Ch. 15: Price Levels and the Exchange Rate in the Long Run

1
Ch. 15 Price Levels and the Exchange Rate in the
Long Run
2
The Behavior of Exchange Rates

• What models can predict how exchange rates
  behave?
• In last chapter we developed a short run model
  and a long run model that used movements in the
  money supply.
• In this chapter, we develop 2 more models,
  building on the long run approach from last
  chapter.
• Long run means that prices of goods and services
  and factors of production that build those goods
  and services adjust to supply and demand
  conditions so that their markets and the money
  market are in equilibrium.
• Because prices are allowed to change, they will
  influence interest rates and exchange rates in
  the long run models.

3
The Behavior of Exchange Rates

• The long run models are not intended to be
  completely realistic descriptions about how
  exchange rates behave, but ways of generalizing
  how market participants form expectations about
  future exchange rates.

4
Law of One Price

• The law of one price simply says that the same
  good in different competitive markets must sell
  for the same price, when transportation costs and
  barriers between markets are not important.
• Why? Suppose the price of pizza at one restaurant
  is 20, while the price of the same pizza at a
  similar restaurant across the street is 40.
• What do you predict to happen?
• Many people would buy the 20 pizza, few would
  buy the 40.

5
Law of One Price

• Consider a pizza restaurant in Seattle one across
  the border in Vancouver.
• The law of one price says that the price of the
  same pizza (using a common currency to measure
  the price) in the two cities must be the same if
  barriers between competitive markets and
  transportation costs are not important
• PpizzaUS (EUS/Canada) x (PpizzaCanada)
• PpizzaUS price of pizza in Seattle
• PpizzaCanada price of pizza in Vancouver
• EUS/Canada US dollar/Canadian dollar exchange
  rate

6
Law of One Price

• Assumptions
• Competitive markets
• No trade barriers
• No transportation costs
• Identical products must sell at the same price.
• A Sony TV selling for 100 in the US and 12,000
  in Japan implies an exchange rate of 120 per
  dollar.

7
Law of One Price

• If the Sony TV sold for 100 or 12,000 but the
  exchange rate were 100 per dollar, what would
  happen in a frictionless trade environment?

• People would buy TVs in US, and sell them
• in Japan. For a Japanese entrepreneur, 10,000
• would get him 100, buy the TV, and sell it for
• 12,000. A sure 20 return.

ARBITRAGE
8
Law of One Price

• If people from Japan embarked on this endeavor,
  there would be more demand for and more supply
  of in the forex market.
• USD would appreciate and would depreciate.
• The forex market would feel the pressure of
  appreciation until 120 per dollar rate is
  reached.

9
Law of One Price

• If prices in both localities are equal, then
• P (/) P or P (/) P.
• By the same token, P/P (/) or
• P/P (/).

10
Purchasing Power Parity

• Generalizing from the law of one price, the price
  levels representing similar basket of goods and
  products should be equal to the exchange rate.
• PUS/PJapan (/)
• Alternatively, PUS (/) PJapan or price level
  in US is the same as price level in Japan when
  measured in terms of .

11
Purchasing Power Parity

• If law of one price holds and both countries have
  exactly same baskets, PPP will hold, too.
• PPP should indicate general tendency even if law
  of one price fails in some cases
• The higher priced goods will lose demand and the
  currency will depreciate.
• The increased demand for lower priced goods will
  force the currency to appreciate.

12
Purchasing Power Parity

• Say, PUS / PJapan gt (/).
• Demand for Japanese products, hence yen, will
  rise.
• Demand for American products, hence USD, will
  fall.
• Yen will appreciate and will depreciate.
• PUS / PJapan (/).

13
Relative PPP

• PUS / PJapan (/) implies that if inflation in
  US were greater than in Japan, then should
  appreciate and depreciate.
• PUS0 / PJapan0 (/)0
• PUS1 gt PJapan1 (/)0
• PUS1 PJapan1 (/)1

14
Purchasing Power Parity

• Purchasing power parity comes in 2 forms
• Absolute PPP Exchange rates equal price levels
  across countries.
• E/ PUS/PEU
• Relative PPP changes in exchange rates equal
  changes in prices (inflation) between two
  periods
• (E/,t - E/, t 1)/E/, t 1 ?US, t - ?EU,
  t
• where ?t inflation rate from period t-1 to t

15
Monetary Approach to Exchange Rate Determination

1. This is a long run, flexible price condition.
2. Assume PPP holds.
3. Assume price level in a country is determined by
   the supply and real demand for money.
4. The result is exchange rate, which is equal to
   relative price levels in two countries under PPP,
   is determined by relative money supplies and
   demands.

16
Monetary Approach to Exchange Rate Determination
(/) PUS/PEurope (PPP condition) Md P
L(R,Y) (Money demand) Md/P L(R,Y) (Real
money demand) Md Ms or Md/P Ms/P
(Equilibrium) Ms/P L(R,Y) (Equilibrium) P
Ms/L(R,Y) (Equilibrium) (/)
Ms/L(R,Y)US/Ms/L(R,Y)Europe
17
Monetary Approach to Exchange Rates

• To the degree that PPP holds and to the degree
  that prices adjust to equate real money supply
  with real money demand, we have the following
  prediction
• The exchange rate is determined in the long run
  by prices, which are determined by the relative
  supply of money across countries and the relative
  real demand of money across countries.

18
Monetary Approach to Exchange Rate Determination

• A permanent increase in the US money supply will
  cause a proportional increase in the US price
  level and force to depreciate and to
  appreciate.
• For instance, a 15 increase in US money supply
  will raise the price level by 15 and appreciate
  the euro by 15.

19
Monetary Approach to Exchange Rate Determination

• If Europe grew faster than US, European Y will be
  relatively higher.
• Real demand for money in Europe will rise.
• Given the same money supply, and interest rates
  not fully accommodate demand, price level in
  Europe will fall.
• Euro will appreciate and USD will depreciate.

20
Monetary Approach to Exchange Rate Determination

• A drop in the interest rates in the US increases
  the real demand for money.
• To fulfill the equilibrium condition, as long as
  money supply hasnt changed, price level has to
  fall.
• If there was no change in Europe, the euro will
  depreciate and the USD will appreciate.

21
Monetary Approach to Exchange Rate Determination

• This analysis yields two results
• Long run exchange rate depreciates with
  increasing money supply.
• Increases in interest rates depreciate the
  currency by lowering the real demand for money.
• The second conclusion contradicts what interest
  parity condition predicts.

22
The Contradiction

• The way a change in interest rate affects the
  exchange rate depends on the reason why interest
  rates have changed in the first place.
• If the interest rate has risen because of
  inflation, the expected depreciation of the
  currency will force the spot rate to depreciate
  as well.
• If the interest rate rose because of lower
  savings or higher investments, then interest
  parity will force the spot rate to appreciate.

23
More Contradiction

• Suppose people in US decide to save more.
• What happens to real interest rate?
• What happens to inflation?
• What happens to nominal interest rate?
• What happens to P in US?
• What happens to ?

24
Chronic Inflation

• An ongoing inflation of 20 would require the
  money supply to increase continually at the rate
  of 20, too.
• The long run equilibrium in this case, will reach
  the same real values as no inflation case but
  will have higher nominal values.
• Using the relative PPP concept, one expects the
  currency to depreciate by 20.

25
Inflation and Interest Parity

• ?(PUS/PEurope) ? (/)
• If this becomes part of the expectation, then the
  interest parity condition can be rewritten as R
  R ? (/).
• Alternatively, R - R US inflation Euro
  inflation.
• The difference between interest rates has to
  reflect the expected inflation in both countries.

26
The Fisher Effect

• Nominal interest rate is equal to real interest
  rate plus the expected inflation rate.
• In the long run, real interest rate, like other
  real variables, has no bearing to the monetary
  sector.
• An increase in the money growth that increases
  the inflation rate will raise the nominal
  interest rate by the additional inflation rate.

27
Notation

• Suppose in the long run the growth rate of
• money supply, (M1-M0)/M0, is given by p.
• Inflation will also equal to p.
• From the previous discussion, the depreciation of
  the currency should also equal p.
• If the long run path of the money growth
  increases to p?p, then inflation and
  depreciation will also increase to p?p.

28
Time Paths
Interest rate
Money supply
SlopepDp
RDp
R
Slopep
t1
time
time
t1
Price level
/
SlopepDp
SlopepDp
Slopep
Slopep
t1
time
t1
time
29
Future Rate of M Growth Up, P Flexible
Future M growth up. P rises. M/P drops.
R
R
Expected inflation makes expected value of the
depreciate.
M/P
R
/
/
Current value of USD falls even though R has
increased Fisher effect.
PPP
M/P
R
30
Source of R Increase

• In the sticky price case, R increases due to M
  decrease.
• Lower M/P matches the real demand at higher R.
• Inflationary expectations are lower.
• Expected exchange value of USD rises because of
  lower expected inflation relative PPP.
• Current exchange value of USD rises because of
  interest parity.

31
Graphical Explanation
R
/
Money supply decrease raised R and appreciated .
32
Source of R Increase

• In the flexible price case, R increases due to
  rise in inflationary expectations.
• An increase in the future growth rate of money
  supply means prices in the future will rise at
  the same growth rate as the money growth.
• Perfect flexibility makes current price level
  rise.
• Real supply of money drops.
• Expected inflation depreciates the expected value
  of USD in the forex market relative PPP.
• Interest parity makes current forex value of USD
  drop.

33
Empirical Evidence on PPP

• Tests to confirm absolute PPP have largely
  failed.
• Tests to confirm relative PPP have mixed results.
• Tests to confirm law of one price did not fare
  well, either.
• The Economists Big Mac PPP shows wide
  divergences.

34
2006
WHEN our economics editor invented the Big Mac
index in 1986 as a light-hearted introduction to
exchange-rate theory, little did she think that
20 years later she would still be munching her
way, a little less sylph-like, around the world.
As burgernomics enters its third decade, the Big
Mac index is widely used and abused around the
globe. It is time to take stock of what burgers
do and do not tell you about exchange rates. The
Economist's Big Mac index is based on one of the
oldest concepts in international economics the
theory of purchasing-power parity (PPP), which
argues that in the long run, exchange rates
should move towards levels that would equalise
the prices of an identical basket of goods and
services in any two countries. Our basket is a
McDonald's Big Mac, produced in around 120
countries. The Big Mac PPP is the exchange rate
that would leave burgers costing the same in
America as elsewhere. Thus a Big Mac in China
costs 10.5 yuan, against an average price in four
American cities of 3.10 (see the first column of
the table). To make the two prices equal would
require an exchange rate of 3.39 yuan to the
dollar, compared with a market rate of 8.03. In
other words, the yuan is 58 undervalued
against the dollar. To put it another way,
converted into dollars at market rates the
Chinese burger is the cheapest in the table.
http//www.economist.com/finance/displaystory.cfm
?story_idE1_GJSNQSS
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36
Failure of PPP

1. Failure of the law of one price.
2. Transport costs and government regulations to
   restrict trade.
3. Monopolistic and oligopolistic practices. Product
   differentiation.
4. Differences in commodity baskets of different
   countries.
5. Cost of nontradable inputs.

37
Law of One Price

• If the law of one price doesnt hold, then its
  extension absolute PPP should not be expected to
  hold, either.

38
Transport Costs

• If a computer costs 1000 in the US and FF5000 in
  France, transportation costs could keep the
  exchange rate different than FF5 per USD, the PPP
  rate.
• If it costs 50 to ship the computer from the US
  to France, and the exchange rate is FF4 per USD,
  a French importer has to pay FF4000 FF200.
• If the exchange rate is FF4.80 per , the
  computer will cost FF4800 FF240 no trade.
• If the exchange rate is FF4.75, the cost will be
  FF4750FF237.50 and trade will take place.

39
Tariffs

• Instead of the transport costs, if the French had
  5 import tariff, the previous calculations would
  still be true.
• There would be no exports of computers from US to
  France if FF4.77 per USD or above.
• There would be no exports of computers from
  France to US until the exchange rate were above
  FF5.26 per USD.
• FF5000/5.26 950.57 for the computer plus 50
  transportation.

40
Nontradables

• There is a range of exchange rates within which
  transportation costs prohibit trade.
• The higher the transport costs, the more likely a
  good or service becomes nontradable.
• The more nontradables in a countrys basket of
  goods and services included in the price
  calculation, the less the probability of PPP
  holding.

41
Nontradables

• The prices of nontradables are determined through
  the interaction of domestic supply and demand.
• The higher the prices of nontradables, the higher
  will be CPI or PPI, and the lower will be the
  purchasing power of a currency, lowering the
  standard of living.
• In LDCs where there is a huge informal sector
  that employs most of the urban populations,
  prices of nontradables can be very low.

42
Nontradables

• If services plus construction comprise a large
  percentage of GDP (3/5 in US), baskets will not
  satisfy PPP.
• Even if the weights of different items in the CPI
  were the same in both countries, a land scarce
  country like Hong Kong, Japan or Singapore will
  have a higher impact of nontradable housing
  prices than US.

43
Imperfect Markets

• For PPP to hold, markets have to be competitive.
• If markets are segmented so that the same
  producer can charge different prices in different
  markets, there is no reason for the law of one
  price to hold.
• Likewise, monopolistic or oligopolistic market
  power will make prices higher than competitive
  prices, undermining PPP.

44
CPI Weights

• Depending on consumer tastes, mobility of the
  population, settlement patterns, different items
  entering into the consumer basket will get
  different weights.
• This further undermines the PPP.
• However, if all the prices had increased by the
  same percentage, weights would not matter in
  relative PPP. Currency would depreciate by the
  same percentage.

45
CPI Weights

• If relative prices between goods had changed,
  then relative PPP could not be satisfied.
• If fish prices rose worldwide, it would have a
  larger impact on Japanese CPI than on US CPI.

46
Balassa-Samuelson Theory

• Productivity in tradable sector is higher in the
  rich countries.
• Productivity in the nontradables sector does not
  diverge between the rich and the poor countries.
• Average wages (reflecting average productivity)
  are higher in rich countries to make nontradables
  prices higher.
• Price levels in rich countries, therefore, are
  higher.

47
Bhagwati-Kravis-Lipsey Theory

• Rich countries have high capital-labor ratios.
• Marginal productivity in rich countries is,
  therefore, higher resulting in higher wages.
• Nontradables are primarily labor-intensive,
  cheaper labor from poor countries keep their
  prices lower in poor countries, lowering the
  price level.

48
The Real Exchange Rate

• q/ (/) (P/P)
• q/ ( per ) times P per Japanese basket
  divided by P per US basket (/) (P/P) US
  basket per Japanese basket.
• ((/) P /Jb)/(P /USb) ((/) P USb/ P Jb
  ((/) P / P ) (USb/Jb) q/ USb per Jb
• The real exchange rate shows the USD price of
  Japanese basket relative to the US basket.

49
The Real Exchange Rate

• If PPP were to hold always, the real exchange
  rate would be always one.
• Because PPP hardly holds, the real exchange rate
  deviates from one.
• The real exchange rate is the nominal exchange
  rate adjusted for the price levels in both
  countries.

50
Real Exchange Rates

• An increase in q/ is a real depreciation of
  USD.
• It can happen by nominal depreciation of USD or
  increase in Japanese price level or drop in US
  price level.
• Reread the sentence above. It is contrary to
  relative PPP.

51
The Real Exchange Rate

• When the q/ rises, the dollars purchasing
  power over Japanese goods and services falls
  relative to its purchasing power over US goods
  and services.
• Americas goods and services become cheaper
  relative to Japan.
• A rise in q/ is of course a real depreciation
  of USD.

52
Real Exchange Rates and PPP

• If real exchange rates do not comply with
  absolute PPP, i.e., q/ does not necessarily
  equal to 1, then relative price level changes
  will affect the real exchange rate.
• Relative price levels can change because of
  demand or supply changes.
• q/ / (PJ/PUS)

53
Demand for Japanese Products Increases

• If total world spending on Japanese goods and
  services rises relative to that of American GS,
  there will be excess demand for Japanese products
  at the original real exchange rate.
• The relative price of Japanese output in terms of
  US basket has to rise or the amount of US basket
  per Japanese basket has to increase.

54
Demand for Japanese Products Increases

• q/ ( per ) times P per Japanese basket
  divided by P per US basket (/) (P/P) US
  basket per Japanese basket.
• q/ rises.
• Real appreciation of yen takes place.
• A drop in the world demand for US products cause
  a real depreciation of USD.

55
Relative Output Supply

• Suppose productivity of US labor and capital
  increases.
• There will be an excess supply of American goods
  and services at the original q/ .
• The relative price of American basket falls.
• US basket per Japanese basket is larger.
• q/ rises ( per ) times P per Japanese
  basket divided by P per US basket (/)
  (P/P) US basket per Japanese basket.

56
Productivity Increase

• Higher productivity increase in a country causes
  a real depreciation of its currency in the long
  run.
• Higher demand for a countrys output causes a
  real appreciation of its currency in the long run.

57
Nominal and Real Exchange Rates

• If q/ (/) (P/P), then (/) q/
  (P/P).
• Nominal exchange rate of USD per yen is equal to
  real exchange rate of USD per yen times relative
  US price level to Japanese price level.
• Recall the monetary approach to FX determination
  where PPP was assumed to hold (/) (P/P).
• By including the q/ we can drop the PPP
  requirement.

58
Nominal and Real Exchange Rates

• (/) q/ (P/P) implies that
• for a given real USD per yen exchange rate, money
  supply and demand in each country will determine
  the price levels and, hence, nominal per yen
  rate.
• Given price levels, changes in the real per yen
  rate also affects the nominal rate.

59
Long Run Nominal Exchange Rate
60
A Shift in Relative Money Supply Levels

• Suppose Japanese money supply has a permanent
  one-time increase.
• In the long run, there should be no change in
  real values only nominal values should change.
• Furthermore, there should be no change in the
  interest rate. Graph this.

61
A Shift in Relative Money Supply Levels
In the long run price level will rise
proportionately to money increase.
R
Real money supply
R0
R1
M/P
62
A Shift in Relative Money Supply Levels

• Along with other real variables, real exchange
  rate does not change, either.
• Ms/L(Y,R)J P
• (/) q/ (P/P)
• If P rises at the same proportion as Japanese
  money supply, the nominal exchange rate (/)
  should fall.

63
A Shift in Money Growth Rates

• A permanent increase in the US money growth rate
  raises the US inflation, and through the Fisher
  effect, raises the dollar interest rate.
• US price level has to rise to keep the money
  demand equal to money supply.
• USD returns from yen deposits increase because
  USD is expected to depreciate.
• Slide 26.

64
A Shift in Money Growth Rates

• The change is monetary it is neutral in long run
  real variable effects.
• Real exchange rate does not change.
• (/) q/ (P/P) implies the rise in the
  price level of US has to be matched by the
  depreciation of USD.

65
A Change in Relative Output Demand

• National price levels will only respond to demand
  and supply of money.
• Ms/L(Y,R)US P and Ms/L(Y,R)J P
• Demand changes, therefore, will not affect price
  levels.
• A relative increase in demand for US output will
  raise the Japanese basket per US basket.
• Alternatively, it will decrease the US basket per
  Japanese basket.

66
A Change in Relative Output Demand

• q/ ( per ) times P per Japanese basket
  divided by P per US basket (/) (P/P) US
  basket per Japanese basket.
• q/ falls.
• Real depreciation of yen against the USD.
• Real appreciation of USD against the yen.
• (/) q/ (P/P) implies that nominal
  exchange rate of yen falls and USD appreciates.

67
A Change in Relative Output Supply

• A relative increase in Japanese output due to
  productivity increases means the Japanese are
  willing to exchange a higher amount of their
  basket for US goods.
• The US basket per Japanese basket decreases.
• q/ ( per ) times P per Japanese basket
  divided by P per US basket (/) (P/P) US
  basket per Japanese basket.
• Real depreciation of yen q/ falls.

68
A Change in Relative Output Supply

• Productivity increase in Japan raises their
  income, Y.
• The real demand for money rises.
• Ms/L(Y,R)J P implies P has to fall.
• (/) q/ (P/P) nominal exchange rate will
  respond to the fall of q/ and fall of P.
• (/) may increase or decrease.

69
Summary of Money and Real Sector Disturbances in
the Long Run

• When disturbances are monetary, long run nominal
  exchange rates obey relative PPP real exchange
  rates do not change.
• When disturbances are from output markets, the
  nominal exchange rates do not obey the relative
  PPP real exchange rates do change.

70
(/) Rate During the Last 50 Years

• Between 1950 and 1971 the nominal rate of yen was
  fixed at 360 per or 0.00278 per .
• The real exchange rate q/ however, rose because
  Japan had higher inflation rate than US.
• In the seventies the nominal exchange rate became
  flexible.
• Inflation in US on average was higher than
  Japanese inflation the last 25 years.

71
(/) Rate During the Last 50 Years

• The q/ rate should have been falling if the
  nominal exchange rate was fixed,
• (/) q/ (P/P). Both nominal and real
  rates rose.
• The reason for the rise of q/ (US basket per
  Japanese basket) was the much higher productivity
  increase in tradables in Japan that raised the
  price level for nontradables.

72
(/) Rate During the Last 50 Years

• q/ ( per ) times P per Japanese basket
  divided by P per US basket (/) (P/P) US
  basket per Japanese basket.
• (/) q/ (P/P) implies that the nominal
  exchange rate will rise because of an increase in
  q/ and a higher inflation in US.
• The rate is about 120 per .

73
Interest Rates and Real Exchange Rates with
Expectations

• q/ (/) (P/P).
• Dq/ D(/) D(P/P).
• (qe - q)/q (/)e - (/)/ (/) (Pe -
  P)/ P - (Pe -P)/P.
• (qe - q)/q (Ee - E)/E pe - pe .
• Remember interest parity.

74
Interest Rates and Real Exchange Rates with
Expectations

• R R (Ee - E)/E.
• R - R (Ee - E)/E.
• Therefore, R - R (qe - q)/q (pe - pe).
• If US inflation is 3 higher than Japanese
  inflation and the demand and supply conditions
  require 2 real appreciation of the yen, then the
  interest rate differential will be 5.

75
Real Interest Rates

• re R - pe
• re R - pe
• R - R (qe - q)/q (pe - pe).
• re - re (R - pe) - (R - pe)
• re - re (qe - q)/q
• Interest parity holds with real interest rates
  and real exchange rates.