Very interesting report from SSA on chained CPI.
http://www.ssa.gov/policy/docs/ssb/v67n3/v67n3p73.html
Although researchers have identified a number of concerns regarding the CPI-E and do not deny that the issue is worth investigating, many doubt the need for or the practicality of constructing a price index specifically for the elderly.7 Furthermore, the newly developed chain weighted (C-CPI-U) provides strong evidence that the methodology used to construct both the CPI-W and CPI-E implies a substantial upward bias in the measurement of inflation. A correction of this upward bias in the measurement of inflation would actually imply smaller COLAs, not larger ones.8 COLAs based on the Chained C-CPI-U would have averaged 2.32 percent between 2001 and 2006, compared with 2.70 percent and 2.92 percent for annual COLAs based on the CPI-W and CPI-E, respectively, over the same period.9
Table 2 is most interesting showing increases in health and shelter under the chained when compared to the two other methods of figuring COLAs.