Price Levels and the Exchange Rate in the Long Run

1
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

2
Purchasing Power Parity

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

3
The Real Exchange Rate

• 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

4
The Real Exchange Rate

• In general, the real exchange rate is a broad
  summary measure of the prices of one countrys
  goods and services relative to the other's.
• The real dollar/euro exchange rate is the number
  of US reference commodity basketsnot just
  iPodsthat one European reference commodity
  basket is worth
• Equation (15-6)

5
the real dollar/euro exchange rate

• 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.

6
Real depreciation and appreciation

• 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 Europes borders relative to its
  purchasing power within the United States
• Or alternatively, a fall in the purchasing power
  of Americas products in general over Europes.
• Real appreciation of the dollar against the euro
  is the opposite of a real depreciation a fall in
  q/.

7
Absolute PPP

• A very simple theory of the real exchange rate
  (called Absolute Purchasing Power Parity) says
  that
• q 1
• Why?

8
Law of one price

• 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.

9
Absolute PPP logical but not factual

• 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.

10
Law of One Price for Hamburgers?
11
A different theory of q Ch 16

• 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

12
Determinants of Aggregate Demand

• 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)

13
Determinants of Aggregate Demand

• 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.

14
Determinants of Aggregate Demand

• 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.

15
Determinants of Aggregate Demand

• 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.

16
Determinants of Aggregate Demand (cont.)

• 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)

17
Short Run Equilibrium for Aggregate Demand and
Output

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

18
Short Run Equilibrium for Aggregate Demand and
Output (cont.)

Y D(q, Y T, I, G)
19
Goods Market Equilibrium and the Real Exchange
Rate DD Schedule

• 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)
20
The DD Curve
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
Y2
Output, Y
Y1
Y D(q, Y T, I, G)
21
Long-Run Output

• 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.

22
Long-Run Output

• 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

23
Real Exchange Rate long run

• 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
24
Shifts of the DD Curve
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
Y2
Output, Y
Y1
Y D(q, Y T, I, G)
25
Real Exchange Rate long run

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

Real Exchange Rate, q
DD1
DD2
q1
q2
Yp
Output, Y
26
Real Exchange Rate long run

• 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

27
Real Exchange Rate long run

• 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 ?)

28
The current account

• 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

29
Real Exchange Rate long run

• 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

30
Money and Prices

• 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).

31
Nominal and Real Exchange Rates in Long-Run
Equilibrium

• 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.

32
Mathematics of growth rates

• Consider three variables x, y, and z
• and their rates of growth xg, yg, and zg.
• Growth rates are computed as followsxg
  (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, where
  xge (xfuturee xnow) / xnow is the expected
  growth rate of x.

33
Exchange rates and inflation

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

34
Real interest rate parity

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

35
Relative Purchasing Power 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)

36
Exchange rates and inflation

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

37
Purchasing Power Parity

• Absolute PPP
• Relative PPP

38
Exchange rates and inflation

• According to Relative Purchasing Power Parity,
• If the expected US inflation rate is 4 (?eUS
  4) and Europes 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

39
Long-run effect of the growth rate of the money
supply

• We saw in Ch. 14 that in the long run any change
  in Mg 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 and ?eUS
  increase by the same amount ?e ? Mg.

40
Long-run effect of the growth rate of the money
supply

• 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

41
The Fisher Effect

• A rise (fall) in a countrys 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.

42
The Fisher Effect

• 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.

43
Figure 15-2 Inflation and Interest Rates in
Switzerland, the United States, and Italy,
1970-2000
44
Figure 15-2 Continued
45
Figure 15-2 Continued
46
Long-run effect of the growth rate of the money
supply

• 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

47
Long-Run Nominal Exchange Rates

• 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.
48
Figure 15-1 Long-Run Time Paths of U.S. Economic
Variables after a Permanent Increase in the
Growth Rate of the U.S. Money Supply
49
(No Transcript)
50
(No Transcript)
51
The Long-Run Effect of the Growth of the Money
Supply Summary

• 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

52
(No Transcript)
53
Real interest rate parity

• 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

54
Real Interest Parity

• 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 countrys
  output)
• Also referred to as expected real interest rates

55
Real Interest Parity

• 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)

56
Interest Parity Nominal and Real

• Nominal interest parity
• RUS RE (Ee/ E/)/E/
  (13-2)
• Real interest parity
• reUS reE (qe/ q/)/q/ (15-10)

57
Real Interest Parity

• 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.

58
()
MUS/PUS
MgUS
(-)

• Long run effects are shown in blue
• The rest of the chart is from Chapters 13 and 14

()
R
YUS
(-)
US preference for cash
()
E
()
(-)
MEUROPE/PEUROPE
R
()
YEUROPE
(, prop)
Ee
()
European preference for cash
(, prop)
(, more than prop)
MUS
MgUS