Intra-national, intra-continental, and intra-planetary PPP

This paper presents a general framework to address several issues that have arisen in recent work that investigates purchasing power parity (PPP) and other inter-regional relative price movements: (1) How can we model real exchange rate movements in a consistent manner, so that our model for the real exchange rate for country B relative to country C is commensurate with our models for country A/ country B and country A/ country C real exchange rates? For example, can things be modeled so that our tests do not depend on the "base country"? (2) How should we handle correlation across real exchange rates in panel tests of PPP? (3) Are speeds of adjustment toward PPP different for intra-national, cross-national and cross-continental real exchange rates? (4) Is the innovation variance different for intra-national, cross-national and cross-continental real exchange rates; and, if so, how does that influence how we model and test PPP?