Spatial Chaining in International Comparisons of Prices and Real Incomes

Multilateral international comparisons of the purchasing power of currencies and real income often use as building blocks bilateral comparisons between all possible pairs of countries. The standard approach in the literature weights all these bilaterals equally. One problem with this approach is that some bilaterals are typically of lower quality, and their inclusion therefore can undermine the integrity of the multilateral comparison. Formulating multilateral comparisons as a graph theory problem, we show how quality can be improved by replacing bilateral comparisons with their shortest path spatially chained equivalents. We consider a few variants on this approach, and illustrate these multilateral methods using data from the 2011 round of the International Comparisons Program (ICP). Using some novel bounds criteria, we demonstrate how spatial chaining improves the quality of the overall multilateral comparison.