price levels and exchange rates in the long runbd892/p and e in lr16.pdf1. purchasing power parity...
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Price Levels and Exchange Rates in the LongRun
Chapter 16
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1. Purchasing Power Parity (PPP)
2. Monetary Approach to the Exchange Rate
3. Empirical Evidence on PPP
4. General model of long-run exchange rate
5. Real interest rate parity
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1 Purchasing Power Parity
1.1 Law of one price (LOOP)
� Price of a particular good i should be the same when priced in the samecurrency
Pi = EP�i
� Arbitrage
� Ignores
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� Barriers to trade like tari¤s
� Transportation costs
� Costs of retailing
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1.2 PPP from LOOP
� If LOOP holds, and if weights in consumption basket for goods are identicalacross countries, the PPP holds
PUS = EPJ
� Determine exchange rate from relative price levels
E =PUSPJ
� Absolute PPP requires identical price levels � not likely to hold for realworld baskets
EPJPUS
= 1
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� Relative PPP requires the relative price to be constant, but not unityEPJPUS
= constant
� Taking logarithms and di¤erentiating1
E
dE
dt=
1
PUS
dPUSdt
� 1
PJ
dPJdt
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2 Monetary Approach to the Exchange Rate
2.1 Building blocks
� Purchasing power parity (PPP)
E =PUSPJ
� Money demand in each countryMUS
PUS= L
�R$; YUS
� MJ
PJ= L
�R=Y; YJ
�
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implying
PUS =MUS
L�R$; YUS
� PJ =MJ
L�R=Y; YJ
�
� Combine
E =PUSPJ
=L�R=Y; YJ
�MUS
L�R$; YUS
�MJ
� Take logarithms
lnE = lnMUS � lnMJ + lnL�R=Y; YJ
�� lnL
�R$; YUS
�
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3 Comparative statics
lnE = lnMUS � lnMJ + lnL�R=Y; YJ
�� lnL
�R$; YUS
�
� MUS increases (other variables constant)
� YUS increases (other variables constant)
� R$ increases (other variables constant)
� Might not make sense to consider a change in a single variable with othersconstant
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3.1 Characteristics of Long-Run Equilibrium
3.1.1 Monetary Neutrality
� Prices
Pt+1 � PtPt
= �t+1 =Mt+1 �Mt
Mt
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� Exchange rates
Et+1 � EtEt
=Pt+1;US � Pt;US
Pt;US�Pt+1;J � Pt;J
Pt;J= �US � �J
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3.1.2 Fisher e¤ect
� Real interest rate is una¤ected by in�ation
R$ � �US
� When �US increases, R$ increases by the same amount
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3.1.3 Graphs of e¤ects of an increase in money growth with �exibleprices
� MUS
� R$
� PUS
� E
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3.2 Increase in money growth, interest rates, and exchange
rates
� Interest rate parity
R$ = R=Y +Eet+1 � Et
Et
� Sticky prices (short run) � increase in money with price �xed reduces R$.Therefore Et must rise by more than Eet+1
� Flexible prices (long run) � the expected rate of change of the exchangerate and the expected rate of in�ation equal the higher money growth,raising R$
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4 Empirical Evidence on PPP
4.1 What is required for PPP to hold?
� Perfectly �exible prices �not in short-run
� LOOP
� trade barriers
� non-traded goods and services
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� Belassa-Samuelson e¤ect
� labor force in poor countries is less productive than in rich countriesfor tradeables
� labor force equally productive for non-tradeables
� price of tradeables determined on world market
� since wage = MPN x P for traded goods, MPN lower and P thesame, then wage is lower
� non-traded goods have lower wage and world MPN, implying lowerprice of non-tradeables and lower price level
� All goods are tradeable and all countries have same goods with identicalweights in baskets or absence of real shocks
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� If all shocks were nominal, relative PPP would hold
� Absolute PPP �holds in levels
PUS = EPJ
� Relative PPP �holds in proportionate rates of change
Et+1 � EtEt
=Pt+1;US � Pt;US
Pt;US�Pt+1;J � Pt;J
Pt;J= �US � �J
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4.2 Does PPP hold?
� No
� Holds better in the long-run than in the short-run
� Even in the long-run, real shocks can require relative price changes
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5 General Model of Long-Run Exchange Rate
5.1 Real Exchange Rate
� Relative price of foreign goods
q =EPJPUS
� Real domestic depreciation is an increase in q �Japanese goods becomeexpensive relative to US goods
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� Determined by relative demand and supply for foreign goods compared toUS goods
� Real exchange rate could never change if PPP held
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5.2 Changes in the Real Exchange Rate
� Increase in world demand for US goods relative to foreign goods � q falls� real appreciation
� US technological improvement increases relative supply of US goods � qrises � real depreciation
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5.3 Adjust Monetary Approach to the Exchange Rate for
Absence of PPP
� Real exchange rate replaces PPP
E = q � PUSPJ
� Money demand in each country solved for price
PUS =MUS
L�R$; YUS
� PJ =MJ
L�R=Y; YJ
�
� Combine
E = qPUSPJ
= qMUSL
�R=Y; YJ
�MJL
�R$; YUS
�
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� Comparative statics � q up raises E
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6 Real Interest Rate Parity
� Real exchange rate
q =EPj
PUS
� Take logarithms
ln q = lnE + lnPj � lnPUS
� Take time derivatives1
q
dq
dt=1
E
dE
dt+1
PJ
dPJdt
� 1
PUS
dPUSdt
This is approximately
qt+1 � qtqt
=Et+1 � Et
Et+ �J � �US
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� Real interest rate parity
� nominal interest rate parity
R$ �R=Y =Eet+1 � Et
Et
� de�nition of real exchange rate
qet+1 � qtqt
� �eJ + �eUS =
Eet+1 � EtEt
� combine
R$ �R=Y =qet+1 � qt
qt+ �eUS � �
eJ
the interest rate di¤erential is the expected change in the real exchangerate plus the expected in�ation di¤erential
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� de�ne expected real interest rate
re = R� �e
� real interest rate parity
reUS � reJ =
qet+1 � qtqt
the real interest rate di¤erential is the expected rate of change of thereal exchange rate