THE REPUBLICANS in Detroit had a lot to say about the current rates of unemployment and inflation. The general thought was that President Carter is inescapably and personally responsible for both catastrophes. But that's a subject with a history, a bit of which might be recited here as an attempt at political pollution control -- a nonpartisan application of the Clean Air to conventions in general.

The present inflation began in late 1965, with the acceleration of the Vietnam War. It reached its first peak in 1974, receded, then began to surge again in late 1977. It has run through four presidencies -- two of them Democratic, two Republican.The long trend has been upward, which means that each president has usually left the rate higher than he found it. The exception was Mr. Ford, who was spared that misfortune only through the wholly unintended intervention of the deepest recession in postwar history.

To say that Mr. Carter has done no more badly than his predecessors is thin praise. But if the convention in Detroit had a fault, it was a failure of memory. The convention seemed to have no recollection of the years from 1969 to 1977.

American political rhetoric takes it as obvious and demonstrable that no recession can occur except through the criminal negligence of the president of the moment. Each candidate assures the nation, with total sincerity, that he will permit nothing of the sort to happen while he is in office. Unfortunately, the record argues that the ability of presidents to avert recessions, or even to influence their course, is greatly exaggerated.

There have been three recessions in the last 15 years. The first began in late 1969 and continued for nearly a year. The Nixon administration's wildly excessive efforts to forestall a repetition during the 1972 campaign led to the boom and soaring inflation that followed. Another recession began in late 1973 and continued for 16 months. An incautious listener at Detroit might easily have acquired an impression that the current rate of unemployment -- 7.7 percent of the labor force -- is the highest in human history, or at least since 1933. But after the last recession, in May 1975, the rate went to 9 percent. It might conceivably go that high again next winter. While both parties hope to do better in the future, the past record on unemployment does not necessarily cut in favor of the Republicans.

Mr. Reagan attributes much of the country's economic malfunction to excessive deficit spending over the years. But the purpose of that deficit spending -- and the budget was consistently in deficit from 1970 through 1977, as well as since then -- was to reduce unemployment. How does Mr. Reagan propose to reduce employment and to ward off future recessions? That's a question for the campaign ahead.