Marc Goldwein, policy director of the Committee for a Responsible Federal Budget, and his colleague Adam Rosenberg have written a paper making the case for the chained CPI. Because a panoply of government benefits are tied to the consumer price index, “over-indexation,” i.e., overestimating inflation and adjusting transfer payments accordingly, represents a costly error. The chained CPI essentially corrects for substitution bias:

Substitution bias occurs because the regular measure of CPI assumes consumers will buy the same basket of goods regardless of relative prices, not realizing that consumers can often soften the blow of increased relative prices by consuming more of a relatively cheaper good. …

For example, if consumers respond to the price increase for Granny Smith apples by buying more Red Delicious apples instead (lower level substitution bias – changes within categories), this is accounted for in the current CPI. But if consumers respond to the price of Granny Smith apples increasing by buying less apples altogether and purchasing more oranges instead (upper level substitution bias – changes between categories), this is not accounted for. …

Moving to the chained CPI would address this bias by using a superlative index which updates expenditure weights and formulas in order to address consumer response to substitution between categories.

This makes intuitive sense, and moving to the chained CPI would yield considerable savings: 

Since 2000, the chained CPI has, on average, been 0.25 to 0.3 percentage points lower per year than the standard CPI measures. Though this difference is small on average, it compounds over time; depending on which index you use, prices have either increased by 30 percent (CPI-U and CPI-W) or 26 percent (chained CPI) since 2000 (see Figure 1).  Over a longer time frame, this difference would become even more pronounced.

Moreover, Goldwein and Rosenberg suggest that this proposal could garner support from across the political spectrum. The Washington Post has just published an editorial in favor of the using the chained CPI, which hopefully means that Congress will take notice.