Whose Inflation? A Characterization of the CPI Plutocratic Gap

Prais (1958) showed that the standard CPI computed by most statistical agencies can be interpreted as a weighted average of household price indexes, where the weight of each household is determined by its total expenditures. In this paper, we analytically decompose the difference between the standard CPI and a democratically weighted index (ie, the CPI plutocratic-democratic gap) as the product of expenditure inequality and the sample covariance between the elementary individual price indexes and a parameter which is a function of the expenditure elasticity of each good. This decomposition allows us to interpret variations in the size and sign of the plutocratic-democratic gap, and also to discuss issues pertaining to group indexes.