Nominal and real exchange rates

The nominal exchange rate e is the price in foreign currency of one unit of a domestic currency.
The real exchange rate (RER) is defined as , PER = e(P/Fp) where Pf is the foreign price level and P the domestic price level. P and Pf must have the same arbitrary value in some chosen base year. Hence in the base year, RER = e.

The RER is only a theoretical ideal. In practice, there are many foreign currencies and price level values to take into consideration. Correspondingly, the model calculations become increasingly more complex. Furthermore, the model is based on purchasing power parity (PPP), which implies a constant RER. The empirical determination of a constant RER value could never be realised, due to limitations on data collection. PPP would imply that the RER is the rate at which an organization can trade goods and services of one economy (e.g. country) for those of another. For example, if the price of a good increases 10% in the UK, and the Japanese currency simultaneously appreciates 10% against the UK currency, then the price of the good remains constant for someone in Japan. The people in the UK, however, would still have to deal with the 10% increase in domestic prices. It is also worth mentioning that government-enacted tariffs can affect the actual rate of exchange, helping to reduce price pressures. PPP appears to hold only in the long term (3–5 years) when prices eventually correct towards parity.

More recent approaches in modelling the RER employ a set of macroeconomic variables, such as relative productivity and the real interest rate differential.
NRi = (RRi + 1) (Expected Inflation + 1) - 1