THE SENATE, led by its Budget Committee, has done the Reagan administration a very considerable favor. It has voted to revise -- very modestly -- the automatic formula that indexes Social Security benefits to the inflation rate. Changing the indexation formula is an unpleasant duty, and highly unpopular. Mr. Reagan refused to propose it. But it's necessary, and the Senate has relieved the administration of a severe political burden by taking the initiative.

The vote was only a preliminary one, on the budget resolution rather than on substantive legislation. Whether this drive goes any further depends on the administration's next move and whether it is willing at least to support the Senate. Some of the House Democrats have spoken openly of the need to revise the indexation of Social Security, but they are not likely to do much about it unless Mr. Reagan share the responsibility.

Nine years ago, Congress tied the Social Security benefits to the Consumer Price Index, which, later experience has showed, tends to overstate inflation. Meanwhile, wages have been rising much less rapidly than the index. The effect is to shift the division of resources favorably to people who have retired and adversely to those who are working and paying the Social Security payroll tax. Indexation has meant an improvement in living standards for Social Security recipients at the expense of people who are employed. That's the distortion that the Senate now proposed to correct.

It would be the narrowest of all possible remedies, merely adjusting the formula to raise benefits, at a maximum, no faster than wages. That change would apply, incidentally, not only to Social Security but to all of the other federal retirement programs as well. Even this slight change, plus a three-month deferral in the date of annual adjustment, would save $7.9 billion next year.

Perhaps, to many people, any change in the Social Security legislation will seem unfair. But if retirement benefits are left untouched, that $7.9 billion will have to be found somewhere else. Another large rise in the payroll tax hardly seems likely. If taxes aren't raised, the $7.9 billion will have to come out of that very vulnerable remainder of the budget that is neither defense spending nor retirement checks. That means squeezing even harder such things as welfare, health care for the poor and nutrition. At a time when this kind of assistance is being cut, it is neither fair nor reasonable to expect federal retirement benefits to be fully compensated for inflation -- and a bit more.