THE CONSUMER Price Index is probably the most influential statistic that the federal government publishes--and it is notoriously inaccurate. Over the past year, it has produced a measurement of inflation that is too high by about 20 percent. Nearly one-third of the federal budget, including Social Security and all the other pensions, is directly geared to the CPI by law; directly or indirectly, more than half of the budget is affected by it. Mismeasurement of inflation, by the most widely used indicator, has serious implications throughout both the public and private economy. Janet L. Norwood, the commissioner of labor statistics, has decided that now's the time to fix it.

The main source of inaccuracy lies in the way that the CPI attempts to measure the cost of housing. Housing has a double meaning in the economic life of most American families. It's not only shelter; it's also an investment asset, like shares of stock. People have been buying houses not only to get in out of the rain, but to put their money in the one kind of asset that seemed to stay ahead of inflation. But counting the speculative value of houses in the CPI is as improper as counting, say, stock market prices or the price of gold. The CPI is supposed to count the cost of things that people consume--in this case, shelter.

The way to track shelter costs is by following the rents that people pay, or that they would pay if they were renters. That can make quite a difference. From August to September, the CPI in its present form rose 1.2 percent. Under the alternate formula, using rental value, it would have risen only 0.8 percent.

There's already a very audible lobby against this change, led by some of the unions and Social Security recipients who benefit from the overstatement of inflation. But this change may serve them better than they think. If the prices of houses level off, or fall, under the weight of high interest rates, a CPI based on rentals would rise faster than the present one. Reforming the statistical method won't necessarily save the government money.

Mrs. Norwood's chief reason for making this change now is Congress' decision last summer to index the federal income tax brackets and exemptions to the CPI beginning in 1985. That decision was grossly unwise, as an increasing number of people in Congress are coming to realize, and it will probably be revoked before it ever actually takes effect. But with or without tax indexation, the case for accurate measurement of inflation is compelling. This improvement is overdue.