Book excerpt: This paper presents a methodology for calculating bilateral equilibrium exchange rates for a panel of currencies in a way that guarantees global consistency. The methodology has three parts: a theoretical model that encompasses the balance of payments and the Balassa-Samuelson approaches to real exchange rate determination; an unobserved components decomposition in a cointegration framework that identifies a time-varying equilibrium real exchange rate; and an algebraic transformation that extracts bilateral equilibrium nominal rates. The results uncover that, by the start of Stage III of the European Economic and Monetary Union (EMU), the euro was significantly undervalued against the dollar and the pound, but overvalued against the yen. The paper also shows that the four major EMU currencies locked their parities with the euro at a rate close to equilibrium.