Session 14. Exchange Rate Determination

Transcription

1 Session 14. Exchange Rate Determination v Exchange Rates in the Long Run v Absolute PPP: a long-run theory of real exchange rates v Relative PPP: predicting exchange rates using inflation rates v Productivity, or Why do poor countries have lower prices? v Short Run: Currencies as Assets v Interest parity conditions v Putting everything together: monetary policy, interest rates and exchange rates v Are foreign exchange markets efficient? The overvaluation of the USD in the 80 s. v The $/ exchange rate from 1975 to 2012 Exchange Rates: Definitions Nominal Exchange rate Relative price of the currencies of two countries How many units of foreign currency one can buy with one unit of domestic currency Real exchange rate How many foreign goods one can buy with one unit of a domestic good; or simply the ratio of prices. ε = e P P* ε real exchange rate e nominal exchange rate P price of a domestic good (basket of goods) P* price of a foreign good (basket of goods) 1

2 Theory #1: Arbitrage ensures that prices are equal across countries (Absolute PPP theory) PPP theory If all goods were subject to perfect arbitrage then the real exchange rate would always be equal to 1. This theory implies that the nominal exchange rate will be simply the ratio of the prices in the two countries: ε = 1 => e = P * P 2

3 Exchange rates: PPP Let s determine the real exchange rate between a Microsoft Xbox 360 Kinect sold in France and in the US (source: Amazon.com and Amazon.fr on May 8, 2012) (France is the home country in this example) P France = 186; P US = $199; e = 1.30$/ 1.30 *186 ε = = According to this example is the euro over/undervalued? What is the nominal exchange rate that will preclude arbitrage? Theory #1: Arbitrage ensures that prices are equal across countries. Absolute PPP theory. Theory #2: Prices are not identical across countries but their differences remain constant (because barriers to trade, transportation costs, do not change much). Relative PPP theory. 3

4 Relative Purchasing Power Parity v Trade barriers, imperfect competition, transportation costs and the existence of non-traded goods i.e. the factors that are responsible for the failure of PPP are stable over time and they cannot account for differences in inflation across countries. So even if the real exchange rate is not equal to 1, we can assume (for the time being) that it is constant. Recall that: % change in RER = % change in NER + Domestic inflation - Foreign inflation % Δ RER = 0 => % ΔNER = π* π Relative PPP: Inflation and the Nominal Exchange Rate Percentage change in nominal exchange rate Sweden Australia New Zealand Spain Ireland Canada South Africa France UK Belgium 0-1 Germany Netherlands - 2 Switzerland - 3 Japan Inflation differential Source: Mankiw (Fig.5.13). Averages for Italy Depreciation relative to U.S. dollar Appreciation relative to U.S. dollar 4

5 Theory #1: Arbitrage ensures that prices are equal across countries. Absolute PPP theory. Theory #2: Prices are not identical across countries but their differences remain constant (because barriers to trade, transportation costs, do not change much). Relative PPP theory. Theory #3: There is more than just barriers to trade and transportation costs. There are other factors and these factors might not be constant over time. 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. Plainly, prices in initially poor countries increase as these countries catch up with the advanced economies. To understand these changes we have to start with a set of assumptions: 1. There is a tradable and a non-tradable sector. Prices of tradables are roughly the same around the world but this is not true for nontradables, because there is no possibility for arbitrage. 2. There is enough labor mobility across sectors so that wages in the two sectors (i.e. tradables and non-tradables) are equal (or the ratio between the wages in the two sectors is constant). 3. Productivity differences are large in the tradable sector but small for non-traded goods. 5

6 Productivity and Exchange Rates Example: Germany versus Spain. Number of hours required to Spain Germany Produce a car Serve a beer Price of a car is the same in both countries because of arbitrage: 20,000 Euros Wage in Germany: 20 euros/hour Wage in Spain: 10 euros/hour Price of a beer in Germany: 4 euros Price of a beer in Spain: 2 euros As productivity in Spain increases, wages and therefore prices of non-tradables in Spain will increase and the real exchange rate will appreciate. Because Spain and Germany share a currency, this can happen only 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). Productivity and Exchange Rates This theory (due to Balassa and Samuelson) makes several very strong predictions: 1. Price levels should be lower in less productive (poor) 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 rates appreciating. 3. The effect of the catching up process can manifest itself in two ways: via nominal appreciation or via higher inflation in the poor country. 6

7 Price Levels are Different across Countries India Botswana China Turkey Brazil Germany Japan Switzerland Price Differences (Relative to the US) in 2009 Exchange rates: PPP 7

8 Exchange rates: PPP Price Levels are Correlated with Level of Development Rich countries generally have higher prices (i.e. a higher real exchange rate) Price Level (relative to the US, Index US=100) 1.6 Denmark 1.4 Switzerland 1.2 UK Portugal 1 USA China 0.8 Korea India Turkey Vietnam Real GDP per Capita in USD (2009) 8

9 Closing the Productivity Gap Requires that the RER Appreciates Example: Productivity growth in Japan in the period outpaced that of the U.S. This led to an increase in the price level in Japan relative to the U.S. This is what we call a real exchange rate appreciation. Most of it happened through a nominal appreciation of the exchange rate (and not through differences in inflation rates) Productivity and Exchange Rates: Japan vs. US Index 1960= Relative Productivity (Japan/US) Real Exchange Rate (Japan/US) Real appreciation can happen in two ways. v In Japan it happened predominantly through nominal exchange rate appreciation: In 1970 one US dollar could buy 358 Yen, by 2001 the nominal exchange rate was about 120 Yen/$. v Most of the time it happens as a mixture of the two nominal appreciation and some inflation. v In the European Monetary Union today we observe inflation differences between Spain and Portugal on the one hand, and Germany and France on the other. Most of this inflation differences can be explained with the catching up hypotheses. In other words most of the real exchange rate appreciation comes from increases in prices of non-tradables. v In China, we have seen some nominal appreciation combined with higher inflation. 9

10 PPP does not work in the short run. Exchange rates are too volatile. Australia (AUD/USD) Japan (JPY/USD) Nominal Exchange Rate PPP-Implied Exchange Rate Nominal Exchange Rate PPP-Implied Exchange Rate UK (GBP/USD) Nominal Exchange Rate PPP-Implied Exchange Rate Theory #1: Arbitrage ensures that prices are equal across countries. Absolute PPP theory. Theory #2: Prices are not identical across countries but their differences remain constant (because barriers to trade, transportation costs, do not change much). Relative PPP theory. Theory #3: There is more than just barriers to trade and transportation costs. Some goods are not traded. Can this help us explain the behavior of exchange rates in some countries? Theory #4: Currencies are assets and exchange rates represent their prices. Let s use asset pricing to think about exchange rates. 10

11 Exchange Rates as Asset Prices Stylized Fact #1: exchange rates are extremely volatile Stylized Fact #2: volume on foreign exchange markets is very large Daily Turnover Foreign Exchange Markets Billions USD Exchange Rates as Asset Prices v In the short run, think about currencies as assets. Deposits in different currencies represents different assets. The returns on these deposits will be affected by exchange rate movements. Arbitrage will ensure that returns are equalized across currencies. v To understand how arbitrage will determine the evolution of the exchange rate, let s suppose that you have USD1,000 to invest. You consider two strategies: A. Put your money for 1 year in a bank deposit in USD that pays 1.05% interest. B. Convert the money to AUD dollars today, invest in a one-year AUD deposit which pays 5.85%, and at maturity convert the dollars back to USD. v The two investment strategies should give you (in expectation) the same return: USD 1,000 Convert at the current exchange rate: 0.94 AUD/USD AUD % Convert back to USD at: AUD/USD ( expected exchange rate) 5.85% USD 1,010.5 USD 1,010.5 AUD

12 Exchange Rates as Asset Prices Some notation: e t = Nominal exchange rate today (defined as foreign currency/local currency) e t+1 = Nominal exchange rate tomorrow i = Domestic nominal interest rate (from t to t+1) i* = Foreign nominal interest rate (from t to t+1) (1+i) = (1+i*) e t e t+1 Or approximately: i+%δe t,t+1 i* If i > i*, i.e. domestic interest rates are higher than foreign, then our currency must depreciate! 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 ) This equation is called uncovered interest parity condition (UIP). Advanced: Forward Rates In the previous equation the exchange rate tomorrow is not known today. In a risky world this condition might not hold because financial markets do not simply equalize expected returns, they need to adjust for risk. One way to get rid of this problem is to use as tomorrow s exchange rate, the forward rate for the exchange rate (i.e. the forward rate quoted today for the spot rate tomorrow). No risk involved here. If we call this forward rate f t, then it has to be the case that: (1+i) = (1+i*) e t f t This is called covered interest parity and it always holds. In fact, forward rates are quoted from interest rates. It is always the case that if a country has a low interest rate, the forward rate signals an appreciation of the currency. Example: Here is the data for the US and Japan on June 11, 2008: Interest rate Japan (one year) = 0.73% Spot rate: e t = JPY/USD Interest rate U.S. (one year) = 2.5% Forward rate (one year) = JPY/USD 12

13 Monetary Policy, Interest Rates and Exchange Rates v The interest parity condition predicts that countries with higher interest rates will see their currencies depreciating. There is, however, a common belief that higher interest rates appreciate the currency. Furthermore, while the interest parity condition has a prediction about the exchange rate, so does the purchasing power parity. How to reconcile all this? v Consider a permanent increase in money supply in the US, while in Europe all factors are kept constant. We know from the money market that the increase in money supply will lower initially interest rates, but when prices start moving, the economy will return to the same interest rate as the one before the monetary expansion. Adjustment following monetary expansion Money Nominal Exchange Rate 1. In the long run the exchange depreciates by an amount equal to the increase in the price level (PPP) Time 0 Time Interest rates Time 0 Time Time 0 Time Prices Time 0 Time 3. On impact, the nominal exchange rate depreciates. It does so up to the point where the future appreciation matches the difference in interest rates and leads towards the new PPP longrun value. There is a unique value today that satisfies these two conditions. Intuitively, the exchange rate depreciations because lower interest rates trigger a capital outflow (the IS-LM model). 2. During the period where interest rates are lower (and there are no news) the exchange rate appreciates to ensure that there are no excess returns ( arbitrage in capital markets). The appreciation happens at a rate which is equal to the difference in interest rates. 13

14 The Exchange Rate 1.75 USD/EUR Exchange Rate What is the right value? PPP? ( ) PPP M1 1978M5 1981M9 1985M1 1988M5 1991M9 1995M1 1998M5 2001M9 2005M1 2008M5 2011M9 In the past, Central Banks have intervened when the currency moved too far from its fundamental value as it happened in September 1985 (Plaza Accord), February 1987 (Louvre Accord) and the interventions of November But the recent need to rebalance the large US current account deficit has led to a persistent (and large) undervaluation of the USD. The current Euro crisis is bringing the exchange rate back to PPP. Can the theory explain the data? The USD/EUR Exchange Rate What works: 1. Long term trend shows depreciating USD (because of higher inflation). 2. Some episodes of fast US growth and high interest rates (the early 80 s led to an appreciating USD. What cannot be explained: 1. The exchange rate is too volatile. 2. The link between interest rates and exchange rates is too weak. The spot rate is a better prediction than the interest rate differential. 3. Some short-term trends cannot be explained by any consistent economic theory. 4. There are too many episodes where the exchange rate appreciates (or depreciates) continuously over a long period of time. This is only possible if there is a continuous flow of news about monetary policy that always go in the same direction (very unlikely). 14

15 Summary: What Do We Know about Exchange Rates? 1. In the long run, exchange rates are determined by arbitrage of tradable goods. There is a long-run equilibrium value of the nominal exchange rate implied by arbitrage and the actual nominal exchange rate fluctuates around it. 2. In the long run, we can describe movements in nominal exchange rates as reflecting differences in inflation rates (adjusted for productivity changes). 3. In the short run, we think of exchange rates as asset prices. Interest rate determine the evolution of nominal exchange rates in the short run. An unexpected increase in the interest rate, leads to immediate appreciation of the currency. Once the interest rate has gone up, higher interest rates predict depreciation of the currency. The reason is arbitrage. Make the distinction between an increase in interest rates vs. higher interest rates. 4. Empirically, nominal exchange rates are much more volatile than any of the macroeconomic fundamentals and even the overshooting result cannot explain why exchange rates are so volatile. 5. Be aware that the theories that explain exchange rate movements are much more ex-post rationalization than tested hypothesis. Only way to anticipate changes in the exchange rate is if you are good at guessing what the theory of the day will be. Graphical Representation: Adjustment of Exchange Rates Following a Monetary Expansion i Money supply 1. Money supply (M) increases permanently by 10%. Because of higher liquidity interest rates drop. Equilibrium Nominal interest rate Short-run nominal interest rate M/P 2. Over time prices increase by 10%. This brings back the interest rate back to its initial level Money demand Real balances (M/P) 15