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I. Exchange Rates and the Foreign Exchange MarketAn exchange rate is the price of one country's currency in terms of another. Consequently, exchange rates affect the relative cost of foreign versus domestic goods, services, and financial assets for a country.
From the viewpoint of any one domestic country, there is a different exchange rate for every foreign currency. In practice, summary measures are used to represent the average cost of foreign currencies for domestic citizens. In the U.S., for example, use is frequently made of effective exchange rate indices constructed as a weighted average of the exchange rates of various trading partners of the U.S., with the exchange rates of larger trading partners receiving relatively larger weights. Mishkin (Chapter 17, Figure 9) presents U.S. time series data for one such effective exchange rate from 1974 through 2006.
The international financial market where exchange rates are determined is called the foreign exchange market. This market is organized as an over-the-counter market run by several hundred dealers (typically banks) who stay in close contact with each other.
The most common type of transaction in the foreign exchange market involves the (approximately) immediate exchange of one currency for another, called a spot transaction. An exchange rate used in a spot transaction is called a spot exchange rate. In contrast, a forward transaction is an agreement to exchange currencies at some specified future date, and an exchange rate used in a forward transaction is called a forward exchange rate.
As stressed by Mishkin (Chapter 17), however, most trades in the foreign exchange market actually involve the buying and selling of bank deposits denominated in desired currencies rather than the direct buying and selling of currencies per se. Moreover, these trades consist of transactions in excess of $1 million. Smaller purchases of currencies for purposes such as travel must be obtained second-hand (and at higher cost) in the currency retail market from banks and other dealers who participate in the foreign exchange market.
Hereafter, for expositional simplicity, it is assumed that the world is divided into a home country (HC) and the rest-of-the-world (ROW). Following Mishkin (Chapter 17, footnote 2, p. 438), the exchange rate for the HC during any time period T, denoted by E(T), is always reported as ROW currency per HC currency unit.
Exchange Rate for the HC in Period T:
(1) E(T) = Number of ROW currency units received
in exchange for each HC currency unit
in period T
Consequently, an increase in E(T) denotes a strengthening (or appreciation) of HC currency relative to ROW currency, in the sense that each HC currency unit now exchanges for more ROW currency units. Conversely, a decrease in E(T) denotes a weakening (or depreciation) of HC currency relative to ROW currency.
Given fixed prices in the HC and in ROW, the exchange rate E(T) determines the relative cost of goods, services, and financial assets in ROW versus the HC. For example, if E(T) increases (all else remaining the same), the goods, services, and financial assets in ROW become cheaper for HC citizens to buy, in the sense that one unit of HC currency now buys more of each of these ROW quantities than before.
However, the exchange rate E(T) is nominal in the sense that it does not take into account possible changes in the aggregate price levels in the ROW and the HC. To obtain a more accurate measure of the relative cost of goods, services, and financial assets in the ROW versus the HC, the nominal exchange rate needs to be transformed into a "real" exchange rate that corrects for such price changes.
Suppose the period-T aggregate price level in ROW -- denoted by PROW(T) -- is measured by the ROW GDP deflator. Similarly, suppose the period-T aggregate price level in the HC -- denoted by P(T) -- is measured by the HC GDP deflator in period T.
The period-T real exchange rate for the HC, denoted by Er(T), is then defined as follows:
Real Exchange Rate for the HC in Period T:
E(T)*P(T)
(2) E (T) = ---------
r PROW(T)
E(T)*( [HC Nominal GDP(T)]/[HC Real GDP(T)] )
= ---------------------------------------------
[ROW Nominal GDP(T)/ROW Real GDP(T)]
E(T)*[HC Nominal GDP(T)]
= ------------------------ * K
ROW Nominal GDP(T)
Period-T Value of HC production in ROW currency
= ----------------------------------------------- * K
Period-T Value of ROW production in ROW currency
Period-T Value
of HC Production
= Measured in Terms * K ,
of Period-T ROW
production
where K denotes the ratio of ROW real GDP(T) to HC real GDP(T). Recall that real GDP is assumed to be the traditional base-year price measure of production. Consequently, by construction, K is independent of any variations in current HC or ROW prices of goods and services.
Y(2002) = U.S. real GDP = 6 bushels of U.S. wheat ;
YN(2002) = U.S. nominal GDP = $12.00 ;
P(2002) = U.S. price of U.S. wheat
= YN(2002)/Y(2002) (U.S. GDP deflator)
= $12.00/[6 bushels of U.S. wheat]
= $2.00 per 1 bushel U.S. wheat;
E(2002) = U.S. Exchange Rate
= 1.5 yen per 1 dollar;
PROW(2002) = yen price of Japanese wheat
= 4 yen per 1 bushel Japanese wheat;
2002 transport costs, import duties, etc. = 0
1.5 yen $2.00
E(2002)*P(2002) = ------- * -------------------
$1.00 1 bushel U.S. wheat
= 3 yen per 1 bushel U.S. wheat
= yen price of U.S. wheat ;
1/PROW(2002) = 1/4 bushel Japanese wheat per yen .
Hence, supressing the period indicator 2002 for ease of notation,
E*P 1.5 yen $2.00 1/4 bushel J wheat
E = ------ = ------- * ------------------- * -------------------
r PROW $1.00 1 bushel U.S. wheat 1 yen
3/4 bushels of J wheat Price of 1 bushel U.S. wheat
= ---------------------- = measured in terms of J wheat .
1 bushel U.S. wheat
II. Exchange Rates in the Long and Short RunAs stressed by Mishkin (Chapter 17, page 438), the basic trick to understanding what effect a factor has on the movement of exchange rates is to keep in mind the following common-sense observation: If a factor increases (decreases) the demand for domestic goods relative to foreign goods, then the domestic currency will tend to appreciate (depreciate) relative to the foreign currency.
Can anything more be said? In particular, assuming traders in the foreign exchange market are "rational" profit-seekers, can arbitrage conditions (i.e., conditions ensuring all profit opportunities are fully exploited) be used to predict more carefully the movement of exchange rates in the long and short run? This question is explored in the next two subsections.
Suppose that the HC and ROW always produce exactly the same bundle of goods and services, that there are no barriers to trade (i.e., no transportation costs, import duties, quotas, etc.), and that all traders are perfectly informed about the availability of goods and services in both the HC and ROW.
In this case, one would expect to find that the value of HC production measured in ROW currency units is exactly the same as the value of ROW production measured in ROW currency units. That is, recalling (2), one would expect to find that the following purchasing power parity (PPP) condition holds:
Basic Purchasing Power Parity Condition:
(3)
For how could differences in valuation persist for identical bundles of goods and services, apart from barriers to trade, if traders are rational? ROW and HC buyers would presumably always seek out the goods and services with the lowest price, which would tend to drive ROW and HC prices into approximate equality. This is often referred to as the law of one price.
In this example, the dollar price of a bushel of U.S. wheat (given by P) is $2, and the dollar price of a bushel of Japanese wheat (given by PROW/E - why?) is $2.67. Moreover, the yen price of a bushel of U.S. wheat (given by E*P) is 3 yen and the yen price of a bushel of Japanese wheat (given by PROW) is 4 yen. Consequently, a bushel of U.S. wheat is cheaper than a bushel of Japanese wheat, measured either in U.S. dollars or in yen.
Note that E*P/PROW=1 can also be expressed as P = PROW/E, i.e., the dollar price P of a bushel of U.S.wheat equals the dollar price PROW/E of a bushel of J wheat.
An interesting alternative way of expressing the PPP condition (3) is in terms of rates of change.
Suppose that the PPP condition (3) holds from T to T+1, which implies that the real exchange rate Er = E*P/PROW remains constant (at 1) over this time interval. This constancy can hold only if E*P and PROW are growing at exactly the same rate over time. The latter condition guarantees that any percentage increase or decrease in E*P is exactly offset by an equal percentage increase or decrease in PROW, keeping the value of the ratio E*P/PROW constant.
Moreover, it can be shown that the rate of change of any product X*Y is equal to the sum of the separate rates of change of X and Y. Consequently, another way of expressing the assumption that the ratio E*P/PROW remains constant from T to T+1 is as follows:
Rate of Change of E*P = Rate of Change of PROW
from T to T+1 from T to T+1
or
E(T+1)-E(T) P(T+1)-P(T) PROW(T+1) - PROW(T)
----------- + ----------- = -------------------
E(T) P(T) PROW(T)
Rate of change Inflation Rate in Inflation Rate in
in the HC exchange in the HC from T ROW from T to T+1
rate from T to T+1 to T+1
Subtracting the HC inflation rate from each side of this equation, one obtains the following interesting relation:
Alternative Form for the Purchasing Power Parity Condition (3):
E(T+1)-E(T) PROW(T+1)-PROW(T) P(T+1)-P(T)
(4) ----------- = ----------------- - ----------- .
E(T) PROW(T) P(T)
Rate of change Inflation Rate in Inflation Rate in
in the HC exchange ROW from T to T+1 in the HC from T
rate from T to T+1 to T+1
The PPP condition in the rate-of-change form (4) has the following important implication. If inflation is higher in ROW than in the HC, then the HC currency should be appreciating in the sense that E(T+1) is greater than E(T). And conversely, if inflation is lower in ROW than in the HC, then the HC currency should be depreciating. Compare Mishkin (Chapter 17, pp. 435-438).
This makes intuitive sense, since (all else remaining constant) the relatively higher rate of increase in the ROW price level should cause ROW citizens to increase their demand for HC goods, services, and financial assets relative to those in ROW, which puts upward pressure on the HC exchange rate.
Mishkin (Chapter 17, Figure 2) presents time series evidence for the U.S. and United Kingdom that supports the PPP condition in form (4) over the long run, i.e., when the data points are averaged over fairly long periods of time (e.g., 20 years).
Unfortunately, this same evidence also indicates that the PPP condition (4) does not necessarily hold over shorter periods of time. For additional evidence of the failure of the PPP to hold over the short run, see K. Rogoff, "The Purchasing Power Parity Puzzle" (Journal of Economic Literature 34, June 1996, 647-668.) This failure has been disappointing to advocates of flexible exchange rates, because volatility in real exchange rates can disrupt the operations of firms specializing in exports and imports.
The key reason why real exchange rates fail to remain constant over short periods of time is that currency demands and supplies depend on factors in addition to foreign and domestic aggregate price levels. Some of these factors are listed below.
Consequently, whether in form (3) or form (4), to date the PPP condition has not provided an adequate explanation of how real exchange rates are determined in the short run.
Although we still lack a theory allowing us to predict short-run movements in real exchange rates with satisfactory accuracy, a second type of arbitrage (profit exploitation) condition -- interest parity -- has helped in practice to guide these predictions. This condition is taken up in the next subsection.
Empirically, it has long been noted for the U.S. that real interest rates and exchange rates tend to move together relative to their "norms" -- i.e., either both are higher than normal or both are lower. For example, Mishkin (Chapter 17, Figure 9) presents time series evidence for the U.S. from 1974 through 2006 that shows this positive co-movement between real interest rates and one particular effective exchange rate index (i.e., a weighted average of the exchange rates for various major trading partners of the U.S.).
What underlying factors might explain this observed positive correlation between real interest rates and exchange rates?
The first important point to note is that changes in exchange rates can open up exploitable profit opportunities from pure currency "swaps" -- e.g., switching from ROW to HC currency now in anticipation of a later switch back from HC to ROW currency. Consider the following example.
3/4 bushels of Japanese wheat
E (T) = ------------------------------ ;
r 1 bushel U.S. wheat
1 4/3 bushels of U.S. wheat
----- = ------------------------- .
E (T) 1 bushel Japanese wheat
r
Suppose that a Japanese investor with 100 yen in period T anticipates a rise in the U.S. real exchange rate from T to T+1. Specifically, suppose that the Japanese investor expects to see
e 1 bushel of Japanese wheat
E (T+1) = -------------------------- .
r 1 bushel U.S. wheat
Then the Japanese investor can conduct the following arbitrage: In period T, use the 100 yen to buy 25 bushels of Japanese wheat. Exchange these 25 bushels of Japanese wheat for [25*4/3] = 100/3 bushels of U.S. wheat. Then, in period T+1, convert the 100/3 bushels of U.S. wheat back to [(100/3)*1] = 33.3 bushels of Japanese wheat. If his expectations are correct, the Japanese investor will then end up with [33.3 - 25] = 8.3 additional units of Japanese wheat in period T+1.
The possibility of making money from pure currency swaps affects the flow of international financial investments. To see this more carefully, consider the case of investing in ROW versus HC deposit accounts.
Let the real interest rate on an investment in an HC bank deposit account held from T to T+1 be denoted by rHC(T) and let the real interest rate on an investment in a ROW bank deposit account held from T to T+1 be denoted by rHC(T). For simplicity, suppose that transaction costs are zero and that the risk characteristics of ROW bank deposit accounts and HC bank deposit accounts are the same.
In considering whether to put his money into a ROW bank deposit account, the ROW resident will consider the ROW real interest rate rROW(T). However, in considering whether to put his money into an HC bank deposit account, the ROW resident must consider both the HC real interest rate rHC(T) and the rate of change in the HC real exchange rate from T to T+1 given by
E (T+1) - E (T)
(7) r r
----------------- .
E (T)
r
Any increase (decrease) in Er from T to T+1 represents a gain (loss) to the ROW investor in and of itself. This is so because the ROW resident must convert HC currency back to ROW currency in order to repatriate any earnings from his HC bank deposit account.
If Er stays constant from T to T+1, the change from ROW currency to HC currency in period T and back to ROW currency in period T+1 is a wash in and of itself -- that is, ignoring interest payments, the ROW investor neither gains nor loses ROW purchasing power on this currency transaction. However, if Er increases (or decreases) from T to T+1, the ROW investor gains (or loses) ROW purchasing power on each unit of ROW currency exchanged.
Assuming there are no barriers to currency flows between the HC and ROW, we would therefore expect interest parity to hold between the HC and ROW in the following sense:
Interest Parity (Real Form):
e
E (T+1) - E (T)]
r r
(8) rHC(T) + ----------------- = rROW(T) .
E (T)
r
Real interest Expected real return rate Real interest
rate from T to on HC currency held from rate from T
T+1 on HC bank T to T+1 to T+1 on ROW
deposit accounts bank deposit
secured with HC accounts secured
currency in T with ROW currency
in T
Suppose, for example, that the real interest rates in the HC and ROW from T to T+1 are given by rHC(T) = .10 and rROW(T) = .05, respectively. Seeing the 5 percent HC real interest rate advantage, should a ROW resident put his money into an HC bank deposit account from T to T+1 rather than a ROW bank deposit account from T to T+1?
The answer depends on whether or not the ROW resident expects the HC real exchange rate Er to depreciate by more than 5 percent from T to T+1, thereby offsetting the 5 percent HC real interest rate advantage. If this expected depreciation rate is more than 5 percent, he should choose a ROW bank deposit account, and if it is less than 5 percent, he should choose an HC bank deposit account. If the expected depreciation is exactly 5 percent, he will be indifferent between the two options. [Recall that the risk characteristics of ROW and HC bank deposit accounts are assumed to be identical.]
An important implication of the interest parity condition (8) is that the HC real interest rate rHC will tend to be high relative to the ROW real interest rate rROW when investors anticipate that the HC currency is going to depreciate, i.e., that Er(T+1) is going to be smaller than Er(T). But an anticipated depreciation in the HC exchange rate is exactly what one would expect to occur when the HC currency is stronger than normal -- that is, when the HC exchange rate is high relative to its historic norm.
Bottom Line: The interest parity condition (8) helps to explain why, empirically, real interest rates and exchange rates tend to move together over time.
In (8), rHC and rROW are real interest rates, hence the appropriate exchange rate in (8) is the real exchange rate Er. If the real interest rates rHC and rROW are instead replaced with nominal interest rates iHC and iROW for the HC and ROW, then the real exchange rate in (8) should be replaced with the nominal exchange rate E for the HC. Consequently, the interest parity condition (8) in nominal form is as follows:
Interest Parity (Nominal Form):
e
E (T+1) - E (T)
(9) iHC(t) + ----------------- = iROW(T) .
E(T)
Nominal interest Expected nominal Nominal interest
rate from T to return rate on HC rate from T to
T+1 on HC bank currency held from T+1 on ROW bank
deposit accounts T to T+1 deposit accounts
secured with HC secured with ROW
currency in T currency in T
Relation (9) is the form of the interest parity condition given in Mishkin (Chapter 17, equation (2), page 441). Mishkin provides an extensive discussion of how relation (9) can be used to help understand and predict actual exchange rate movements.
To understand how (9) is derived from (8), use the fact that the expected rate of change for the real exchange rate Er from T to T+1 -- the second expression appearing in (8) -- is approximately given by
e e e
E (T+1)-E(T) P (T+1) - P(T) P ROW(T+1)-PROW(T)
(10) ----------- + --------------- - ------------------- .
E(T) P(T) PROW(T)
Expected Rate Expected Inflation Expected Inflation
of Change in Rate in HC from T Rate in ROW from T
the HC nominal to T+1 to T+1
exchange rate
from T to T+1
Replacing the expected rate of change of Er in (8) by expression (10), and recalling that the nominal interest rate is given by the sum of the real interest rate and the expected inflation rate, one obtains the desired nominal form (9) for the interest parity condition.
Finally, combining (9) with the PPP condition (4) expressed in expectational form, one obtains a relation expressing the famous "international Fisher effect":
International Fisher Effect:
e e
P (T+1)-P(T) PROW (T+1)-PROW(T)
(11) iHC(T)-iROW(T) = ------------ - ------------------ .
P(T) PROW(T)
In short, under conditions in which purchasing power parity and interest parity both hold over time, any difference in nominal interest rates between the HC and ROW will be equal to the difference in their expected inflation rates because the real interest rates in the HC and in ROW will be the same.
III. Pondering the Introduction of the EuroNote: This section expands on the discussion of the European Union and euro-related issues provided by Mishkin in Chapter 3, Chapter 17, and Chapter 18.
The European Union (EU) currently consists of 27 member countries. The eurozone consists of the subset of EU member countries that have adopted the euro as their only currency. Currently the eurozone consists of 13 EU member countries.
In order to join the EU, countries need to fulfill economic and political conditions generally known as the Copenhagen criteria (after the Copenhagen summit in June 1993). In order to further be eligible for participation in the eurozone, countries must satisfy a set of rules known as the Maastricht convergence criteria.
NOTE: As of 11/04/07, three EU member countries have no plans in place to transit to the euro. The UK and Denmark obtained special opt-outs, and Sweden rejected the adoption of the euro in a referendum vote held on September 14, 2003. The implications of Sweden's rejection of the euro in terms of its status as a EU member in good standing are still unclear.
Potential Benefits:
Potential Costs:
III. Basic Concepts and Key Issues from Mishkin Chapter 17