Macroeconomics for MBA by Antonio Fatás and Ilian Mihov. Chapter 18: Exchange rate determination

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1 Macroeconomics for MBA by Antonio Fatás and Ilian Mihov Preliminary draft Comments are encouraged Do not distribute without explicit permission from the authors Chapter 18: Exchange rate determination I. Definitions of exchange rates II. The long-run determination of exchange rates 1. Law of one price. Absolute purchasing power parity. 2. Relative PPP. 3. Productivity and the real exchange rate. III. The short-run determination of exchange rates 1. The interest parity condition. 2. Putting everything together: Monetary policy, interest rates and exchange rates. The overshooting model. 2004, 2005, 2006 by Antonio Fatás and Ilian Mihov. All rights reserved.

2 Page 2 I. Definitions: The Real Exchange Rate and Relative Prices The real exchange rate measures the price of domestic goods relative to foreign goods. As a result, the real exchange rate behaves as any other relative price; it obeys the law of demand and supply and responds to changes in consumers tastes or firms costs (technology). (1) ε = e P P* The important thing to remember is that the real exchange rate is simply the ratio of prices at home and abroad. The role for e, the nominal exchange rate, in the formula is to express these prices in the same currency. II. The long-run determination of exchange rates 1. Trade and the Law of One Price. Absolute Purchasing Power Parity. When similar goods are produced in different countries and they are traded internationally, arbitrage will tend to equalize the price of these goods. In other words, the real exchange rate for an individual commodity cannot be far from one. Examples of such commodities are oil, metals, agricultural products traded on commodity exchanges, etc. In this case the nominal exchange rate will be determined by the ratio of prices in the two countries: (2) ε = 1 => e = P * P Example: Price of a gallon of oil in Japan is 480 Yen, while in the US it is $2.40. Arbitrage will ensure that the two prices are equal and the exchange rate must be then: e = 480/2.40 = 200 Yen/$. If the actual exchange rate is different from this one (as it is now at 110 Yen/$), then there are possibilities for arbitrage: Buy a gallon in the US for 2.40 and sell it in Japan for 480 Yen. Then convert the Yen into US dollars at 110 Yen/$ and you will get 4.36 US dollars. This arbitrage operation will lead to a higher demand for dollars and the dollar will appreciate until it reaches 200 Yen/$. The Big Mac index is based on the same reasoning as the example above. In the table below in the first column is reported the actual price of a Big Mac in local currency. In the second column is the price of a Big Mac in US dollars converted at the current exchange rate (for April 22, 2003; it is given in the fourth column). You can calculate the real exchange rate (as defined in equation 1 above) for Big Macs by simply dividing the price in column 2 by the US price of a Big Mac given in the first row. For example the real exchange rate between Japan and the US is 2.18/2.71 = 0.80, which means (obviously) that in Japan Big Macs are 20% cheaper than in the US.

3 Page 3 Country (1) (2) (3) (4) (5) Alternatively, we can use the formula provided in equation (2) to calculate what should be the exchange rate that will stop arbitrage. In this case, as equation (2) indicates, all you need is the local-currency price. So, we can use column (1) to find out that the Yen/$ exchange rate should be 262/2.71 = 96.7Yen/$. This result is given in column (3).

4 Page 4 Finally, the exchange rate that precludes arbitrage (column 3) and the actual exchange rate are compared, and on the basis of this comparison the currency is determined to be under- or over-valued in column 5. The over- and under-valuation of a currency tells you in what direction one can expect that the exchange rate will move. In fact, the Big Mac predicts relatively well the direction of exchange rate movements, but there are several caveats: (1) There is an implicit assumption that monetary policy does not change. If it does, then the exchange rate might have a different trajectory compared to the one predicted by the index (Think why the Japanese yen did not appreciate to 96Yen/$). (2) The prediction generated by the Big Mac index does not work well for developing countries in the following sense: All of the currencies are undervalued according to the index. This only means that in developing/emerging economies prices are lower than in the developed countries. We will see below why this is the case and then we will provide a more in-depth interpretation of the movements predicted by the Big Mac index for developing countries. Can we apply this reasoning to the whole economy? We certainly can calculate the exchange rate consistent with no arbitrage as per equation (2) and explore deviations of the actual exchange rate from this equilibrium or PPP rate. How can we do this? We have to plug in equation (2) foreign price index divided by the US price index. The problem is that these indices have different baskets of goods and they are normalized at different years to 100, so we will not be able to get a number for the nominal rate. There is a simple short-cut: For each country, we have two calculations for nominal GDP one is the usual GDP based on local-currency prices, while the other one is the so-called GDP at PPP. This second construct simply uses US prices but these prices are applied to the same basket of goods (whatever enters GDP). Hence the simple shortcut is: P * e PPP = = P GDP in local Prices GDP at PPP (US prices) The theory that states that the nominal exchange rate between two countries should be equal to the ratio of their prices (so that the real exchange rate is equal to 1 and there is no arbitrage) is known as absolute PPP. On the graphs below you can find the actual nominal exchange rate (the dashed line) and the equilibrium or PPP nominal exchange rate (the solid line).

5 Page 5 Great Britain (USD/GBP) Australia (A$/US$) Although, there is a tendency of the nominal exchange rate to go to the equilibrium one, the deviations can be long and persistent. There are (at least) two reasons why the arbitrage argument might fail when we apply it to the real exchange rate of an economy: Real exchange rates will be equal to one only if there are no trade restrictions, transportation costs are negligible and there are no significant deviations from perfect competition. In the real world all these assumptions are not satisfied and, empirically, there are significant differences in prices of traded commodities across countries. Some goods are not traded (we will call these goods non-tradables) and therefore, they are not subject to the possibility of arbitrage. As a result, even if the real exchange rate for traded commodities is equal to one, the real exchange rate for all commodities will be different than one as there are goods that are not traded. The distinction between traded goods and non-traded goods is crucial in the understanding of real exchange rates.

6 Page 6 2. Deviations from Absolute PPP: Relative PPP Trade barriers, imperfect competition, transportation costs and the existence of non-traded goods are responsible for the failure of PPP. Most of these factors will certainly have an effect in the price level but they are stable over time and they cannot account for differences in inflation across countries. In other words, the real exchange rate can be different from one but it should remain fairly constant over time. This leads to what we will refer to as relative PPP theory of exchange rates. The main conclusion of this theory is that differences in inflation are compensated by changes in the nominal exchange rate and, as a result, the real exchange rate stays constant. % RER = 0 => % NER = π* π As an illustration of the good empirical fit of the relative PPP theory, the following graph presents inflation differentials with the US (average ) and depreciation of nominal exchange rates versus the USD. The fit is almost perfect. Countries with higher inflation have depreciating currencies, currencies with lower inflation, have appreciating currencies. (To map the graph to the equation above think of the US as the home country. When foreign inflation (π*) is above US inflation (π), then the US dollar appreciates, or equivalently the foreign currency depreciates) Percentage 10 change 9 in nominal exchange 8 South Africa rate Italy New Zealand 3 Sweden Australia Spain Ireland 2 Canada 1 France UK Belgium 0-1 Germany Netherlands -2 Switzerland -3 Japan Inflation differential Depreciation relative to U.S. dollar Appreciation relative to U.S. dollar

7 Page 7 The relative PPP theory is a good tool to predict long-run changes in nominal exchange rates. However, from a practical point of view, it encounters two main difficulties. To make a prediction about future exchange rates, one first needs to determine the absolute level towards which exchange rates are converging (the equilibrium level of the real exchange rate). If we want to go beyond the simple calculation using GDP, then the task is quite difficult as it requires knowledge of the importance of non-tradables, trade barriers, transportation costs, degree of market power... Once the equilibrium level of the exchange rate has been determined, one still needs to make a forecast of inflation and productivity growth differentials (the role of productivity is discussed below). With respect to inflation, while past inflation can help to forecast future inflation, there are many instances where dramatic changes of monetary policy by the central bank will make that type of forecast extremely imprecise. So, in the process of forecasting exchange rates, it is necessary not to take current monetary (or generally macroeconomic) conditions as constant, but you have to allow for the possible future evolution monetary policy and macroeconomy. 3. Productivity and the Real Exchange Rate The most serious challenge to PPP (both absolute and relative) as a theory of exchange rate determination comes from the fact that the real exchange rate does not remain constant over time, as we assumed in Section II.2 (i.e. the change in the real exchange rate is not zero). Instead, it is determined by productivity growth in the country. To see this, let s first disaggregate the price level into prices of tradables and prices of non-tradables. The price level - and therefore the real exchange rate - is an average of the price of goods that are traded and the goods that are not traded across countries. The PPP theory predicts that the price of traded goods has to be similar across countries. The theory so far does not say anything about the relative price of non-traded goods. We need to introduce additional elements to our model in order to compare the relative price of non-traded goods. We start with the assumptions that determine prices of non-traded goods: 1. There is a tradable and a non-tradable sector. Let s use subscripts NT to denote the non-tradable sector and T to denote the tradable sector. Prices of tradables are roughly the same around the world but this is not true for non-tradables, because there is no possibility for arbitrage. ep T = P T * but ep NT P NT *

8 Page 8 2. To get a grip on prices in the non-tradables sector we assume that wages in the two sectors (i.e. tradables and non-tradables) are equal. The salary in both sectors must be similar to avoid shifts of workers from lower-wage sectors to higher-wage sectors. It is in fact sufficient to assume that there is a constant ratio between the wages in the two sectors. Let s call this ratio k. W NT = kw T 3. Price setting. Prices of tradables are determined in the world market. What about non-tradables? Their prices will be given as a mark-up (call this m) over wages. P NT = mw NT 4. Finally, we make the standard assumption that wages are determined by productivity. Once we have this, we can say something about productivity and the real exchange rate: Suppose that the productivity in the tradables sector goes up. Then the wages, W T, increase (point 4 above). There will be an outflow of workers from non-tradables to tradables. To stop this outflow, the nontradables sector raises also wages W NT (point 2 above). But with higher wages they will have to increase also prices (point 3 above). The overall price level increases, or the real exchange rate appreciates. Example. Let s consider Germany and Spain. Suppose that there are only two economic activities: producing cars (tradable good) and serving beer (non-tradable service). Workers in both countries have the same productivity in serving beer 12 minutes per beer, but Germans are more productive in making cars: Number of hours required to: In Spain In Germany Produce a car 2,000 1,000 Serve beer Price of a car is the same in both countries because of arbitrage: 20,000 Euros For simplicity let s assume that the revenue from the sale of the car is paid out as a salary (taking into account compensation for capital will only introduce unnecessary algebra without changing the results). In this case the hourly wage in Germany will be 20 euros/hour (20,000/1000), while in Spain it will be 10 euros/hour (20,000/2,000). Since wages across sectors must be roughly equal then the waiters in Germany will be better paid (at 20 euros/hour) than the waiters in Spain (at 10 euros/hour). So, the wage component in the final price of a beer served in a German bar must be 4 euros (since 5 beers are served in one hour and the hourly wage is 20 euros

9 Page 9 for the waiter), while the wage component in the price of a beer in Spain will be only 2 euros. Thus beer in a German bar should have a higher price than beer in a Spanish bar. This example shows that there are differences in prices of non-tradables that cannot be arbitraged. More importantly, the differences in the prices of nontradables are linked to the productivity of the workers. If the workers in Germany and Spain have equal productivity, then they would have equal wages. This will result in equal prices of non-tradables. We can restate this result slightly differently: As productivity differences disappear between Germany and Spain, prices in Spain will increase and the real exchange rate will appreciate. This effect of productivity on the real exchange rate is known as the Balassa-Samuelson effect. Because Spain and Germany share a currency, this has to happen through a high inflation in Spain. If there was a nominal exchange rate it could also happen through nominal appreciation (or a combination of both). This theory makes several very strong predictions: 1. Price levels should be lower in less productive countries. 2. During a period of catching up (i.e. reaching the productivity levels in the rich countries) poor countries will see their real exchange rate appreciate. 3. The effect of the catching up process can manifest itself in two ways: via nominal appreciation or via higher inflation (of non-tradables) in the poor country. Is there evidence in support of these predictions? Let s start with the first claim. The figure shows that poor countries (like China and India) have lower price levels compared to the US, while rich countries have roughly the same prices. India China Russia Brazil Botswana Singapore Germany Japan Switzerland Price Differences (Relative to the US)

10 Page 10 On the second item catching up shows up as real exchange rate appreciation we can look at Japan: Over the period Japan was still closing the productivity gap with the US. Higher productivity growth in Japan resulted in increases in wages, which in turn implied increases in the real exchange rate Productivity and Exchange Rates: Japan vs. US Relative Productivity (Japan/US) Real Exchange Rate (Japan/US) How does the real exchange rate actually appreciate? In Japan the real appreciation was carried out by nominal appreciation while in 1970 one could buy 358 Yen with 1 US dollar, today the exchange rate is 120 Yen/$. In the EMU countries nowadays there is no nominal exchange rate so all of the adjustment must be carried out by inflation differentials. And indeed we observe that in Spain inflation rates are higher compared to Germany. In the case that a country has an exchange rate, then how will real exchange rate appreciation take place via nominal appreciation or via inflation? It is up to the monetary authority to decide how to allow the real appreciation to proceed. For simplicity let s assume that the inflation rate in the foreign country is 0, so that: % RER = % NER + π Suppose that productivity gains imply that wages will go up by 10% and suppose that there is a 50/50 split between tradables and non-tradables. In general inflation in this economy will be a weighted average of the inflation in the two sectors: π = 0.5* π π NT + 0.5* T

11 Page 11 Then inflation in the economy will be 0.5*10% + 0.5*0% = 5%. Remember that if the nominal exchange rate is unchanged there is no inflation in tradables because their prices must be the same as abroad. At the same time the 10% increase in wages (throughout the economy) requires that nontradable sectors raise their prices by 10%. Now monetary authority enters the scene they view 5% inflation as too high. They want an average inflation of 2% so they reduce the growth of money supply. To attain this goal, inflation has to be lower by 3% both for tradables and non-tradables. This implies that non-tradable prices must increase only by 7% (10%-3%), while tradable prices will decline by 3% (0% - 3%). But if tradable prices decline by 3% then there will be an arbitrage opportunity foreigners will start buying more domestic goods (as they are cheaper), and this demand will increase the demand for local currency. The currency will start appreciating. It must appreciate by 3% to offset the decline in the price of domestic goods. In this example, the productivity increase in the tradables sector requires 5% appreciation of the real exchange rate. It happened by a combination of 2% inflation and 3% nominal exchange rate appreciation. III. The short-run determination of the exchange rate 1. Interest parity condition In the short run nominal exchange rates have to be thought of as the price of an asset. The asset is the currency. In that sense, exchange rates react to differences in the returns of the assets, most notably to differences in interest rates. Holding assets denominated in a currency leads to a return that is composed of two parts: the interest rate and the expected appreciation/depreciation of the currency. As a result, differences in nominal interest rates reflect the market expectations of future evolution of the currency. There are two types of parity conditions we expect to see in foreign exchange markets. Covered Interest Parity: The difference in interest rates between two countries is equal to the expected appreciation as measured by the forward exchange rate. This condition always holds because of arbitrage (no risk involved). Uncovered Interest Parity: The difference in interest rates between two countries is equal to the expected rate of appreciation in the spot market. Let s consider only the UIP condition. The basic statement is that (in expectation) returns across countries should be the same when converted to

12 Page 12 the same currency. In other words the following two investment strategies should give you the same return: A. Putting 1000 US dollars in a US bank which pays an interest rate i for 1 year. B. Using 1000 US dollars to buy yen (1000x110 = ), then depositing the money in a Japanese bank for 1 year and finally converting the proceeds at the prevailing exchange rate 1 year from now into US dollars. We can express the equality in the returns for these two strategies as follows: 1000 e t 1000 * (1 + i) = e (1 + i*) t+ 1 Where the following applies: e t = Exchange rate today (defined as foreign/local currency) e t+1 = Exchange rate one year from now i = Domestic nominal interest rate (from t to t+1) i* = Foreign nominal interest rate (from t to t+1) By cancelling 1000 on both sides we can simplify it to: e (1 + i) = t (1 + i*) e t+ 1 To understand the intuition for this relationship it is useful to rewrite the above equation as an approximation (in %): i* i + % NER Intuition: if the domestic interest rate is higher than the foreign interest rate, there has to be a depreciation of the local currency to equalize returns in the two currencies (e t > e t+1 or equivalently % NER < 0). 2. Putting everything together: Monetary Policy, Interest Rates and Exchange Rates How can we reconcile the purchasing power theory of exchange rates with the interest parity condition? Furthermore, the interest parity condition gives

13 Page 13 somewhat a counterintuitive prediction: many people would think that higher interest rate will lead to appreciation (and not depreciation) of the currency. Is this intuition wrong? Fortunately, the answer is No intuition is correct, but as we will see below the question is different. The following example will illustrate how the explicit consideration of the timing of the effect is crucial in reconciling our intuition with the interest parity condition and with PPP. Suppose we consider a permanent increase in money supply in the US while the foreign country EMU, holds its money supply (and therefore interest rates and prices) constant. Looking at the money market in the US we know that initially there will be a decline in interest rates in the US, but over time prices will start increasing and the interest rate will go back to where they were before the monetary expansion. In the long run a permanent increase in money supply will be reflected in an increase in the price level, and no change in interest rates. The figure below describes only the short run effect. In the long run the real money supply is back at its original position. We can describe these events in a dynamic setting. At time 0, money supply changes by 10%. The thin dotted line gives the long-run value of the variable.

14 Page 14 Money Money supply changes permanently by 10%. Time 0 Interest rates Time 0 Prices Time Time Because of higher liquidity in the economy interest rates drop. But over time as prices start increasing, interest rates return to the initial level. Prices increase slowly to their equilibrium value, which should be 10% above the initial price level. Time 0 Time What happens to the exchange rate? We can use now purchasing power parity, which as we know works in the long run: If prices are higher in the US, then the nominal exchange rate must depreciate to keep the prices of tradable goods equal across countries (when converted in the same currency). So, after full adjustment, the US dollar must depreciate by 10% -- this is given by the purchasing power parity condition. How will the adjustment to equilibrium occur? We can use the interest parity condition: In the period after the increase in money supply interest rates in the US are lower. To ensure that investors get the same return in US dollars and in euros (where interest rates did not change), it must be true that the dollar appreciates over the adjustment period. But how is it possible to have appreciation if the long run value of the dollar is lower than the initial one? The answer is that immediately after the change in money supply the dollar must depreciate so much that it overshoots its equilibrium value. Then in the process of adjustment the dollar appreciates. The overshooting happens because US investors leave the country when interest rates drop, which puts pressure on the exchange rate. Capital outflows continue until the exchange rate is so low that it must appreciate to reach its long term value, i.e. when the low returns from US

15 Page 15 interest rates are matched by appreciation of the dollar, which will make the dollar returns equal to euro returns. Exchange rate Time 0 Time In the long run the dollar will depreciate by 10%. The adjustment to this value is by sharp depreciation immediately after the change in money supply and slow appreciation afterwards. Summary: 1. The intuition works for the immediate impact a reduction in interest rate leads to immediate currency depreciation. 2. Interest parity condition applies to the process of adjustment lower interest rates imply appreciation of the currency. 3. Purchasing power parity guides exchange rates in the long run increase in the price level implies depreciation of the nominal exchange rate.