True Measures of GDP and Convergence

Widely-used purchasing power parity measures of per capita GDP are subject to substitution bias and are not true quantity indexes. Varian's (1983) non-parametric construction of a true multilateral quantity index is extended to a range of true indexes and Afriat's (1981) pairwise bounds are generalised to define bounds to the variance of such indexes. We propose the Ideal Afriat Index, each observation representing the mid-point to the range of deviation from the true index mean. We find that changes in the extent of substitution bias cause constant price indexes to underestimate GDP convergence amongst OECD countries 1980-90.