Chapter 8
Purchasing Power Parity and Real Exchange Rates
questions
1. What does the purchasing power of a money mean? How can it be measured?
Answer: The purchasing power of a money is also known as its real value and indicates the amount of goods and services that can be purchased with a given amount of the money. We measure purchasing power by first calculating the price level, which is a weighted average of the prices of the goods and services that people consume. The weights in the price level reflect the shares of these goods and services in the consumption bundle of a typical individual. The purchasing power of the money is then found by taking the reciprocal of the price level. The units of the price level are an amount of money per consumption bundle, and the units of purchasing power are consumption bundles per unit of money.
2. Suppose the government releases information that causes people to expect that the purchasing power of a money in the future will be less than they previously had expected. What will happen to the exchange rate today? Why?
Answer: Typically, when people think that the purchasing power of a money is going to decline in the future, due to higher expected inflation, they try to sell that currency today to get into a currency that will have more stable purchasing power. This reduced demand for the currency causes that currency to weaken or depreciate immediately.
3. What is the difference between a price level and a price index?
Answer: The price level is a weighted average of the prices of the goods and services that people consume. The price index is a ratio of a price level at one point in time to the price level in some base year, with the ratio usually multiplied by 100. Thus, if the price level in a given year is 30% higher than the price level in the base year, the price index would be 130. Price levels give you information about the purchasing power of a currency. Price indexes give you information about the rate of inflation between two points in time.
4. What do economists mean by the law of one price? Why might the law of one price be violated?
Answer: The law of one price says that the price of a good, when denominated in a particular currency, is the same wherever in the world the good is being sold. The law of one price relies on arbitrage in the goods market. If the good is being sold in one place at a low price and is being sold in a different place at a high price, people have an incentive to arbitrage the two markets. Therefore, anything that makes it difficult or costly to arbitrage in the goods market can create a deviation from the law of one price. Clearly, transaction costs, such as the costs of shipping, generate deviations from the law of one price that cannot be arbitraged. Tariffs and quotas on imports and exports also create deviations. If markets are not competitive and firms have some monopoly power, the corporation may decide to charge different prices in different countries, but it must be able to segment the markets to prevent arbitrage. If arbitrage cannot be done instantaneously, there will be a speculative element that enters the calculations and the speculator may have to be compensated for the risk of loss with an expected profit from buying in one market and selling in another market at a later point in time. Finally, various goods markets are subject to a certain amount of price stickiness because of the costs of changing prices. Because exchange rates are asset prices and freely flexible, unanticipated changes in exchange rates will create deviations from the law of one price if goods prices are sticky.
5. What is the value of the exchange rate that satisfies absolute PPP?
Answer: Absolute purchasing power parity requires that the internal purchasing power of a currency equals its external purchasing power. The internal purchasing power is calculated by taking the reciprocal of the price level, and the external purchasing power is calculated by first exchanging the domestic money into the foreign money in the foreign exchange market and then calculating the purchasing power of that amount of foreign currency in the foreign country. Hence, the prediction of absolute PPP for the exchange rate of domestic currency per unit of foreign currency is found by equating the internal purchasing power of the domestic currency to the external purchasing power of the domestic currency:
where P(DC) is the domestic price level, P(FC) is the foreign price level, and SPPP signifies the exchange rate of domestic currency per unit of foreign currency that satisfies the PPP relation. By solving for SPPP, we find
6. If the actual exchange rate for the euro value of the British pound is less than the exchange rate that would satisfy absolute PPP, which of the currencies is overvalued and which is undervalued? Why?
Answer: The terminology of “overvalued” and “undervalued” refers to the relationship of the exchange rate to the PPP theory. If the actual exchange rate of euros per pound is less than the PPP prediction, the euro is overvalued and the pound is undervalued. We know this is the correct answer because if the actual exchange rate were to move to the PPP prediction, the euro would have to weaken, and the pound would correspondingly have to strengthen, on the foreign exchange market. The weakening of the euro would correct its overvaluation, and the strengthening of the pound would correct its undervaluation.
7. What market forces prevent absolute purchasing power parity from holding in real economies? Which of these represent unexploited profit opportunities?
Answer: Any of the forces that create a deviation from the law of one price can also cause a deviation from PPP. See the answer to question 4. In addition, even if the law of one price were satisfied for all goods, if the consumption bundles in the two countries put different weights on the goods because of taste differences across countries, relative price changes would be reflected in deviations from PPP. It is our opinion that deviations from PPP do not represent unexploited profit opportunities.
8. Why is it better to use a PPP exchange rate to compare incomes across countries than an actual exchange rate?
Answer: When comparing incomes across countries, one is interested in comparing the quality of life that occurs from earning such incomes and consuming in those countries. One way to do such a comparison is to examine the real values of the nominal incomes, that is, to multiply each of the nominal incomes times the respective purchasing powers of the currencies (which is equivalent to dividing the nominal income by the price level). The real value of the income tells you the command over goods and services that the nominal income provides when you consume in that country. If the real incomes in countries A and B were the same, we would have
If we multiply this expression by the price level in country A, we get
In the above expression, the ratio of the price level in country A to the price level in country B is the purchasing power parity exchange rate. Hence, if we multiply the nominal income in country B by the purchasing power parity exchange rate we get a nominal income that is in the units of the currency of country A and that can be compared to the nominal income in country A. If the nominal income in country A is higher than the purchasing power exchange rate multiplied by nominal income in country B, people in country A are better off in terms of their ability to consume than those in country B.
If you use the actual exchange rate rather than the PPP exchange rate to convert the nominal income in country B into currency of country A, you are effectively saying you would like to earn the income in country B, but you want to consume it in country A. This can create incorrect inferences about where is the best place to live. Suppose currency B is overvalued relative to PPP. Then, the market exchange rate of currency A per unit of currency B, denoted S, is greater than the PPP prediction,
SPPP =
That is S > SPPP. In such a situation, it can happen that
in which case we know from the above discussion that we would prefer to earn income in country A and consume there. Yet, when we compare incomes with the actual exchange rate, we might find that the
The overvaluation of currency B causes us to think that the income in country B is preferred. But, this is only correct if we earn the income in country B but consume in country A after converting our income into the currency of country A.
9. What is relative PPP, and why does it represent a weaker relationship between exchange rates and prices than absolute PPP?
Answer: The theory of relative PPP specifies that exchange rates adjust in response to differences in inflation rates across countries to leave the deviation of the actual exchange rate from absolute PPP unchanged. Intuitively, inflation is the rate of loss of the internal purchasing power of a currency. Thus, if two currencies are losing internal purchasing power at different rates because the rates of inflation in the two countries are not equal, the rate of change of the exchange rate can offset the differential rates of inflation to leave the same absolute relationship between the internal and external purchasing powers of the currencies. The relative PPP theory is weaker than absolute PPP because relative PPP could be satisfied even though there are deviations from absolute PPP. The requirement for relative PPP to hold is that the deviations from absolute PPP do not change over time.
10. What is the real exchange rate, and how are fluctuations in the real exchange rate related to deviations from absolute PPP?
Answer: The real exchange rate, say, of the dollar relative to the euro, is denoted RS(t,$/€). It is defined to be the nominal exchange rate multiplied by the ratio of the price levels:
Notice that the real exchange rate would be 1 if absolute purchasing power parity held because the nominal exchange rate, S(t,$/€), would equal the ratio of the two price levels, P(t,$)/P(t,€). Similarly, if absolute PPP is violated, the real exchange rate is not equal to 1. Thus, fluctuations in the deviations from absolute PPP are fluctuations in the real exchange rate.
11. If the nominal exchange rate between the Mexican peso and the U.S. dollar is fixed, and there is higher inflation in Mexico than in the United States, which currency experiences a real appreciation and which experiences a real depreciation? Why? What is likely to happen to the balance of trade between the two countries?
Answer: If the peso is pegged to the dollar and the rate of inflation in Mexico is greater than in the rate of inflation in the United States, the peso is appreciating in real terms and the dollar is experiencing a real depreciation. The logic is that the rate of inflation in Mexico measures the loss of internal purchasing power, while because the exchange rate is pegged, the loss of the peso’s external purchasing power is measured by the U.S. rate of inflation. If a currency’s loss of internal purchasing power is greater than its loss of external purchasing power, that currency experiences a real appreciation.
The real appreciation of the peso tends to make Mexican residents think that U.S. goods are relative bargains, while the real depreciation of the dollar relative to the peso, makes U.S. residents think that Mexican goods are relatively expensive. Thus, the balance of trade between Mexico and the United States on the Mexican balance of payments should deteriorate with an increase in imports from the United States and a decrease in exports to the United States.
problems
1. If the consumer price index for the United States rises from 350 at the end of a year to 365 at the end of the next year, how much inflation was there in the United States during that year?
Answer: Price indexes are ratios of the price level in a given year to the price level in a base year. Because the base year is the same in the two price indexes under consideration, we can take the ratio of the two price indexes and find the rate of inflation over that year. The ratio is 365/350 = 1.0429 or an inflation rate of 4.29%.
2. As a wheat futures trader, you observe the following futures prices for the purchase and sale of wheat in 3 months: $3.00 per bushel in Chicago and ¥320 per bushel in Tokyo. Delivery on the contracts is in Chicago and Tokyo, respectively. If the 3-month forward exchange rate is ¥102/$, what is the magnitude of the transaction cost necessary to make this situation not represent an unexploited profit opportunity?
Answer: The forward dollar price of wheat in Tokyo is the ratio of the futures price, ¥320 per bushel, to the forward exchange rate, ¥102/$. This ratio is ¥320 per bushel / (¥102/$) = $3.14 per bushel. Since we can buy wheat for delivery in Chicago at $3 per bushel, if transaction costs of shipping wheat from Chicago to Tokyo are smaller than $0.14 per bushel, we could make an arbitrage profit. Thus, the minimum magnitude of the transaction cost necessary to make this situation not represent an unexploited profit opportunity is $0.14 per bushel.
3. Suppose that the price level in Canada is CAD16,600, the price level in France is EUR11,750, and the spot exchange rate is CAD1.35/EUR.
a. What is the internal purchasing power of the Canadian dollar?
Answer: It is probably best to calculate the purchasing power of CAD10,000. If we divide this amount by the price level in Canada of CAD16,600, we find
b. What is the internal purchasing power of the euro in France?
Answer: Performing a similar calculation to the one in part a., we find
c. What is the implied exchange rate of CAD/EUR that satisfies absolute PPP?
Answer: The implied PPP exchange rate equates the internal purchasing power of the CAD to its external purchasing power. This implies that the PPP exchange rate is the ratio of the Canadian price level in Canadian dollars to the French price level in euros:
d. Is the euro overvalued or undervalued relative to the Canadian dollar?
Answer: Because the actual exchange rate of CAD1.35/EUR is less than the PPP exchange rate, the euro is undervalued on the foreign exchange market because it would have to strengthen to move from CAD1.35/EUR to CAD1.4128/EUR.
e. What amount of appreciation or depreciation of the euro would be required to return the actual exchange rate to its PPP value?
Answer: The exchange rate moves from the actual value of CAD1.35/EUR to the PPP value of CAD1.4128/EUR for a percentage change of1.4128/1.35– 1 = 0.0466. This is a 4.66% appreciation of the euro versus the Canadian dollar.
4. Suppose that the rate of inflation in Japan is 2% in 2011. If the rate of inflation in Germany is 5% during 2011, by how much would the yen strengthen relative to the euro if relative PPP is satisfied during 2011?
Answer: The approximately correct answer is that the yen should strengthen by the differential in the rates of inflation or 5% - 2% = 3%. The exact answer is found from equation (8.4) of the text, which incorporates a denominator correction, and we get
Since we are concerned about the strengthening of the yen, let the yen be the foreign currency (FC), and let the euro be the domestic currency (DC). Then, the relative PPP formula states that the rate of appreciation of the yen is
5. One of your colleagues at Deutsche Bank thinks that the dollar is severely undervalued relative to the yen. He has calculated that the PPP exchange rate is ¥140/$, whereas the current exchange rate is ¥105/$. Because interest rates are 3% p.a. lower in Japan than in the United States, he thinks that this is a good time to speculate by borrowing yen and lending dollars. What do you think?
Answer: Deviations from PPP are a weak reason to engage in speculation. While the data in the problem indicate that the dollar is 33.33% undervalued, because that is the amount of dollar appreciation that would be required to take the actual exchange rate from ¥105/$ to the PPP prediction of ¥140/$, we know that the return to PPP will not be an overnight event.
The empirical analysis of the issue indicates that the half-life of PPP deviations is around 5 years. Thus, you might expect that the dollar will appreciate by 16.67% over the next 5 years. But, uncovered interest rate parity actually suggests that the yen will appreciate in the short run, because the yen interest rate is 3% less than the dollar interest rate. Notice, though, that the correction back toward PPP can take place with differential rates of inflation in the two countries. If Japanese rate of inflation falls below the U.S. rate of inflation, the PPP prediction will begin falling toward the actual exchange rate. Finally, although the dollar is 33.33% undervalued, there is no guarantee that the undervaluation will begin to be corrected now. It may, in fact, get worse. If the undervaluation of the dollar goes to 50% over the next 2 years, you would lose 16.67% in the foreign exchange market which would not be compensated by the approximate 6% that you would earn by borrowing yen and lending dollars. Finally, do not forget that your boss in proprietary trading at Deutsche Bank would not be happy with such a situation.
6. Suppose that you are trying to decide between two job offers. One consulting firm offers you $150,000 per year to work out of its New York office. A second consulting firm wants you to work out of its London office and offers you £100,000 per year. The current exchange rate is $1.65/£. Which offer should you take, and why? Assume that the PPP exchange rate is $1.40/£ and that you are indifferent between working in the two cities if the purchasing power of your salary is the same.
Answer: We know from the extensive discussion in Question 8 that we should use the PPP exchange rate to compare the pound salary to the dollar salary. If we do so, we find $1.40/££100,000 = $140,000. This is less than the $150,000 that you are being offered in New York. The fact that the dollar is undervalued on the foreign exchange markets makes the perceived salary of $1.65/£
£100,000 = $165,000, calculated with the spot exchange rate, seem more attractive. But, the key point is that to achieve $165,000 of spending in the United States, you would have to work in London and consume in New York.
7. Suppose that in 2011, the Japanese rate of inflation is 2%, and the German rate of inflation is 5%. If the euro weakens relative to the yen by 10% during 2011, what would be the magnitude of the real depreciation of the euro relative to the yen?
Answer: The real exchange rate is
We also know that a real depreciation of the euro means that this real exchange rate decreases. The new real exchange rate will be the old real exchange rate with each term multiplied by one plus the respective percentage rate of change. Thus, one plus the percentage rate of change of the real exchange rate is
So, we conclude that the real depreciation of the euro is 7.35%.
8. Pick a particular brand of appliance, like a Bosch dishwasher with certain features, and use the internet to compare its prices across countries. Be sure to have exactly the same style of appliance in each country. How different are the prices when expressed in a common currency?
We found the Bosch Ascenta series Model SHX6AP05UC on sale at Sears-Canada for CAD1,149.99. The exact same model in the United States was available from Amazon through AJ Madison for $728.10. The exchange rate on June 4, 2011 was CAD0.9772/USD. Thus, a Canadian could purchase the U.S. dishwasher for CAD0.9772/USD x $728.10 = CAD711.50. Buying the dishwasher from Sears-Canada would have cost 61.6% more.
9. Go to the IMF’s web site at www.imf.org, find the Data and Statistics tab, locate World Economic Outlook (WEO) data, and download the “Implied PPP conversion rate” for the Indonesian rupiah and the Philippines peso versus the dollar. Calculate a rupiah per peso PPP rate and compare it to the actual exchange rate. Which currency is overvalued, and by how much?
Go to the IMF’s WEO site at
http://www.imf.org/external/pubs/ft/weo/2010/02/weodata/index.aspx
Request data for Indonesia and the Philippines on their Implied PPP rates versu the U.S. dollar. The 2011 rates were 6,402.79 for Indonesia and 25.143 for the Philippines. The ratio of these two gives the Implied PPP rate of IDR/PHP:
The actual exchange rate was IDR197.153/PHP. Hence, the Philippines peso is undervalued relative to the Indonesian rupiah because the peso would have to strengthen if the actual exchange rate were to go to the Implied PPP rate. The peso would have to strengthen by 29.16%.
本文来源：https://www.2haoxitong.net/k/doc/1d9947f349649b6648d74745.html
文档为doc格式