EXCHANGE RATE (Encyclopedia)

1. The nominal exchange rate (NER)

The nominal exchange rate (NER) is the relative price of a domestic currency in terms of foreign currency. For instance, if the dollar/euro exchange is equal to 1.4, it means that to buy one unit of the European currency it takes 1.4 dollars (or alternatively, to buy one dollar, 0.71 euros are needed). The graph in Figure 1 shows the evolution of the dollar/euro exchange.
The NER can be left free to vary in currency markets (flexible exchange rates), or it can be fixed by the monetary policy to a given value in terms of another currency or group of currencies (fixed exchange rates). In the latter case, the central bank is committed to intervening in markets to defend the equal stability (endogenous monetary policy).
The use of the NER is essential for the comparison between goods and services produced in different countries, as it allows us to express prices in a common currency. The NER can be listed in two ways. It can express the number of units of domestic currency required to purchase a unit of foreign currency (uncertain for certain). Or, alternatively, it defines the number of units of foreign currency needed to purchase a unit of domestic currency (certain for uncertain). Here we will refer to the first quotation. Thus, a positive variation of S will indicate a nominal depreciation; conversely, a negative variation of S will indicate a nominal appreciation.

2. The real exchange rate (RER)

The real exchange rate (RER) is the relative price of goods and services produced within the domestic country in terms of goods and services produced abroad. 
The economic literature provides three different definitions of the RER.
1. The first definition comes directly from PPP and states that it is possible to define the RER as the ratio between the index of foreign prices (expressed in domestic currency) and the index of domestic prices. Thus, it constitutes a measure of the consumption basket of all goods required for the purchase of a basket of products abroad. In formulas:
-  is the price index of the basket of goods produced in the foreign country and  is the weight of the i-th good in the foreign representative basket of consumption; 
-  is the price index of the basket of goods produced in the domestic country and is the weight of the j-th good in the domestic representative basket of consumption;
- St is the nominal exchange rate (NER) and it expresses the number of units of domestic currency required to purchase a unit of foreign currency.
On the basis of equation (1) then, the RER can be seen as a nominal exchange rate deflated by the domestic prices and the foreign prices.
2. The second definition of RER relies on the assumption that all goods are traded internationally. Under this assumption P can be seen as the price index of exported goods and as the price index of imported goods. The RER can be defined then as: 
where the ratio  indicates the terms of trade. Hence, if all goods are traded on international markets, the RER may be defined as the inverse of the terms of trade. In this case, a real appreciation corresponds to an improvement in terms of trade, and, vice versa, a real depreciation corresponds to a deterioration in terms of trade.
3. The third definition of RER is based on the evidence that not all goods are traded on international markets. The distinction between tradable goods and non-tradable goods is very important since it is obvious that only the prices of the first group of goods are affected by the international competition. Labelling with  the price index of the tradable goods and with  the price index of the non-tradable goods, it is possible to define the general level of prices Pt as the following geometric average:  where  is the weight of the non-tradable goods.
Equation (3) states that the RER is proportional to the ratio between the price index of tradable goods and the price index of non-tradable goods. In other words, equation (3) defines an “internal terms of trade”. When non-tradable goods become more expensive in terms of tradable goods, then a real appreciation occurs (a fall in Q). On the contrary, when non-tradable goods become cheaper in terms of tradable goods, then the economy experiences a real depreciation (an increase in Q). 
From the foregoing, it is clear that, regardless of the approach chosen for the formal definition of the RER, it is in fact a relative price. A depreciated real exchange rate indicates, ceteris paribus, that the domestic goods are more convenient as compared to the goods produced abroad. This means that an increase in Q should imply an increase in the demand for goods produced by the household, and therefore a contraction of imports and an expansion of exports. In other words, ceteris paribus, a real depreciation implies an improvement in the trade balance (TBt). In formulas:            

3. NER, Trade Balance (TB) and the J-curve 

In more rigorous terms, it is possible to define the relationship between TB and RER using the elasticity of aggregate demand to price, thus leading to the definition of the so-called Marshall-Lerner (or Marshall-Lerner-Harberger) conditions. The idea is that a devaluation can exert a positive impact on trade balance if the sum of the price elasticity of exports and imports (in absolute value) is greater than 1.
To analyse the effects of a devaluation of the exchange, the expression of TB is rewritten in terms of value:
- EXt are the exports, whose value is equal to the product of the price index of the exported goods and the quantity of exported goods ;
IMt are the imports, whose value is equal to the product of the price index of the imported goods, expressed in domestic currency, and the quantity of imported goods ;
the price indexes PIM and PEX are assumed be constant. 
Let's sssume also that:
- PEX = PIM = 1;
- the national income does not vary; 
- at the beginning of the period TBt = 0.
Differentiating equation (4) with respect to S yields:
Equation (5) can be rewritten as follows:
Recalling that the elasticity of exports () and the elasticity of imports () are defined as:
Equation (5’) becomes :
Recalling that the equilibrium of the trade balance implies that , equation (6) can be rewritten as:

From equation (6’) emerges that: 
The net effect of a devaluation of the exchange rate on the balance of trade depends on the elasticities of demand to prices. The Marshall-Lerner conditions state that, starting from a situation of equilibrium in the balance of trade, the impact will be positive if and only if the sum of the price elasticity on () is greater than 1. This is because the devaluation produces two distinct effects: a price effect (EP) and a quantity effect (EQ). The nominal depreciation entails on the one hand a reduction in the value of exports (by reducing the prices that consumers pay for foreign goods exported), and an increase in the value of imports (because it increases the price of domestic currency imported). Thus, the EP has a negative impact on the trade balance. Conversely, reducing the foreign currency price of the exported goods should help to increase the volume of exports, as well as the increase in the price of imported goods should lead to a decline in import volumes (quantity effect). We can therefore conclude that the EQ always exerts a positive effect on trade balance.
In symbols:
The Marshall-Lerner conditions determine which of the two effects is predominant. If (7) is satisfied, then EQ dominates EP and the trade balance benefits from the depreciation. 
There is a vast empirical literature that analyses the effects of the exchange rate fluctuations on trade balance. The results of the econometric analyses that estimate the equations of imports and exports and the relative elasticities have essentially corroborated the predictions of the Marshall-Lerner theory. In particular, studies conducted on data from advanced economies show that the exchange rate depreciation tends to deteriorate the trade balance in the short term (the so-called J-curve effect), but it exerts a positive impact on TB in the long term. 
In the short term, it is likely to have a prevalence of EP due to the fact that operators employ a certain amount of time to change their decisions and therefore, in spite of price changes, they do not alter the volumes exchanged. In the long run however, the improvement of the TB would be due to the EQ that prevails over time. Figure 2 describes the time course of the balance of trade in the periods following the depreciation.
Dornbusch, R., (1976), "Expectations and Exchange Rate Dynamics", Journal of Political Economy, Vol. 84(6), pp. 1161-76
Frankel J. and Rose A., (1995), ""Empirical research on nominal exchange rates", Handbook of International Economics, G. M. Grossman & K. Rogoff (ed.), Vol. 3, chapter 33, pages 1689-1729 Elsevier
P., (2007), "Real Exchange Rate Levels and Economic Development: Theoretical Analysis and Empirical Evidence," Sao Paulo Business Administration School, Getulio Vargas Foundation
Harberger A.C (1950), "Currency Depreciation, Income and the Balance of Trade", Journal of Political Economy, Vol. 58, pp. 47-60.
Hooper P., Johnson K. and Marquez J. (2000) "Trade elasticities for G-7 countries", Princeton Studies in International Economics, Vol. 87.
Lerner A.P. (1936), "The Symmetry Between Export and Import Taxes", Economica, Vol. 3, pp. 306-313.
Marshall A. (1923), Money, Credit and Commerce, London, MacMillan.
Mussa M. (1976), "The Exchange Rate, the Balance of Payments and Monetary and Fiscal Policy Under a Regime of Controlled Floating", Scandinavian Journal of Economics, Vol. 78, pp. 229-248. 
Rodrik D., (2008), "The purchasing-power parity doctrine: A reappraisal" Brookings Papers on Economic Activity, Fall 2008, Vol 2, pp. 365-412.
Samuelson P.A. (1964), "Theoretical notes on trade problems", The Review of Economics and Statistics, Vol 46, pp.145-154.
Sarno L. and Taylor M.P. (2002), The Economics of exchange rate, Cambridge University Press, Cambridge, UK.
Editor: Lorenzo CARBONARI