TRUE, AMERICANS save less of their money than they did at the beginning of this decade. To a good many social commentators -- President Carter, for one -- that reduction constitutes positive evidence of the erosion of American optimism, discipline and confidence. You may recall that a month ago, in his famous diagnosis of the alleged national malaise, Mr. Carter lamented that "the willingness of Americans to save for the future has fallen below that of all other people in the Western world."

The savings rate is a genuinely important subject, for savings provide money that is invested. Investment in turn is necessary to raise productivity and the standard of living. But it is always perilous to mingle economic statistics and psychological diagnosis.

You don't have to rummage around in the national psyche to account for the lower savings rate. There's a much simpler explanation. A good many people have perceived that it doesn't pay to put money into a savings account at 5 percent interest when the inflation rate is over 13 percent. That means a real loss of 8 percent a year. At that price, it's astonishing that the savings rate isn't even lower. Americans are rapidly catching on to the peculiar arithmetic of inflation.

That's the interesting and sinister thing about the pattern of savings. In the past, savings tended to increase during surges of inflation. Economists reasoned that the inflation made people uneasy about the future, and more cautious in conserving their cash. But that's changed. Since the last recession, a lot of those people have evidently decided that high inflation is here to stay, and that they had better adjust to it. They have learned that inflation penalizes the savers and rewards the borrowers. So while savings were falling, consumer credit has been rising rapidly.

Over the years, there have been deep changes in American society affecting people's attitudes toward saving. Since families have more money than they did a generation ago, they might reasonably be expected to save a higher proportion of it. But the strongest reasons for saving, traditionally, were to provide for illness and old age. With health insurance and Social Security, those anxieties have been mitigated. There are strong indications that the improvements in Social Security benefits, in particular, have induced people to save significantly less than they otherwise would have done. But those slow and deep changes can hardly have much to do with the sharp drop in savings since 1975.

A number of bright ideas for new tax breaks to encourage savings are now circulating in Congress. None seems very promising. The basic reason for the poor savings record currently is high inflation, and the only real cure is to bring the inflation rate down. As long as it goes rocking along at 13 percent a year, there is not likely to be much improvement in savings, or productivity, or Americans standards of living.