The "chained CPI" method of computing Social Security's Cost of Living Adjustments (COLAs) is being touted on two grounds. First, it saves money. Second, it's more accurate. Undoubtedly, it would save money but the second point is debatable. The chained CPI method is based upon the observation that if green beans get more expensive, consumers are more likely to substitute broccoli. A COLA based in small part on the price of green beans may be inaccurate because consumers will substitute an equivalent lower priced item. However, as Dean Baker at FDL argues, there is no proof that the chained CPI method is more accurate when applied to the elderly. The Bureau of Labor Statistics computes the CPI-E, the Consumer Price Index for the Elderly, that takes into account the increased health care expenses of the elderly among other age related spending differences. The CPI-E has been running higher than the chained CPI but has not been used in the computation of the Social Security COLA. There is no chained CPI-E, that is a chained CPI computed for the elderly. No one knows what it would show but the odds are high that a chained CPI-E would not be so unfavorable for the elderly as the plain chained CPI. It might be even more favorable for the elderly than what is being used currently to compute the Social Security COLA.
In the end, the chained CPI has one real advantage -- it would save money. There's no proof that the chained CPI method of computing the COLA would be more accurate. Of course, I should mention that the chained CPI method has one big political advantage. It's so abstruse that few Social Security recipients understand it. However, they could probably understand a television ad criticizing a politician for "cutting" Social Security and that ad would have the advantage of being accurate.