A unified framework of trade in value added : physical, monetary, exchange rates, and GHG emissions

Koopman et al. (2014) developed a method to consistently decompose gross exports in value-added terms that accommodate infinite repercussions of international and inter-sector transactions. This provides a better understanding of trade in value added in global value chains than does the conventional gross exports method, which is affected by double-counting problems. However, the new framework is based on monetary input--output (IO) tables and cannot distinguish prices from quantities; thus, it is unable to consider financial adjustments through the exchange market. In this paper, we propose a framework based on a physical IO system, characterized by its linear programming equivalent that can clarify the various complexities relevant to the existing indicators and is proved to be consistent with Koopman's results when the physical decompositions are evaluated in monetary terms. While international monetary tables are typically described in current U.S. dollars, the physical framework can elucidate the impact of price adjustments through the exchange market. An iterative procedure to calculate the exchange rates is proposed, and we also show that the physical framework is also convenient for considering indicators associated with greenhouse gas (GHG) emissions.