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Price Levels and the Exchange Rate in the Long Run

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Price Levels and the Exchange Rate in the Long Run

Lecture Notes on Ch. 15 of Krugman and Obstfeld, 7th Ed.

Udayan Roy, December 2008

- The simplest theory of prices and exchange rates for the long run is (absolute) purchasing power parity.

- Let us consider the price of an iPod in US and Europe:
- In US, it is PUS = $200
- In Europe, it is PE = €150
- The value of the euro is E = 2 dollars per euro
- So, Europe's price in dollars is E × PE = $300
- So, each iPod in Europe costs as much as 1.5 iPods in US
- E × PE / PUS= 1.5
- This is the Real dollar/euro Exchange Rate for iPods

- In general, the real exchange rate is a broad summary measure of the prices of one country’s goods and services relative to the other's.
- The real dollar/euro exchange rate is the number of US reference commodity baskets—not just iPods—that one European reference commodity basket is worth:
- Equation (15-6)

- Example: If the European reference commodity basket costs €100, the U.S. basket costs $120, and the nominal exchange rate is $1.20 per euro, then the real dollar/euro exchange rate (q$/€) is 1 U.S. basket per European basket.

- Real depreciation of the dollar against the euro
- A rise in the real dollar/euro exchange rate (q$/€↑)
- is a fall in the purchasing power of a dollar within Europe’s borders relative to its purchasing power within the United States
- Or alternatively, a fall in the purchasing power of America’s products in general over Europe’s.

- A rise in the real dollar/euro exchange rate (q$/€↑)
- Real appreciation of the dollar against the euro is the opposite of a real depreciation: a fall in q$/€.

- A very simple theory of the real exchange rate (called Absolute Purchasing Power Parity) says that:
q = 1

- Why?

- Going back for a second to the iPod example, one can argue that PUS, the dollar price in the US, ought to be equal to E × PE, the dollar price in Europe. That is,
- E × PE = PUS.
- In general, E$/€ x PE = PUS.
- Therefore, q$/€ = (E$/€ x PE)/PUS = 1.
- This is the Law of One Price or Absolute Purchasing Power Parity.

- Despite the logical appeal of Absolute Purchasing Power Parity, available data suggests that it is not true
- We need to look for another theory of the real exchange rate, q.

- In search of a more useful theory of the real exchange rate, we briefly skip ahead to Chapter 16
- That chapter is about the short run.
- But parts of it can help us study the long run as well

- Aggregate demand (D) is the aggregate amount of goods and services that people are willing to buy.
- It consists of the following types of expenditure:
- consumption expenditure (C)
- investment expenditure (I)
- government purchases (G)
- net expenditure by foreigners: the current account (CA)

- Consumption expenditure (C) depends on Disposable income (Y-T), which is income (Y) minus taxes (T).
- More disposable income means more consumption expenditure
- But consumption typically increases less than the amount by which disposable income increases.

- Real interest rates may influence the amount of saving and consumption, but we assume that they are relatively unimportant here.
- Wealth may also influence consumption, but we assume that it is relatively unimportant here.

- More disposable income means more consumption expenditure

- The current account (CA) depends on:
- Real exchange rate (q), which is the price of foreign products relative to the price of domestic products, both measured in domestic currency: q = EP*/P
- As q rises, expenditure on domestic products rises and expenditure on foreign products falls. Therefore, when q rises, CA rises as well.

- Disposable income: more disposable income (Y-T) means more expenditure on foreign products (imports). Therefore, when Y-T rises, CA falls.

- Real exchange rate (q), which is the price of foreign products relative to the price of domestic products, both measured in domestic currency: q = EP*/P

- Determinants of the current account include:
- Real exchange rate: an increase in the real exchange rate increases the current account.
- Disposable income: an increase in the disposable income decreases the current account.

Current account

depends on the real

exchange rate and

disposable income.

Consumption

depends on

disposable

income

Investment and

government

purchases, both

exogenous

- Aggregate demand is therefore expressed as:
D = C(Y – T) + I + G + CA(q, Y – T)

- Or more simply:
D = D(q, Y – T, I, G)

Aggregate demand as a function of the

real exchange rate, disposable income,

investment, government purchases

Value of output,

income from

production

- Equilibrium is achieved when the value of output Y equals aggregate demand D.
Y = D(q, Y – T, I, G)

Output is greater

than aggregate

demand: firms

decrease output

Aggregate

demand is

greater than

production:

firms increase

output

Y = D(q, Y – T, I, G)

- How does the real exchange rate (q) affect the equilibrium of aggregate demand and output?
- Therefore, a rise in the real exchange rate (q) makes foreign goods more expensive relative to domestic goods.
- As a result, CA increases and, therefore, D increases. That is, D increases when q increases.
- In equilibrium, Y = D. Therefore, Y increases when q increases.
- This gives the DD curve.

Y = D(q, Y – T, I, G)

Aggregate Demand, D

45° line

Aggregate Demand (q2)

Aggregate Demand (q1)

- As q, the price of foreign goods, increases
- Aggregate demand for domestic goods increases
- Therefore, equilibrium output also increases
- This gives us the DD curve

Y2

Output, Y

Y1

Real Exchange Rate, q

DD Curve

q2

q1

Output, Y

Y2

Y1

Y = D(q, Y – T, I, G)

- In the long run, output equals potential output
- In the short run, which we will discuss in chapter 16, recessions can happen
- During recessions, labor and other resources may remain unemployed and output may fall below the potential level
- But in the long run markets for labor and other resources are assumed to function normally and to make supply equal to demand, thereby making unemployment impossible

- Potential output is also called full-employment, and is denoted Yp.
- In the long run, Y = Yp.

- Full-employment output (Yp) increases when
- The availability of labor increases
- The quality of labor (human capital) increases
- The availability of physical capital (equipment, structures, infrastructure) increases
- The technology improves
- Economic policies and institutions favor productive activity

- The DD curve tells us that
- If the full-employment output is known, the long-run value of the real exchange rate can be obtained
- If the full-employment output increases, so does the real exchange rate

Real Exchange Rate, q

DD Curve

q2

q1

Output, Y

Yp = Y2

Yp = Y1

Aggregate Demand, D

45° line

Aggregate Demand2

Aggregate Demand1

- Suppose the real exchange rate stays unchanged at q1. But
- If either
- Taxes (T) ↓
- Investment (I) or Government Purchases (G) ↑
- Worldwide preference for domestic goods ↑
- Or if some combination of the above happens

- Then aggregate demand will increase and equilibrium output will increase even though q is unchanged
- This implies that the DD curve will shift to the right

Y2

Output, Y

Y1

Real Exchange Rate, q

DD1

DD2

q1

Output, Y

Y2

Y1

Y = D(q, Y – T, I, G)

- Suppose Yp remains unchanged
- If the DD curve shifts right, the real exchange rate decreases

Real Exchange Rate, q

DD1

DD2

q1

q2

Output, Y

Yp

- Now we can list all the causes that make the real exchange rate decrease (q↓):
- Domestic full-employment output (Yp)↓
- Demand for domestic output ↑
- Taxes (T) ↓
- Investment (I) or Government Purchases (G) ↑
- Worldwide preference for domestic goods ↑
- Domestic preference for foreign goods ↓

- Some combination of the above happens

- Nothing else affects q

- Recall that the real exchange rate is the price of foreign goods
- That is, q is the amount of domestic goods that one unit of foreign goods is worth

- This price of foreign goods will decrease (q↓) if
- Either the supply of domestic goods decreases (Yp↓)
- Or the demand for domestic goods increases (T ↓, I↑, G↑, worldwide demand for domestic goods ↑)

- Recall that CA = CA(q, Y – T)
- Therefore, CA↑ if
- I↓, G↓
- T↑, Yp↑
- Nothing else can affect the current account balance

- Tariffs and other protectionist policies will not work!
- CA = Yp – C(Yp – T) – G – I

- Note that our analysis of the real exchange rate has not even mentioned the money supply (Ms)
- In the long run, changes in the supply of money or in the rate of growth of the supply of money have no effect on q

- We saw in the last chapter that any increase in the domestic money supply (Ms) leads to a proportional increase in the domestic price level (P).
- Moreover, changes in the domestic money supply (Ms) cannot affect the foreign price level (P*)
- And we have just seen that q = EP*/P is unaffected by any increase in Ms
- Therefore, E must increase proportionally.
- That is, in the long run, any increase in the domestic money supply (Ms) will cause a proportional increase in the value of the foreign currency (E).

- Note equations (15-6) and (15-7) above
- The nominal dollar/euro exchange rate is
- the real dollar/euro exchange rate times
- the U.S.-Europe price level ratio.

- Consider three variables: x,y, and z …
- … and their rates of growth: xg,yg, and zg.
- Growth rates are computed as follows:xg = (xfuture – xnow) / xnow.
- It can then be shown that
- If z = x× y, then zg = xg+ yg
- If z = x/ y, then zg = xg- yg

- The same is true for expected growth rates, wherexge = (xfuturee – xnow) / xnow is the expected growth rate of x.

- Recall equation (15-7)
- So, the results in the previous slide imply
- Inflation is
- expected inflation is
- Then, we get equation (15-8)

- We start with interest rate parity
- We end with real interest rate parity

- I have discussed the various factors that can affect the real exchange rate (q)
- However, I will assume that changes in q are isolated events and that there is no reason for people to expect continuous or sustained changes in q
- That is, I will assume (qe–q)/q = 0
- This assumption is also called Relative Purchasing Power Parity (RPPP)

- Recall equation (15-8)
- Under relative purchasing power parity, (qe–q)/q = 0.
- Then,
- see p. 376.

- Absolute PPP
- Relative PPP

- According to Relative Purchasing Power Parity,
- If the expected US inflation rate is 4% (eUS = 4) and Europe’s inflation rate is 7% (eE = 7), then the value of the euro will be expected to fall by 3%.
- (Ee–E)/E = eUS–eE = 4 – 7 = – 3.
- In short, whichever country has the higher expected inflation rate will face an expected loss in the value of its currency

- We saw in Ch. 14 that in the long run any change inMg causes an identical change in .
- I will assume that there are no other causes of inflation in the long run
- In that case, one can write = Mg.
- In the long run, inflation expectations are assumed to be, on average, accurate: e = .
- So, when MgUS increases, both US andeUS increase by the same amount: e = = Mg.

- R$ – R€ = (qe – q)/q + (eUS–eE)(15-9)
- By relative PPP, R$ – R€ = eUS–eE
- R$ – R€ = MgUS–eE.
- R$ = R€ –eE + MgUS.
- Therefore, in the long run, the domestic (nominal) interest rate can increase if (and only if)
- The foreign real interest rate (R€ –eE) increases, or
- The growth rate of the domestic money supply (MgUS) increases

- A rise (fall) in a country’s expected inflation rate will eventually cause an equal rise (fall) in the interest rate that deposits of its currency offer.
- Figure 15-1 illustrates an example, where at time t0 the Federal Reserve unexpectedly increases the growth rate of the U.S. money supply to a higher level.

- In this example, the dollar interest rate rises because people expect more rapid future money supply growth and dollar depreciation.
- The interest rate increase is associated with higher expected inflation and an immediate currency depreciation.
- Figure 15-2 represents the main long-run prediction of the Fisher effect.

Figure 15-2: Inflation and Interest Rates in Switzerland, the United States, and Italy, 1970-2000

Figure 15-2: Continued

Figure 15-2: Continued

- PUS = MUS/L(R$,YUS) (15-3)
- The domestic price level increases if (and only if)
- The domestic money supply (MUS) increases or
- L(R$,YUS) decreases, which happens if
- YUS decreases or
- The domestic willingness to hold cash decreases or
- R$increases, which happens if
- the foreign real interest rate (R€ –eE) increases, or
- the growth rate of the domestic money supply (MgUS) increases

- E$/€ = q$/€ x PUS/PE(15-6)
- Therefore, the nominal exchange value of the foreign currency (E) increases if (and only if)
- The foreign price level (PE) decreases
- or, q increases, which happens if
- Domestic full-employment output (Yf) ↑
- Demand for domestic output ↓
- Taxes (T) ↑
- Investment (I) or Government Purchases (G) ↓
- Worldwide preference for domestic goods ↓
- Domestic preference for foreign goods ↑

- or, the domestic price level (PUS) increases, which happens if
- The domestic money supply (MUS) increases
- Yf decreases or
- The domestic willingness to hold cash decreases or
- the foreign real interest rate (R€ –eE) increases, or
- the growth rate of the domestic money supply (MgUS) increases

Note that the effect of the domestic full-employment output on the exchange rate is ambiguous.

(a) U.S. money supply, MUS

(b) Dollar interest rate, R$

R$2 = R$1 +

Slope = +

MUS, t0

R$1

Slope =

t0

t0

Time

Time

(d) Dollar/euro exchange rate, E$/€

(c) U.S. price level, PUS

Slope = +

Slope = +

Slope =

Slope =

t0

Time

t0

Time

- When Mg increases:
- The domestic inflation rate, , increases by the same amount
- The domestic interest rate, R, increases by the same amount
- The domestic price level, P, increases
- The value of the foreign currency, E, increases by the same proportion as the increase in P
- Or, the value of the domestic currency decreases by the same proportion as the increase in P

- Ee increases proportionately more than does P and E.
- And nothing else changes

- We know from Chapter 13 that interest rate parity requires R$ = R€ + (Ee – E)/E or R$ – R€ = (Ee – E)/E.
- (qe–q)/q = (Ee–E)/E – (eUS–eE) (15-8)
- R$–R€ = (qe–q)/q + (eUS–eE)(15-9)
- Thus, the dollar-euro interest difference is the sum of two components:
- The expected rate of real dollar depreciation against the euro
- The expected inflation difference between the U.S. and Europe

- Economics makes an important distinction between two types of interest rates:
- Nominal interest rates
- Measured in monetary terms

- Real interest rates
- Measured in real terms (in terms of a country’s output)
- Also referred to as expected real interest rates

- Nominal interest rates

- The expected real interest rate (re) is the nominal interest rate (R) minus the expected inflation rate (e).
- R$–R€ = (qe–q)/q + (eUS–eE) (15-9)
- This yields the real interest parity condition:
reUS – reE = (qe$/€–q$/€)/q$/€(15-10)

- Nominal interest parity:
RUS – RE = (Ee$/€ – E$/€)/E$/€(13-2)

- Real interest parity:
reUS – reE = (qe$/€ – q$/€)/q$/€(15-10)

- The real interest parity condition explains differences in expected real interest rates between two countries by expected movements in the real exchange rates.
- Expected real interest rates in different countries need not be equal, even in the long run, if continuing change in output markets is expected.