recession of 1973-1975. It's normal for productivity to dip at least briefly in recessions. The peculiar thing about the past year's performance is that it kept falling although the economy was growing. Productivity is the economic output per hour of labor; and when it falls, it takes the standard of living with it.

But perhaps there's a connection here with two other current economic mysteries. First, employment has continued to rise more strongly than expected by most economists. The number of jobs rose by more than two million in 1979. That's why unemployment stayed lower than predicted. Second, wages have lagged far behind the inflation rate -- to the astonishment of the people who have followed the previous campaigns to catch up.

But perhaps all of these mysteries fit together. While none of them is consistent with past experience, all of them are consistent with each other.

Suppose, as a hypothesis, that most working people understand perfectly well that 13 percent wage increases, matching the galloping Consumer Price Index, will only make inflation spin faster and create higher unemployment. Suppose that most people had tacitly decided to settle for less than that 13 percent inflation rate. It would mean that the effects of slower growth were being spread widely in the form of slightly reduced purchasing power for many people, rather than being concentrated in unemployment and a total loss of earnings for the unlucky few. Then because labor had become a little cheaper, employers could afford a bit more of it. In that case, a decline in productivity might logically result.

But why would working people accept erosion of earnings by inflation? One possible answer is that a recession seems to be coming, which makes it a bad time to press for large raises. Another possibility is that most people know that they haven't suffered as much as the Consumer Price Index suggests. The index overstates the impact of inflation on most families. Except for those who bought houses last year, the actual inflation rate ran much closer to the 9 percent by which wages rose last year.

The pattern implies that the American economy is more resiliant than the Carter administration expected -- and that the president can afford to push harder in his present gingerly attempts to hold down inflation. But it is also true that the signs of strain on family finances are growing more obvious. By the end of last year, the rate at which Americans were saving money had dropped to a shockingly low level. And of those two million additional jobs in 1979, 70 percent were filled by adult women. There comes a point at which working wives and cuts in savings can no longer maintain families' accustomed levels of spending. If productivity keeps dropping, 1980 may well be the year in which a decline in living becomes very visible.