1. Exchange Rates in the Long Run
Chapter 15
Exchange Rates in the Long Run

2. Topics to be Covered An Introduction to Purchasing Power Parity
Uses of Purchasing Power Parity
Tests of Purchasing Power Parity
The Monetary Approach to Exchange Rates (MAER)

3. Purchasing Power Parity
Purchasing Power Parity (PPP)
A unit of any currency should be able to buy the same quantity of goods in all countries.
The relationship between the prices of goods (and services) and exchange rates.
The PPP provides a theory of the long-run equilibrium value of the exchange rate.

4. Short-run vs. Long-run Behavior
Short-run movements in a variable (e.g., the exchange rate) refer to monthly or quarterly changes in the variable.
Long-run refer to trend changes over several decades.
See Figure 15.1 for plot of a trend line.

5. FIGURE 15.1 Japanese Exchange Rate

6. Purchasing Power Parity (PPP)
Purchasing power of 1 unit of foreign currency can buy 1/PF quantity of goods
1 unit of foreign currency can be exchanged into Eppp units of US$, which in turn have purchasing power Eppp/P
If PPP holds, then
(15-1) 1/PF = Eppp/P ⇒ Eppp=P/PF
EPPP is the PPP exchange rate (US dollar price of foreign currency) which equalizes the prices of bundles of domestic and foreign goods

7. The Theory of PPP Basic logic of purchasing-power parity
The law of one price is basic logic of purchasing-power parity
The law of one price: A good must be sold for the same price in all locations
The PPP theory states that the actual exchange rate should converge toward the PPP exchange rate.
In other words, EPPP is the long-run equilibrium value for the exchange rate E.

8. Absolute PPP
If PPP holds, then the actual exchange rate (E) equals the PPP ex-rate (EPPP).
If PPP holds, then the Absolute Purchasing Power Parity relation is given:
(15-2) 𝐸= 𝐸 𝑃𝑃𝑃 = 𝑃 𝑃 𝐹
where P is the domestic price index, PF is the foreign price index, and E is the actual spot exchange rate (Units of US$ per unit of the foreign currency).

9. Absolute PPP (cont.)
Absolute PPP indicates that the exchange rate is equal to the ratio of the two countries’ price levels.
The problems in testing absolute PPP
Price levels are not easily observable.
The bundles of goods are not identical.
National price indexes such as Consumer Price Index (CPI) are used but these may not be comparable in terms of goods coverage and base year used by each country.

10. Relative Purchasing Power Parity
Relative PPP is said to hold if:
(15-3) 𝐸 𝑝𝑝𝑝= 𝑃 − 𝑃 𝐹
where a caret (^) over a variable indicates percentage change.
Relative PPP begins with absolute PPP and then transforms the equation into percentage rates of changes
Relative PPP states that the percentage change in the exchange rate is equal to the differentials of percentage change in the price levels.

11. Relative PPP (cont.)
Relative PPP states that there will be a long-run tendency for the home currency (e.g., the dollar) to fall in value (i.e., E rises) if inflation is higher in the US than abroad.
For the evidence of relative PPP, refer to Figure 15.2
The exchange rate is more volatile than the inflation differential  limited evidence in support of holding the relative PPP
Thus PPP is a weak predictor of exchange rate movements.

12. FIGURE 15.2 U.S.-Japan Purchasing Power Parity
Annual percentage change in the US$ price of the yen
US inflation rate was higher than Japanese inflation rate over the past four decades.
It is consistent with the long-run upward trend in the US$ price of Japanese yen which is shown in Figure 15.1.

13. Undervalued vs. Overvalued Currency
PPP serves as a measure of the “disequilibrium” of a given exchange rate.
If PPP holds, then 1 = EPPP/E
If 1 > EPPP/E, then the foreign currency is overvalued (and the domestic currency is undervalued)
If 1 < EPPP/E, then the foreign currency is undervalued (and domestic currency is overvalued)

14. Tests of PPP Evidence from PPP theory studies is mixed.
However, studies using data covering more than a century provide strong support for PPP theory.
Ways of testing PPP theory examine:
- consumer price indexes
- real exchange rate behavior

15. Using Price Indexes to Test PPP
A country’s consumer price index (CPI) is calculated by:
(15-4) 𝐶𝑃𝐼 𝑡 = 𝑖=1 𝑛 𝜔 𝑖 𝑝 𝑖𝑡 𝑖=1 𝑛 𝜔 𝑖 𝑝 𝑖𝑜 or 𝐶𝑃𝐼 𝑡 = 𝑃 𝑡 𝑃 𝑜
pit is the price of good i in period t, and wi is the weight that good i receives in the price index
Pt is price level at time t and P0 is the price level in the base year.
Similarly, the foreign CPI is given by: 𝐶𝑃𝐼 𝑡 𝐹 = 𝑃 𝑡 𝐹 𝑃 𝑜 𝐹

16. Using CPI to Test PPP (cont.)
Dividing the domestic CPI by the foreign CPI yields:
(15-7) 𝐶𝑃𝐼 𝑡 𝐶𝑃𝐼 𝑡 𝐹 = 𝑃 𝑡 𝑃 𝑡 𝐹 × 𝑃 𝑜 𝐹 𝑃 𝑜  𝑃 𝑡 𝑃 𝑡 𝐹 = 𝐶𝑃𝐼 𝑡 𝐶𝑃𝐼 𝑡 𝐹 ∗ 𝑃 𝑜 𝑃 𝑜 𝐹
Recall that 𝐸0𝑝𝑝𝑝= 𝑃 𝑜 𝑃 𝑜 𝐹 , 𝐸𝑡𝑝𝑝𝑝= 𝑃 𝑡 𝑃 𝑡 𝐹 by definition.
Thus 𝐸𝑡𝑝𝑝𝑝= 𝑃 𝑡 𝑃 𝑡 𝐹
= 𝐶𝑃𝐼 𝑡 𝐶𝑃𝐼 𝑡 𝐹 ∗ 𝑃 𝑜 𝑃 𝑜 𝐹 =𝐸0𝑝𝑝𝑝 ∗ 𝐶𝑃𝐼 𝑡 𝐶𝑃𝐼 𝑡 𝐹

17. Using CPI to Test PPP (cont.)
Assume that absolute PPP held in the base year, then E0=E0PPP  the actual ex-rate in the base year equals the PPP based rate that year.
Cross-multiplying terms in Eq. (15.7) gives an empirical measure of the PPP exchange rate:
(15-8) 𝐸 𝑡𝑃𝑃𝑃 = 𝐸 𝑜𝑝𝑝𝑝 𝐶𝑃𝐼 𝑡 𝐶𝑃𝐼 𝑡 𝐹 ⇒ 𝐸 𝑡𝑃𝑃𝑃 = 𝐸 𝑜 𝐶𝑃𝐼 𝑡 𝐶𝑃𝐼 𝑡 𝐹
Studies show that PPP holds better for more open i.e., less protective (low trade barriers) economies.

18. Using Real Exchange Rate (RER) to Test PPP
RER denotes the relative price of two output baskets at current nominal ex-rates and prices.
That is RER represents relative purchasing power of the currency
RER is measured by the nominal exchange rate adjusted by the ratio of the foreign price level to the domestic price level:
(15-9) 𝐸 𝑅 = 𝐸× 𝑃 𝐹 𝑃
Converting to percentage changes:
(15-10) 𝐸 𝑅 = 𝐸 + 𝑃 𝐹 − 𝑃
If PPP holds, then the RHS of Eq. (15-10) will equal zero  Note that 𝐸= 𝐸 𝑃𝑃𝑃 = 𝑃 𝑃 𝐹
Thus real exchange rate should not change.
For the simple comparison purpose,
- RER denotes the relative price of two output baskets and NER refers to the relative price of two currencies.
- Thus, a rise in the real dollar/euro exchange rate (real depreciation of the dollar against the euro) can be thought of falling in the dollar purchasing power
within Europe’s borders relative to its purchasing power within the US.

19. Monetary Approach to Exchange Rates (MAER) Determination
The MAER is a theory of long-run exchange rate behavior developed by University of Chicago economists in the 1970s.
Main assumptions:
PPP holds.
Economic agents have stable demands for money.
Price level in each country adjusts to clear the money market.

20. Monetary Approach to Exchange Rates (cont.)
The basic assumptions are represented as:
(15-2) 𝐸= 𝐸 𝑃𝑃𝑃 = 𝑃 𝑃 𝐹
(15-11) 𝑀 𝑃 =𝐿
(15-12) 𝑀 𝐹 𝑃 𝐹 = 𝐿 𝐹
M and MF are the money supplies
L and LF are the demands for real money balances in the two countries.

21. Monetary Approach to Exchange Rates (cont.)
Rewriting Equations and to solve for the domestic and foreign price levels:
(15-13) 𝑃= 𝑀 𝐿
(15-14) 𝑃 𝐹 = 𝑀 𝐹 𝐿 𝐹
Combining Equations 15.2, 15.13, and yields:
(15-15) 𝐸=( 𝑀 𝑀 𝐹 )×( 𝐿 𝐹 𝐿 )
Converting Equation to percentage rates of change yields:
(15-16) 𝐸 = 𝑀 − 𝑀 𝐹 + 𝐿 𝐹 − 𝐿

22. Monetary Approach to Exchange Rates (cont.)
Demand for real money balances in the two countries directly depends on real income:
(15-17) 𝐿 =𝑘 𝑌
(15-18) 𝐿 𝐹 =𝑘 𝑌 𝐹
Y (YF) is home (foreign) income
𝑘 is a constant indicating how much money demand changes with a change in income.

23. MAER Equation
Substituting Equations and into Equation gives the fundamental equation of the MAER:
(15-19) 𝐸 = 𝑀 − 𝑀 𝐹 +𝑘 𝑌 𝐹 −𝑘 𝑌

24. Predictions of the MAER
A rise in the growth rate of home country money creation will cause the exchange rate to rise
printing more money causes inflation
lowering the purchasing power of money
ex-rate rise (i.e., depreciation of home currency)
A rise in the growth rate of foreign money creation will cause the exchange rate to fall.
depreciation of foreign currency

25. Predictions of the MAER
A rise in domestic output will cause a decrease in the exchange rate
Growth in home income raises money demand ( 𝐿 =𝑘 𝑌 )
Home prices is falling (𝑃= 𝑀 𝐿 )
And working through PPP ( 𝐸 = 𝑃 − 𝑃 𝐹 ), this lowers the ex-rate (i.e., appreciation of home currency)
A rise in foreign output will cause an increase in the exchange rate.
Appreciation of foreign currency

26. Studies of the MAER The empirical findings of the MAER are mixed.
Early empirical studies found support.
Meese and Rogoff (1983) found that the MAER does not work well in forecasting future values of the exchange rate.
However, there is increasing consensus that the MAER is a useful model in analyzing long-run behavior of exchange rates.