THE CHAIRMAN of the president's Council of Economic Advisers having departed, the White House is apparently looking for a successor. First question: why bother? The Reagan administration, after all, does not care much for economists, or pay any great attention to their advice. The recent chairman, Murray L. Weidenbaum, is only the latest of a parade of Reagan economists to resign in exasperation.

The next question, even harder to answer, is why anyone would take the job. The last person whose public reputation was actually enhanced by service as chairman of the council was probably Gardner Ackley, who left nearly 15 years ago. All of the chairmen since then have been people of superior professional ability and, on returning to private life, all of them continued to contribute, vigorously and usefully, to national debate over public policy. But it is unfortunately also true that all of them, as political figures, suffered erosion of their public standing in the time they were at the White House.

The explanation lies not in personalities but in the nature of the job. It was created by the Employment Act of 1946, when Congress, responding to deep fears of renewed depression, declared a federal responsibility "to promote maximum employment, production and purchasing power." By establishing the Council of Economic Advisers, Congress took the even more daring step of suggesting that professional economists were the people to guide that process.

For two decades, economists rose in stature as the engineers of prosperity, the people who knew how to set the dials and gauges for the fastest possible ascent. It was a technical job, and the techniques worked brilliantly. You hardly need to be told that the trouble started in the middle 1960s, during the Vietnam War, when the inflation rate began to get out of hand.

For the past 15 years, no American president's economic achievements have gotten much applause, and there's been no more glory for the economic advisers to share. No one has found a way--in this country or, incidentally, any other--to bring down unemployment and inflation together. But American presidents keep desperately hoping for the best, and pushing their economists out in front of the microphones to make implausible promises.

If it were simply a matter of pursuing the goals of the Employment Act, economists would know what to do--although, as they did it, inflation would accelerate. President Reagan is no more ready than his predecessors to acknowledge the fundamental collision between his high targets for growth and his low targets for inflation. To reach a consistent position is going to take more than technical advice and tinkering. It is going to require political decisions of great consequence, and they are going to have to be taken at a higher level than the Council of Economic Advisers. Until that happens the life of the house economist, in the White House, is likely to be at best uncomfortable.