Oulton, Nicholas (2012) How to measure living standards and productivity. Review of income and wealth, 58 (3). pp. 424-456. ISSN 0034-6586
I set out a general algorithm for calculating true cost-of-living indices when demand is not homothetic and when the number of products may be large. The non-homothetic case is the important one empirically (Engel's Law). The algorithm can be applied in both time series and cross section. It can also be used to estimate true producer price indices and Total Factor Productivity in the presence of input-biased economies of scale and technical change. The basic idea is to calculate a chain index of prices but with actual budget (cost) shares replaced by compensated shares, i.e. what the shares would have been if consumers (firms) faced actual prices but their utility (output) were held constant at some reference level. The compensated shares can be derived econometrically from the same data as are required for the construction of conventional index numbers. The algorithm is illustrated by applying it to estimating true PPPs for 141 countries and 100 products within household consumption, using data from the World Bank's latest International Comparison Program.
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