This work has two aims. The first is to investigate the causes of the bad performance of many exchange rate models and the second is to determine the optimal exchange rate regime for small countries. With regard to exchange rate performance, the book concludes that the models' bad performance is probably due to the use of semi-reduced form relations in almost all studies on exchange rate determination and to an inappropriate approximation of expectations. Three criteria for approximating expectations are introduced. The book concludes that the rolling regressions technique and multi-state Kalman filters are appropriate procedures for approximating expectations formation. A structural model of exchange rate determination is developed in which exchange rate expectations are approximated by rolling regressions. The book demonstrates how demand functions determine the explanatory power of the exchange rate or interest rate, showing that the derived exchange rate tracks its historical values well. With regard to the second aim of the book - the determining of a small industrial country's optimal exchange rate regime - the book relates this to recent proposals for a European monetary union, with optimal control experiments being used to determine the best means of pegging a small European country's currency to the Deutsche Mark. This monograph on international economics, empirical economics and macroeconomics is intended for the use of researchers.