Homework's Mathematical Methods
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Session3-Part2-chapter3.pptxExchange Rates I: The Monetary
Approach in the Long Run
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Exchange Rates and Prices in the Long Run
Money, Prices, and Exchange Rates in the Long Run
The Monetary Approach
Money, Interest Rates, and Prices in the Long Run
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The goal of this chapter is to set out the long-run relationships between money, prices, and exchange rates. The theory we will develop has two parts:
The first involves the theory of purchasing power, which links the exchange rate to price levels in each country in the long run.
The second involves how price levels are related to monetary conditions in each country.
Combining the monetary and the purchasing power theory we will develop a long-run theory known as the monetary approach to exchange rates.
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Introduction
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1 Exchange Rates and Prices in the Long Run: Purchasing Power Parity and Goods Market Equilibrium
Arbitrage occurs in the international goods markets just as in the international financial markets. Therefore, the prices of goods in different countries expressed in a common currency tend to be equalized.
Applied to a single good, this idea is referred to as the law of one price.
Applied to an entire basket of goods, it is called the theory of purchasing power parity.
We will develop a simple theory based on an idealized world of frictionless trade where transaction costs can be neglected.
We start with single goods and the law of one price then move baskets of goods and purchasing power parity.
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The law of one price (LOOP) states that in the absence of trade frictions and under free competition and price flexibility, identical goods sold in different locations must sell for the same price when expressed in a common currency.
We can state the law of one price as follows, for the case of any good g sold in two locations:
The Law of One Price
Where expresses the rate at which currencies can be exchanged.
1 Exchange Rates and Prices in the Long Run: Purchasing Power Parity and Goods Market Equilibrium
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We can rearrange the equation for price equality
The Law of One Price
to show that the exchange rate must equal the ratio of the goods’ prices expressed in the two currencies:
1 Exchange Rates and Prices in the Long Run: Purchasing Power Parity and Goods Market Equilibrium
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The principle of purchasing power parity (PPP) is the macroeconomic counterpart to the microeconomic law of one price (LOOP). To express PPP algebraically, we can compute the relative price of the two baskets of goods in each location:
Purchasing Power Parity
There is no arbitrage when the basket is the same price in both locations qUS/EUR = 1.
PPP holds when price levels in two countries are equal when expressed in a common currency. This is called absolute PPP.
1 Exchange Rates and Prices in the Long Run: Purchasing Power Parity and Goods Market Equilibrium
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The real exchange rate is the relative price of the baskets.
The U.S. real exchange rate qUS/EUR = E$/€ PEUR/PUS tells us how many U.S. baskets are needed to purchase one European basket.
The exchange rate for currencies is a nominal concept. The real exchange rate is a real concept.
The real exchange rate has terminology similar to the nominal exchange rate:
If the real exchange rate rises (more Home goods are needed in exchange for Foreign goods), Home has experienced a real depreciation.
If the real exchange rate falls, Home has experienced a real appreciation.
The Real Exchange Rate
1 Exchange Rates and Prices in the Long Run: Purchasing Power Parity and Goods Market Equilibrium
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Purchasing power parity states that the real exchange rate is equal to 1.
If the real exchange rate qUS/EUR is below 1 then Foreign goods are relatively cheap.
In this case, the Home currency is said to be strong, the euro is weak, and we say the euro is undervalued.
If the real exchange rate qUS/EUR is above 1, then Foreign goods are relatively expensive.
In this case, the Home currency is said to be weak, the euro is strong, and we say the euro is overvalued.
Absolute PPP and the Real Exchange Rate
1 Exchange Rates and Prices in the Long Run: Purchasing Power Parity and Goods Market Equilibrium
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We can rearrange the no-arbitrage equation for the equality of price levels, to allow us to solve for the exchange rate that would be implied by absolute PPP:
Absolute PPP:
Absolute PPP, Prices, and the Nominal Exchange Rate
(3-1)
Purchasing power parity implies that the exchange rate at which two currencies trade equals the relative price levels of the two countries.
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We now examine the implications of PPP for the study of inflation (the rate of change of the price level) using 3-1.
On the left-hand side, the rate of change of the exchange rate in Home is the rate of exchange rate depreciation in Home given by
Relative PPP, Inflation, and Exchange Rate Depreciation
(3-1)
1 Exchange Rates and Prices in the Long Run: Purchasing Power Parity and Goods Market Equilibrium
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We now examine the implications of PPP for the study of inflation (the rate of change of the price level) using 3-1.
Relative PPP, Inflation, and Exchange Rate Depreciation
(3-1)
On the right, the rate of change of the ratio of two price levels equals the rate of change of the numerator minus that of the denominator:
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If equation (3-1) holds for levels of exchange rates and prices, then it must also hold for rates of change in these variables. By combining the last two expressions, we obtain:
Relative PPP, Inflation, and Exchange Rate Depreciation
This way of expressing PPP is called relative PPP, and it implies that the rate of depreciation of the nominal exchange rate equals the difference between the inflation rates of two countries.
(3-2)
1 Exchange Rates and Prices in the Long Run: Purchasing Power Parity and Goods Market Equilibrium
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Evidence for PPP in the Long Run and Short Run
FIGURE 3-2
Inflation Differentials and the Exchange Rate, 1975-2005 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.
APPLICATION
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Evidence for PPP in the Long Run and Short Run
FIGURE 3-3
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.
APPLICATION
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Research shows that price differences—the deviations from PPP—can be quite persistent.
What Explains Deviations from PPP?
Economists have found a variety of reasons why PPP fails in the short run:
Transaction costs. Include costs of transportation, tariffs, duties, and other costs due to shipping and delays associated with developing distribution networks and satisfying legal and regulatory requirements in foreign markets. On average, they are more than 20% of the price of goods traded internationally.
Nontraded goods. Some goods are inherently nontradable; they have infinitely high transaction costs. Most goods and services fall somewhere between tradable and nontradable.
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Imperfect competition and legal obstacles. Many goods are not simple undifferentiated commodities, as LOOP and PPP assume. Differentiated goods create conditions of imperfect competition because firms have some power to set the price of their good, allowing firms to charge different prices not just across brands but also across countries.
Price stickiness. Prices do not or cannot adjust quickly and flexibly to changes in market conditions.
Selection of the basket of goods.
What Explains Deviations from PPP?
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Home of the undervalued burger?
The Big Mac Index
For more than 20 years, The Economist newspaper has engaged in a whimsical attempt to judge PPP theory based on a well-known, globally uniform consumer good: the McDonald’s Big Mac. The over- or undervaluation of a currency against the U.S. dollar is gauged by comparing the relative prices of a burger in a common currency, and expressing the difference as a percentage deviation from one:
HEADLINES
AP Photo/Greg Baker
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2 Money, Prices, and Exchange Rates in the Long Run: Money Market Equilibrium in a Simple Model
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.
This section recaps the essential elements of monetary theory and shows how they fit into our theory of exchange rates in the long run.
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Economists think of money as performing three key functions in an economy:
Money is a store of value because it can be used to buy goods and services in the future. If the opportunity cost of holding money is low, we will hold money more willingly than we hold other assets.
Money also gives us a unit of account in which all prices in the economy are quoted.
Money is a medium of exchange that allows us to buy and sell goods and services without the need to engage in inefficient barter.
What Is Money?
2 Money, Prices, and Exchange Rates in the Long Run: Money Market Equilibrium in a Simple Model
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The Measurement of Money
FIGURE 3-4
The Measurement of Money This figure shows the major kinds of monetary aggregates (currency, M0, M1, and M2) for the United States from 2004 to 2012. Normally, bank reserves are very close to zero, so M0 and currency are virtually identical, but reserves spiked up during the financial crisis in 2008, as private banks sold securities to the Fed and stored up the cash proceeds in their Fed reserve accounts.
The Supply of Money: In practice, a country’s central bank controls the money supply. We make the simplifying assumption that the central bank’s indirectly, but accurately, control the level of M1.
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