International Comparisons: Multilateral Indices and Nonparametric Welfare Bounds

Abstract: Multilateral index numbers, such as those used to make international comparisons of prices and income, are fundamental objects in economics. However, these numbers are often challenging to interpret in terms of economic welfare, as a data-dependent 'taste bias' can arise for these indices that distorts measurement of price and income levels and dispersion. To study this problem, I develop a means to appraise indices' economic interpretability using non-parametric bounds on a true cost-of-living index. These bounds improve upon their classical counterparts, define a new class of indices that generalises the 'star' system, and show how existing indices can be corrected for preference misspecification. In my main application I appraise existing international comparison methods. I find that taste bias generally leads to overestimates (underestimates) of price (income) levels. Superlative indices, such as the Fisher-GEKS index, lie within the permitted bounds more frequently than non-superlative methods, but the mean size of this bias is modest in all examined cases. My results can thus be interpreted as supporting the economic validity of the myriad multilateral methods which are in practical use.