1 International Macroeconomics Chapter 3 The Monetary Approach in the Long Run

2 Chapter Outline Exchange rates, prices, and money in the long run The monetary approach to exchange rates The Fisher effect The real exchange rate approach

3 Exchange Rates and Prices in the Long Run --- Law of One Price (LOOP) Suppose that a Big Mac is sold for $3.5 in the U.S., if the exchange rate between euro and U.S. dollar is $1.12/€, what should be the price of a Big Mac in terms of euro in a MacDonald restaurant in Italy, ignoring the transportation costs and other costs? $3.5  $1.12/€ = €3.92 The Law of One Price says that identical goods in different competitive markets must be sold for the same price when measured in the same currency, when transportation costs and barriers between those markets are not important. If the Law of one price is violated, an arbitrage opportunity could occur. o Big Mac price index: o iPhone price index:

Law of One Price for Hamburgers?

5 Law of One Price The absolute version of LOOP P i,t = E t · P i,t * The relative version of LOOP P i,t = P i,t-1 E t-1 ·P i,t-1 * E t ·P i,t *, Where E t is of american quote.

6 Purchasing Power Parity Purchasing power parity is the application of the law of one price across countries for all goods and services, or for representative groups (“baskets”) of goods and services. P US = (E US$/C$ ) x (P Canada ) P US = level of average prices in the US P Canada = level of average prices in Canada E US$/C$ = US dollar/Canadian dollar exchange rate

7 Purchasing Power Parity (cont.) Purchasing power parity implies that E US$/C$ = P US /P Canada –Levels of average prices determine the exchange rate. –If the price level in the US is US$200 per basket, while the price level in Canada is C$400 per basket, PPP implies that the C$/US$ exchange rate should be C$400/US$200 = C$2/US$1 –Purchasing power parity predicts that people in all countries have the same purchasing power with their currencies: 2 Canadian dollars buy the same amount of goods as 1 US dollar, since prices in Canada are twice as high. –An application is PPP-based GDP.

8 Purchasing Power Parity (cont.) Absolute PPP: purchasing power parity that has already been discussed. Exchange rates equal the level of relative average prices across countries. E $/€ = P US /P EU Relative PPP: changes in exchange rates equal changes in prices (inflation) between two periods: (E $/€,t - E $/€, t –1 )/E $/€, t –1 =  US, t -  EU, t where  t = inflation rate from period t-1 to t

Real Exchange Rate The real exchange rate is the rate of exchange for goods and services across countries. –In other words, it is the relative value/price/cost of goods and services across countries. –For example, it is the dollar price of a European group of goods and services relative to the dollar price of a American group of goods and services: q $/€ = (E $/€ x P EU )/P US –If q = 1, PPP holds; –If q > 1, euro (overvalued) has a real appreciation against dollar; –If q < 1, euro (undervalued) has a real depreciation against dollar.

Exchange Rates and Prices in the Long Run Building Block: Price Levels and Exchange Rates in the Long Run According to the PPP Theory In this model, the price levels are treated as known exogenous variables (in the green boxes). The model uses these variables to predict the unknown endogenous variable (in the red box), which is the exchange rate.

Exchange Rates and Prices in the Long Run Inflation Differentials and the Exchange Rate, This scatterplot shows the relationship between the rate of exchange rate depreciation against the U.S. dollar and the inflation differential against the United States over the long run, for a sample of 82 countries. The correlation between the two variables is strong and bears a close resemblance to the prediction of PPP that all data points would appear on the 45- degree line.

Exchange Rates and Prices in the Long Run Exchange Rates and Relative Price Levels Data for the U.S. and the UK for 1975 to 2010 show that the exchange rate and relative price levels do not always move together in the short run. Relative price levels tend to change slowly and have a small range of movement; exchange rates move quickly and experience large fluctuations. Therefore, relative PPP does not hold in the short run. It is a better guide to the long run, and we can see that the two series do tend to drift together over the decades.

13 Empirical Evidence of PPP There is little empirical support for absolute purchasing power parity, especially in the short-run. –The prices of identical commodity baskets, when converted to a single currency, differ substantially across countries. Relative PPP is more consistent with data, but it also performs poorly to predict exchange rates.

14 Explanations for the Violation of PPP Reasons why PPP may not be accurate: the law of one price may not hold because of 1.Trade barriers and non-tradable products 2.Imperfect competition 3.Differences in measures of average prices for baskets of goods and services

15 Monetary Approach to Exchange Rates In the long run the exchange rate is determined by the ratio of the price levels in two countries. But this prompts a question: What determines those price levels? Monetary theory supplies an answer: in the long run, price levels are determined in each country by the relative demand and supply of money. How does monetary theory fit into our theory of exchange rates in the long run?

16 What is Money? Money is an asset that is widely accepted as a means of payment. Only assets—things of value that people own—can be considered as money –Can credit cards be considered as money? Only things that are widely acceptable as a means of payment are regarded as money –Can stocks or bonds be considered as money? Money has two useful functions –Provides a unit of account Standardized way of measuring value of things that are traded –Serves as store of value One of several ways in which households can hold their wealth

17 Money Supply –Total amount of money held by the public Governments use different measures of the money supply –Each measure includes a selection of assets that are widely acceptable as a means of payment and are relatively liquid An asset is considered liquid if it can be converted to cash quickly and at little cost –So, an illiquid asset can be converted to cash only after a delay, or at considerable cost

18 Money Supply (cont.) Assets and their liquidity Most liquid asset is cash in the hands of the public Next in line are asset categories of about equal liquidity –Demand deposits (Checking accounts) –Other checkable deposits –Travelers checks Then, savings-type accounts –less liquid than checking-type accounts, since they do not allow you to write checks Next on the list are deposits in retail money market mutual funds Time deposits (called certificates of deposit, or CDs) –Require you to keep your money in the bank for a specified period of time (usually six months or longer) Impose an interest penalty if you withdraw early

19 Money Supply (cont.) Standard measure of money stock (supply) is M1 –Sum of the first four assets in our list M1 = cash in the hands of the public + demand deposits + other checking account deposits + travelers checks –When economists or government officials speak about “money supply,” they usually mean M1 Another common measure of money supply, M2, adds some other types of assets to M1 –M2 = M1 + savings-type accounts + retail MMMF balances + small denomination time deposits

20 Money Supply (cont.) The central bank substantially controls the quantity of money that circulates in an economy, the money supply. –In the US, the central banking system is the Federal Reserve System. The Federal Reserve System directly regulates the amount of currency in circulation. It indirectly influences the amount of checking deposits, debit card accounts, and other monetary assets.

21 Money Demand At any given moment, total amount of wealth we have is given –Total wealth = Money + Other assets –If we want to hold more wealth in form of money, we must hold less wealth in other assets Money demand represents the amount of monetary assets that people are willing to hold (instead of other assets).

22 Money Demand (cont.) What factors influence the demand for money? Interest rates/expected rates of return –A higher interest rate means a higher opportunity cost of holding monetary assets  lower demand of money. Prices of goods and services –A higher level of average prices means a greater need for liquidity to buy the same amount of goods and services  higher demand of money. Income – A higher real national income (GNP) means more goods and services are being produced and bought in transactions, increasing the need for liquidity  higher demand of money.

23 A Model of Money Demand The aggregate demand of money can be expressed as: M d = P x L(R,Y) where: P is the price level Y is real national income R is a measure of interest rates on non-monetary assets L(R,Y) is the aggregate demand of real monetary assets Alternatively: M d /P = L(R,Y) Aggregate demand of real monetary assets is a function of national income and interest rates.

24 Aggregate Real Money Demand and the Interest Rate For a given level of income, real money demand decreases as the interest rate increases.

25 Effect on the Real Money Demand Schedule of a Rise in Real Income When income increases, real money demand increases at every interest rate.

26 Determination of the Equilibrium Interest Rate

27 Effect of an Increase in the Money Supply on the Interest Rate An increase in the money supply lowers the interest rate for a given price level. A decrease in the money supply raises the interest rate for a given price level.

28 Effect on the Interest Rate of a Rise of a Rise in Real Income An increase in national income increases equilibrium interest rates for a given price level.

29 Money Market/Exchange Rate Linkages

30 Monetary Approach to Exchange Rates Monetary approach to the exchange rate: uses monetary factors to predict how exchange rates adjust in the long run. –It uses the absolute version of PPP. –It predicts that levels of average prices across countries adjust so that the quantity of real monetary assets supplied will equal the quantity of real monetary assets demanded: P US = M s US /L (R $, Y US ) P EU = M s EU /L (R €, Y EU )

31 Monetary Approach to Exchange Rates –In terms of growth rates, we have %  P = %  M s - %  L (R, Y) Inflation Rate (  ) Money Supply Growth Rate (  ) Real Money Demand Growth Rate ( ) Real money demand growth rate is an increasing function of real income growth rate (g).

32 Monetary Approach to Exchange Rates (cont.) P$P$ E $/€ = P€P€ M s EU /L (R €, Y EU ) M s US /L (R $, Y US ) = According to PPP, the exchange rate is determined in the long run by prices, which are determined by the relative supply and demand of real monetary assets in money markets across countries.

33 Monetary Approach to Exchange Rates (cont.) P$P$ E $/€ = P€P€ M s EU /L (R €, Y EU ) M s US /L (R $, Y US ) = %  E $/€ =  US -  EUR = (  US -  EUR ) – ( US - EUR ) Since

34 Monetary Approach to Exchange Rates (cont.) Forecasting Exchange Rates: An Example Assume that U.S. and European real money demand growth rates are zero and the European inflation rate is also zero. − A one-time increase in the U.S. money supply, say 10%.  Given that real money demand doesn’t change, the U.S. price level much increase in proportion to its money supply.  If prices are quickly adjusted and PPP holds, E $/€ will increase proportionally, i.e. an increase of 10%. Consequently, U.S. dollar depreciates by 10%. −An increase in the rate of U.S. money growth

35 Monetary Approach to Exchange Rates (cont.) PPP and an assumed stable foreign price level imply that the exchange rate will follow a path similar to that of the domestic price level, so E also grows at the new rate μ + Δμ, and the rate of depreciation rises by Δμ, as shown in panel (d). Forecasting Exchange Rates: An Example

36 Monetary Approach to Exchange Rates (cont.) Predictions about changes in: 1.Money supply: a permanent rise in the domestic money supply  causes a proportional increase in the domestic price level,  causing a proportional depreciation in the domestic currency (through PPP).  same prediction as long run model without PPP 2.Interest rates: a rise in domestic interest rates  lowers the demand of real monetary assets,  and is associated with a rise in domestic prices,  causing a proportional depreciation of the domestic currency (through PPP).

37 Monetary Approach to Exchange Rates (cont.) 3.Output level: a rise in the domestic level of production and income (output) –raises domestic demand of real monetary assets, –is associated with a decreasing level of average domestic prices (for a fixed quantity of money supplied), –causing a proportional appreciation of the domestic currency (through PPP). All 3 changes affect money supply or money demand, and cause prices to adjust so that the quantity of real monetary assets supplied matches the quantity of real monetary assets demanded, and cause exchange rates to adjust according to PPP.

38 Monetary Approach to Exchange Rates (cont.) Evidence for the Monetary Approach Inflation Rates and Money Growth Rates, 1975–2005 This scatterplot shows the relationship between the rate of inflation and the money supply growth rate over the long run. The correlation between the two variables is strong and bears a close resemblance to the theoretical prediction of the monetary model that all data points would appear on the 45-degree line.

39 Monetary Approach to Exchange Rates (cont.) Evidence for the Monetary Approach This scatterplot shows the relationship between the rate of exchange rate depreciation and the money growth rate differential relative to the United States over the long run. The data show a strong correlation between the two variables and a close resemblance to the theoretical prediction of the monetary approach to exchange rates, which would predict that all data points would appear on the 45-degree line.

40 The Fisher Effect The Fisher effect (named after economist Irving Fisher) describes the relationship between nominal interest rates and inflation. –Derive the Fisher effect from the interest parity condition: R $ - R € = (E e $/€ - E $/€ )/E $/€ –If financial markets expect (relative) PPP to hold, then expected exchange rate changes will equal expected inflation between countries: (E e $/€ - E $/€ )/E $/€ =  e US -  e EU –R $ - R € =  e US -  e EU –The Fisher effect: a rise in the domestic inflation rate causes an equal rise in the interest rate on deposits of domestic currency in the long run, when other factors remain constant.

41 The Fisher Effect (cont.) Rearranging the last equation, we find Subtracting the inflation rate (π) from the nominal interest rate (i), results in a real interest rate (r), the inflation-adjusted return on an interest-bearing asset. This result states the following: If PPP and UIP hold, then expected real interest rates are equalized across countries. This powerful condition is called real interest parity. Real interest parity implies the following: Arbitrage in goods and financial markets alone is sufficient, in the long run, to cause the equalization of real interest rates across countries. Real Interest Parity

42 The Fisher Effect (cont.) Suppose that the U.S. central bank unexpectedly increases the growth rate of the money supply at time t 0. Suppose also that the inflation rate is π in the US before t 0 and π +  π after this time, but that the European inflation rate remains at 0%. According to the Fisher effect, the interest rate in the U.S. will adjust to the higher inflation rate. What would happen to the price level? And what would happen to exchange rate ($/€).

Long-Run Time Paths of U.S. Economic Variables After a Permanent Increase in the Growth Rate of the U.S. Money Supply

Long-Run Time Paths of U.S. Economic Variables After a Permanent Increase in the Growth Rate of the U.S. Money Supply (cont.)

45 The Fisher Effect (cont.) Evidence on the Fisher Effect Inflation Rates and Nominal Interest Rates, 1995–2005 This scatterplot shows the relationship between the average annual nominal interest rate differential and the annual inflation differential relative to the United States over a ten-year period for a sample of 62 countries. The correlation between the two variables is strong and bears a close resemblance to the theoretical prediction of the Fisher effect that all data points would appear on the 45-degree line.

46 The Fisher Effect (cont.) Evidence on the Fisher Effect This figure shows actual real interest rate differentials over three decades for the United Kingdom, Germany, and France relative to the United States. These differentials were not zero, so real interest parity did not hold continuously. But the differentials were on average close to zero, meaning that real interest parity (like PPP) is a general long-run tendency in the data.

The Real Exchange Rate Approach to Exchange Rates According to the general real exchange rate approach, exchange rates may also be influenced by the real exchange rate: E $/€ = q US/EU x P US /P EU What influences the real exchange rate? –A change in relative demand of U.S. products The demand for US products relative to the demand for EU products depends on the relative price of these products, or the real exchange rate. When the real exchange rate, q US/EU = (E $/€ P EU )/P US is high, the relative demand for US products is high. –A change in relative supply of U.S. products In the long run, the supply of goods and services in each country depends on factors of production like labor, capital and technology—not prices or exchange rates.

Determination of the Long-Run Real Exchange Rate

The Real Exchange Rate Approach to Exchange Rates (cont.) What are the effects on the nominal exchange rate? E $/€ = q US/EU x P US /P EU When only monetary factors change and PPP holds, we have the same predictions as before. –Nominal exchange rates are determined by PPP. When factors influencing real output change, the real exchange rate changes. –With an increase in relative demand of domestic products, the real exchange rate adjusts to determine nominal exchange rates. –With an increase in relative supply of domestic products, the situation is more complex …

The Real Exchange Rate Approach to Exchange Rates (cont.) With an increase in the relative supply of domestic products, the real exchange rate adjusts to make the price/cost of domestic goods depreciate, but also the relative amount of domestic output increases. –This second effect increases the demand of real monetary assets in the domestic economy: P US = M s US /L (R $, Y US ) –Thus, the level of average domestic price is predicted to decrease relative to the level of average foreign price. –The effect on the nominal exchange rate is ambiguous: E $/€ = q US/EU x P US /P EU ?

Effects of Money Market and Output Market Changes on the Long-Run Nominal Dollar/Euro Exchange Rate, E $/€ ChangeEffect on the long-run nominal $/€ exchange rate, E $/€ Money Market 1. Increase in U.S. money supply levelProportional increase (nominal depreciation of $) 2. Increase in European money supply levelProportional decrease(nominal depreciation of €) 3. Increase in U.S. money supply growth rateIncrease (nominal depreciation of $) 4. Increase in European money supply growth rateDecrease (nominal depreciation of €) Output Market 1. Increase in demand for U.S. outputDecrease (nominal appreciation of $) 2. Increase in demand for European outputIncrease (nominal appreciation of €) 3. Output supply increase in the U.S.Ambiguous 4. Output supply increase in the EuropeAmbiguous