2 International Comparisons Using Spanning Trees

A large number of index number methods have been proposed for making multilateral comparisons across countries. A distinction can be drawn between methods that compare all countries in a comparison simultaneously and those that compare countries by simply linking together bilateral comparisons. Methods of the former type are surveyed in Hill (1997). Here, I focus on meth-ods of the latter type. This procedure of linking bilateral comparisons is often referred to as chaining. Chaining has a long history. In fact, it dates all the way back to Marshall (1887). However, historically, interest in chaining has focused primarily on time-series comparisons. This is because of the natural chronolog-ical ordering of time-series data. In particular, chronological chaining (i.e., linking together bilateral comparisons between adjacent time periods) has been widely advocated for measuring inflation. Nevertheless, some work has been done on chaining across countries. Two notable references are Kravis, Heston, and Summers (1982) and Szulc (1996). Kravis, Heston, and Summers focus on chaining in the context of multilatera