According to a recent book by Christian Broda and David E. Weinstein (Prices, Poverty, and Inequality: Why Americans are Better Off Than You Think) (ht Marginal Revolution) growth in income inequality was less pronounced in the US because of changes to the quality and cost of goods that “poor” people purchased.
This indicates to me that a tiered consumer price index could be a useful thing. Currently the household economic survey (HES) provides an annual tiered income measure (where we see the average income of different income deciles). However, this nominal measure is not particularly useful if the change in prices experienced by different groups are very diverse.
As a result, a similarly tiered CPI measure (so a CPI for each income decile) would actually give us a much better way to figure out change in “real income” and thereby a fairer measure of the distribution of real income – which is something we care about.
Surely the HES has a measure of purchases by different income groups. As the CPI is broken down into different products it should be possible to take these weights and come up with a loose set of indicies that represent the price inflation faced by different income declines shouldn’t it?