ONCE AGAIN the emphasis is on inflation. "The corrosive effects of inflation eat away at the ties that bind us together as a people," said President Carter Thursday in the third of the messages -- the budget, the State of the Union, and the Economic Report -- that make up the traditional January triad. Consumer prices last year rose 9 percent. That was a severe and dismaying increase over the previous year's 6.8 percent, which in turn was an increase over the 4.8 percent rise in the year before that. Where's it coming from?

The conventional explanations begin with the laments about the cold weather last winter and the decline of the dollar. But this country has been through a lot of cold weather without the inflation rates shooting upward, and the dollar began to fall precipitately only in the autumn. There's more to it. The most perplexing, and the most important, part of the explanation appears to be the long, slow drop in American productivity.

Productivity is the average output for every hour of labor, and it's been declining steadily for the past 15 years or so. Last year's performance was particularly poor, running about one-eighth the rate of gain that was normal in the early 1960s. The reasons are not wholly clear. There is an unusually high proportion of young and inexperienced workers inthe labor force. Environmental regulations are diverting a lot of investment into benefits like clean air and water that are not counted in the economic statistics. Technological research and development spending is down. Americans save less of their money that they used to, and nonresidential investment -- the investment in future productivity -- is a smaller share of wealth in the United States than in any other major industrial country.

Everybody can agree that people, in general, ought to show more restraint, spend a little less and help get the inflation rate down.Everybody applauds the president as long as he sticks to theory. It's when the country tries to decide exactly who is to share that burden of restraint, and how it's to be distributed, that the applause dies and people edge toward the exits.

The president's Council of Economic Advisers offers the somber forcast that, over the next five years, American productivity will remain low. The national exonomy as a whole will grow, they think, no faster in the next five years than it did in the past five. It works out to an annual increase in national output of barely 1 percent for each person employed. It's not an absolute drop in the standard of living. But neither is it the accustomed rise.

That, in turn, makes every kind of political issue more difficult. For the generation, Americans have had the good luck of being able to settle their disputes in the pleasant atmosphere of an expanding economy. It's always easier to divide the pies when the pies keep getting larger. More people can be cut in, without requiring anyone actually to cut down. New benefits can be added for some people, without taking anything away from the others. But with very slow and uncertain growth, the tensions and frictions get more serious. If the forecast is correct, it warns not only of economic stringency ahead, but a change in the American political atmosphere as well.