One disturbing trend since the emergence of a plan to cut Social Security benefits via the indexing of benefits to the chained CPI has been a surge of liberal conceptual attacks on the intellectual foundations of chain-type price indexes. I think this is a huge mistake. It's conceptual overkill, it's probably wrong, it would have bad consequences if applied to other areas of policy, and it's not genuinely relevant to the question at hand.
The question is, roughly, what should we do about the fact that the ratio of old people to working age people is rising? One option is to keep transfering the same share of national wealth to the elderly as we've been doing for a while, knowing full well that means cuts in each individual old person's benefits package. The second option is to keep each individual old person's benefits package constant, knowing full well that means increases in the burden on individual workers. And of course you can split the difference. But any particular aggregate level of spending is consistent with any theory of COLA indexing. I'd say that all along we've probably been setting individual benefit levels too low, and making annual COLAs too large relative to ideal policy. Holding total spending volume constant, switching to chained CPI and starting with higher initial benefit levels would favor people with shorter life expectencies relative to those with long life expectencies which seems to me like a small and worthy effort to compensate people for dying young.
But back to basics. Imagine you hear about a middle-income country that's just discovered a problem with its national statistics. It turns out that for some complicated reasons of corruption, the national statistical agency has been deliberately understating the country's inflation rate by 0.15 percentage points a year for the past thirty five years. In other words, in the aggregate the country is actually quite a bit poorer than previously realized. You're not going to respond to that by saying the country needs to make its pension program more generous. You're going to see that the new revelation that the country is poorer than it thought means it needs to cut back on its commitments.
The inflation debate is just the same. To the extent that you think official inflation figures understate inflation, that makes Social Security look less affordable. To the extent that you think official inflation figures overstate inflation, that makes Social Security look more affordable.
It's unfortunate that the current structure of the Social Security Act means index-switching has the opposite consequence, but if one wants to promote or oppose Social Security cuts one should simply argue about the total amount of money that it's appropriate to spend. Switching the terrain to the question of how much inflation there "really is" confuses the issue and gets everyone arguing the wrong side of the case.