On Calculating Cost-of-Living Index Numbers for Arbitrary Income Levels

A method for computing (approximate) cost-of-living index numbers for arbitrary reference income levels is presented. It combines the use of fairly disaggregated data with a relatively modest use of econometric methods. The basis ingredients are (1) a series of chained Tornqvist price index numbers relating to per capital total expenditure, (2) price index numbers for the commodities distinguished, and (3) the income parameters of a differential demand system. This method attains second order precision and is equivalent to a full econometric method based on a translog utility function. The method is demonstrated on Netherlands data for 1952-81.