Transcript Ch. 15: Price Levels and the Exchange Rate in the Long Run.
Ch. 15: Price Levels and the Exchange Rate in the Long Run 1
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.
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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.
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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 $40. 4
Law of One Price
Consider a pizza restaurant in Seattle one across the border in Vancouver. The law of one price says that the price of the same pizza (using a common currency to measure the price) in the two cities must be the same if barriers between competitive markets and transportation costs are not important:
P pizza
US = (
E
US$/Canada$ ) x (
P pizza
Canada )
P pizza
US = price of pizza in Seattle
P pizza
Canada = price of pizza in Vancouver
E
US$/Canada$ = US dollar/Canadian dollar exchange rate 5
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.
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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 7
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.
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Law of One Price
If prices in both localities are equal, then P $ = ($/¥) P ¥ or P ¥ = (¥/$) P $ .
By the same token, P ¥ /P $ P $ /P ¥ = ($/¥).
= (¥/$) or 9
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.
P US /P Japan = ($/¥) Alternatively, P US = ($/¥) P Japan or price level in US is the same as price level in Japan when measured in terms of $.
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Purchasing Power Parity
If law of one price holds and both countries have exactly same baskets, PPP will hold, too.
PPP should indicate general tendency even if law of one price fails in some cases: The higher priced goods will lose demand and the currency will depreciate.
The increased demand for lower priced goods will force the currency to appreciate.
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Purchasing Power Parity
Say, P US / P Japan > ($/¥).
Demand for Japanese products, hence yen, will rise.
Demand for American products, hence USD, will fall.
Yen will appreciate and $ will depreciate.
P US / P Japan = ($/¥).
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Relative PPP
P US / P Japan = ($/¥) implies that if inflation in US were greater than in Japan, then ¥ should appreciate and $ depreciate.
P US0 P US1 P US1 / P Japan0 > P Japan1 = ($/¥) 0 ($/¥) 0 = P Japan1 ($/¥) 1 13
Purchasing Power Parity
Purchasing power parity comes in 2 forms:
Absolute PPP
: Exchange rates equal price
levels
across countries.
E
$/ € =
P
US /
P
EU
Relative PPP
:
changes
in exchange rates equal
changes
in prices (inflation) between two periods: (
E
$/ €,
t - E
$/ €,
t
–1 )/
E
$/ €,
t
–1 = US,
t -
EU, where
t
= inflation rate from period
t-1 t
to
t
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1.
2.
3.
4.
Monetary Approach to Exchange Rate Determination
This is a long run, flexible price condition.
Assume PPP holds.
Assume price level in a country is determined by the supply and real demand for money.
The result is exchange rate, which is equal to relative price levels in two countries under PPP, is determined by relative money supplies and demands.
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Monetary Approach to Exchange Rate Determination
($/€) = P US /P Europe M d = P L(R,Y) (PPP condition) (Money demand) M d /P = L(R,Y) M d = M s or M d /P = M (Real money demand) s /P (Equilibrium) M s /P = L(R,Y) P = M s /L(R,Y) (Equilibrium) (Equilibrium) ($/€) = [M s /L(R,Y)] US /[M s /L(R,Y)] Europe 16
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. 17
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%.
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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.
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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 hasn’t changed, price level has to fall.
If there was no change in Europe, the euro will depreciate and the USD will appreciate.
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Monetary Approach to Exchange Rate Determination
1.
2.
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.
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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.
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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 $?
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Inflation and Interest Parity
%Δ(P US /P Europe )= %Δ ($/€) If this becomes part of the expectation, then the interest parity condition can be rewritten as R $ = R € + %Δ ($/€).
Alternatively, R inflation.
$ - R € = US inflation – Euro The difference between interest rates has to reflect the expected inflation in both countries.
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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.
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Notation
Suppose in the long run the growth rate of money supply, (M 1 -M 0 )/M 0 , is given by π.
Inflation will also equal to π. From the previous discussion, the depreciation of the currency should also equal π.
If the long run path of the money growth increases to π+Δπ, then inflation and depreciation will also increase to π+Δπ.
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Money supply Slope=π+
D
Time Paths
Interest rate R Slope=π Price level t 1 Slope=π+
D
time $/€ t 1 Slope=π+
D
time R+
D
Slope=π t 1 time Slope=π t 1 time
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R
Future Rate of M Growth Up, P Flexible
R
Future M growth up. P rises. M/P drops.
$/€ M/P $/€ R
Expected inflation makes expected value of the $ depreciate.
Current value of USD falls even though R has increased: Fisher effect.
PPP M/P R
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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.
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R $
Graphical Explanation
Money supply decrease raised R and appreciated $.
$/¥
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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.
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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 Economist’s
wide divergences.
Big Mac PPP shows 33
http://www.economist.com/finance/displaystory.cfm?story_id=E1_GJSNQSS 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.
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35
Failure of PPP
1.
2.
3.
4.
5.
Failure of the law of one price.
Transport costs and government regulations to restrict trade.
Monopolistic and oligopolistic practices. Product differentiation.
Differences in commodity baskets of different countries.
Cost of nontradable inputs.
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Law of One Price
If the law of one price doesn’t hold, then its extension absolute PPP should not be expected to hold, either.
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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 FF4750+FF237.50 and trade will take place.
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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.
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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 country’s basket of goods and services included in the price calculation, the less the probability of PPP holding.
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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.
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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.
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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.
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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.
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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.
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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.
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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.
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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.
(($/¥) P ¥ /Jb)/(P Jb = (($/¥) P ¥ Jb $ / P $ /USb) = (($/¥) P ¥ ) (USb/Jb) = q $/¥ USb/ P $ USb per The real exchange rate shows the USD price of Japanese basket relative to the US basket.
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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.
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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.
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The Real Exchange Rate
When the q $/¥ rises, the dollar’s purchasing power over Japanese goods and services falls relative to its purchasing power over US goods and services.
America’s goods and services become cheaper relative to Japan.
A rise in q $/¥ is of course a real depreciation of USD.
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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 $/¥ = $/¥ (P J /P US ) 52
Demand for Japanese Products Increases
If total world spending on Japanese goods and services rises relative to that of American G&S, 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.
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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.
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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.
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Productivity Increase
Higher productivity increase in a country causes a real depreciation of its currency in the long run.
Higher demand for a country’s output causes a real appreciation of its currency in the long run.
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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 $/¥ requirement. we can drop the PPP 57
Nominal and Real Exchange Rates
($/¥) = 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.
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Long Run Nominal Exchange Rate
Change
Money Sector
Increase in US M Increase in Japanese M Increase in US money growth Increase in Japanese money growth
Real Sector
Increase in demand for US output Increase in demand for Japanese output Output supply increase in US Output supply increase in Japan Effect on $/¥ Proportional increase Proportional decrease Increase Decrease Decrease Increase Ambiguous Ambiguous 59
A Shift in Relative Money Supply Levels
Suppose Japanese money supply has a permanent one-time increase.
In the long run, there should be no change in real values; only nominal values should change.
Furthermore, there should be no change in the interest rate. Graph this.
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A Shift in Relative Money Supply Levels
R R 0 R 1 Real money supply
In the long run price level will rise proportionately to money increase.
M/P
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A Shift in Relative Money Supply Levels
Along with other real variables, real exchange rate does not change, either.
[M s /L(Y,R)] J = P ¥ ($/¥) = q $/¥ (P $ /P ¥ ) If P ¥ rises at the same proportion as Japanese money supply, the nominal exchange rate ($/¥) should fall.
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A Shift in Money Growth Rates
A permanent increase in the US money growth rate raises the US inflation, and through the Fisher effect, raises the dollar interest rate.
US price level has to rise to keep the money demand equal to money supply.
USD returns from yen deposits increase because USD is expected to depreciate.
Slide #26.
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A Shift in Money Growth Rates
The change is monetary; it is neutral in long run real variable effects.
Real exchange rate does not change.
($/¥) = q $/¥ (P $ /P ¥ ) implies the rise in the price level of US has to be matched by the depreciation of USD.
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A Change in Relative Output Demand
National price levels will only respond to demand and supply of money.
[M s /L(Y,R)] US = P $ and [M s /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.
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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.
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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 $/¥ falls.
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A Change in Relative Output Supply
Productivity increase in Japan raises their income, Y.
The real demand for money rises.
[M s /L(Y,R)] J = P ¥ implies P ¥ has to fall.
($/¥) = q $/¥ (P $ /P ¥ ) nominal exchange rate will respond to the fall of q $/¥ and fall of P ¥ .
($/¥) may increase or decrease. 68
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.
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($/¥) 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 $/¥ however, rose because Japan had higher inflation rate than US.
In the seventies the nominal exchange rate became flexible.
Inflation in US on average was higher than Japanese inflation the last 25 years.
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($/¥) 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 $/¥ (US basket per Japanese basket) was the much higher productivity increase in tradables in Japan that raised the price level for nontradables.
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($/¥) 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 $.
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Interest Rates and Real Exchange
Rates with Expectations
q $/¥ = ($/¥) (P ¥ /P $ ).
% D q $/¥ = % D ($/¥) + % D (P ¥ /P $ ).
(q e q)/q = [{($/¥) e ($/¥)}/ ($/¥)] + [(P ¥ e P ¥ )/ P ¥ ] - [(P $ e (q e - q)/q = [(E e -P $ )/P $ ].
- E)/E] + [ ¥ e ] - [ $ e ].
Remember interest parity.
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Interest Rates and Real Exchange Rates with Expectations
R $ = R ¥ + [(E e - E)/E].
R $ - R ¥ = [(E e Therefore, R $ - E)/E].
- R ¥ = (q e - q)/q + ( $ e ¥ e ).
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%.
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Real Interest Rates
r r $ r ¥ e = R ¥ R $ e $ e = R $ $ e ¥ e - R - r ¥ ¥ e = (q e - q)/q + ( $ e = (R $ $ e ) - (R ¥ ¥ e ).
¥ e ) r $ e - r ¥ e = (q e - q)/q Interest parity holds with real interest rates and real exchange rates.
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