Purchasing Power Parity
FINC5090 Finance in The Global Economy DR HENRY LEUNG
The University of 1
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Lecture 6 Purchasing Power Parity
– Purchasing power parity
– Monetary approach to exchange rates
– ShortcomingsofPPP
– Real exchange rate
– Real interest parity
The University of 2
– What models can predict how exchange rates behave?
• Last chapter we developed a short-run model and a long-run model that used
movements in money supply.
• This chapter we develop 2 more models, building on long-run approach from last chapter.
• Long run means a sufficient amount of time for prices of all goods and services to adjust to market conditions so that their markets and the money market are in equilibrium.
• Changes in quantity of money supply will only influence nominal values but not real values (Neutrality of money).
• Because prices are allowed to change, they will influence interest rates and exchange rates in long-run models.
The University of 3
– Long-run models not intended to be completely realistic descriptions about how exchange rates behave
– But ways of representing how market participants may form expectations about future exchange rates and how exchange rates tend to move over long periods.
The University of 4
1. Purchasing power parity: Law of One Price (LOP)
– LOP: If markets are competitive and transportation costs and barriers between markets are not important… then identical goods sold in different countries must sell for same price when their prices are expressed in terms of same currency
• Goods market arbitrage: buy low, transport, then sell high
• Example iPhone 12 price
local price
exchange rate
arbitrage?
USD0.77/AUD
• How much should the exchange rate be to prevent arbitrage??
• If we believe there is no difference between an Aussie iPhone and a US iPhone: 1199AUD*E$/A$=799USD
E$/A$=799USD/1199AUD = 0.666USD/AUD
The University of 5
1. Purchasing power parity: absolute PPP
– Absolute purchasing power parity (PPP) implies that the exchange rate is determined by levels of average prices
𝐸$/𝐴$ = US = 0.666$/𝐴$
– Predicts that people in all countries have the same purchasing power with their currencies: 1 Australian dollars buy the same amount of goods as 0.666 U.S. dollar.
– Arbitrage
– export iPhones from US to Australia
– funds flow from Australia to US
– USD appreciates, AUD depreciates
– 0.77USD/AUD moves towards 0.666USD/AUD
The University of 6
1. Purchasing power parity: relative PPP
– Absolute PPP makes a strong (or unrealistic) prediction on the relation between price and exchange rate: transport cost, barriers for trading, local preferences…
– Thus, we accept spot exchange rate as a fair price of USD/AUD, but what if price of one country changes?
local price
exchange rate
changes in price
changes in EX rate
USD 0.77/AUD
– Relative purchasing power parity (PPP): changes in exchange rates equal changes in prices (inflation: 𝜋) between two periods (t-1 and t):
(𝐸$/𝐴$,𝑡 − 𝐸$/𝐴$,𝑡−1) = 𝜋US,𝑡 − 𝜋AU,𝑡 𝐸$/𝐴$,𝑡−1
The University of 7
1. Purchasing power parity: relative PPP
– The rationale for relative PPP
If one currency loses purchasing power relative to another currency, its value must
depreciate in proportion to the lost purchasing power.
(𝐸$/𝐴$,𝑡 − 𝐸$/𝐴$,𝑡−1) = 𝜋US,𝑡 − 𝜋AU,𝑡 𝐸$/𝐴$,𝑡−1
𝐸$/𝐴$,𝑡 =0.77*(0-0.084)+0.77=0.77*(1-0.084)=0.7053$/A$
local price
exchange rate
changes in price
changes in EX rate
0.77 USD/AUD
Inflation in Australia -> AUD loses purchasing power relative to USD
The University of 8
Result is AUD depreciates
2. Monetary approach to exchange rate: assumptions
– Exchange rates are affected by monetary factors, (e.g. money demand, money supply) so we need to assume money market equilibrium.
𝑀𝑑=𝑃×𝐿𝑅,𝑌 =𝑀𝑠
MS MS P=US P=EU
US L(R$,YUS ) EU L(R€,YEU )
– Absolute PPP holds (so that relative PPP also holds): exchange rates are finally
determined by the price levels.
𝑃 𝐸$/€ = US
– Long-run analysis: prices change quickly given changes in relative supply and demand of real monetary assets in money markets across countries.
(Note in topic 4 we have learned that in short-run, prices exhibit rigidity (sticky) so they do not respond instantaneously to changes in money supply/demand)
The University of 9
2. Monetary approach to exchange rate: predictions
Predictions about changes in
1. Money supply: permanent rise in domestic money supply 𝑀𝑆US
• causes proportional increase in domestic price level 𝑃 , US
• thus causing proportional depreciation in domestic currency 𝐸$/€ (through PPP).
2. Interest rates: rise in domestic interest rates 𝑅$
• lowers demand of real monetary assets 𝐿 𝑅 , 𝑌 , $ US
• and associated with long-run rise in domestic prices 𝑃 , US
• thus causing proportional depreciation of domestic currency 𝐸$/€ (through PPP).
3. Output level: rise in domestic level of production and income (output)
• raises domestic demand of real monetary assets 𝐿 𝑅 , 𝑌 , $ US
Seems paradoxical to interest parity theory!!! Answer connecting these predictions lies in next few slides…
• and associated with decreasing level of average domestic prices 𝑃 (for a fixed
• thus causing proportional appreciation of domestic currency 𝐸$/€ (through PPP).
quantity of money supplied 𝑀𝑆US), The University of 10
𝑃𝑃𝑃: 𝐸$/€ = 𝑃US 𝑃EU
2. Monetary approach to exchange rate: inflation and interest rate
– A permanent, one-off change in money supply results in change in level of average prices，but has no effect on long-run values of interest rate or real output (Topic 5 slide 19)
– BUT this is not a realistic description of actual monetary policies. Rather, monetary authorities choose a steady growth rate for money supply
– A change in growth rate of money supply results in a change in growth rate of prices (inflation).
• Inflation does not affect productive capacity of economy and real income from production in long run (endowment of productive resources to a country is fixed).
• Inflation, however, does affect nominal interest rates (see next slide).
The University of 11
𝑃 = 𝑀𝑆 − 𝐿
2. Monetary approach to exchange rate: inflation and interest rate
– From Topic 3, interest parity condition: 𝑅 − 𝑅 = 𝐸𝑒$/€ − 𝐸$/€
– If financial markets expect (relative) PPP to hold, then expected exchange rate changes will equal expected inflation between countries:
𝑅$ −𝑅€ = 𝐸𝑒$/€ −𝐸$/€ =𝜋𝑒US−𝜋𝑒EU 𝐸$/€
– Therefore, we arrive at the Fisher effect: rise in domestic inflation rate causes equal rise in interest rate on deposits of domestic currency in long run, when other factors remain constant.
𝑅$ − 𝑅€ = 𝜋𝑒US − 𝜋𝑒EU
relative PPP: (𝐸$/€,𝑡−𝐸$/€,𝑡−1) = 𝜋US,𝑡 − 𝜋EU,𝑡 𝐸$/€,𝑡−1
The University of 12
2. Monetary approach to exchange rate: inflation and interest rate
– Suppose that U.S. central bank unexpectedly increases growth rateofmoneysupplyattimet0.
– Suppose also that inflation rate is 𝜋 in US before time t0 and 𝜋+𝝙𝜋 after this time, but that European inflation rate remains at 0%.
– According to Fisher effect, interest rate in U.S. will adjust to higher expected inflation rate (interest rate increases).
– Increase in nominal interest rates decreases demand of real
monetary assets 𝐿 𝑅 , 𝑌 . $ US
Δ𝑃 Δ𝑀𝑆 Δ𝐿 𝑃 = 𝑀𝑆 − 𝐿
𝑅$ − 𝑅€ = 𝜋𝑒US − 𝜋𝑒EU
The University of 13
2. Monetary approach to exchange rate: inflation and interest rate
– In order for money market to maintain equilibrium in long run, prices must jump so that
MS L(R$,YUS )
– In order to maintain PPP, euro exchange rate must jump (the dollar must depreciate) so that
The University of 14
Figure 16.1 Long-Run Time Paths of U.S. Economic Variables After a Permanent Increase in the Growth Rate of the U.S. Money Supply
The University of 15
2. Monetary approach to exchange rate: inflation and interest rate
In the long-run model without PPP: (see Topic 5 slide 26)
– Changes in money supply lead to changes in level of average prices.
– Inflation causes nominal interest rate to increase to its long-run value.
– Level of average prices does not immediately adjust even if expectations of higher domestic inflation adjust,
• causing expected return on foreign currency deposits to increase, making domestic currency depreciate before transition period
• causing exchange rate to overshoot (domestic currency depreciates more than) its long-run value.
The University of 16
2. Monetary approach to exchange rate: inflation and interest rate
In the monetary approach (with PPP): (this topic)
– Inflation rate increases permanently when growth rate of money supply increases permanently.
– With persistent domestic inflation (above foreign inflation), monetary approach also predicts increase in domestic nominal interest rate.
– Level of average prices adjusts with expectations of higher domestic inflation,
• causing expected purchasing power of domestic currency to decrease relative to foreign currency, thereby domestic currency depreciates.
• causing domestic currency to depreciate, but with no overshooting.
The University of 17
3. Shortcomings of PPP
– Little empirical support for absolute PPP.
• Prices of identical commodity baskets, when converted to a single currency, differ substantially across countries.
– Relative PPP more consistent with data, but it also performs poorly to predict exchange rates.
Absolute PPP:
𝑃 𝐸$/€ = US
Relative PPP:
(𝐸$/€,𝑡 − 𝐸$/€,𝑡−1) = 𝜋US,𝑡 − 𝜋EU,𝑡 𝐸$/€,𝑡−1
The University of 18
Figure 16.2 The Yen/Dollar Exchange Rate and Relative Japan-U.S. Price Levels, 1980–2012
Relative PPP predicts that E¥/$ and PJ/PUS will move in proportion, but clearly they do not, especially in the early 1980s.
The University of 19
3. Shortcomings of PPP
Reasons why PPP may not be accurate: law of one price may not hold:
Trade barriers and non-tradable products (eg service industries)
– Transport costs and governmental trade restrictions make it expensive to move goods between markets located in different countries
Imperfect competition
– pricing to market: firm sells same product for different prices in different markets
Differences in measures of average prices for baskets of goods and services
– people living in different countries spend their incomes in different
ways, consume relatively higher proportions of their own country’s
products The University of 20
4. Real exchange rate: definition
– Because of shortcomings of PPP, economists tried to generalize monetary approach to PPP to make better theory.
– Real exchange rate is rate of exchange for goods and services across countries.
– In other words, it is the relative value/price/cost of goods and services across countries. (Recall jeans and sweater example in Topic 3 slide 8)
The University of 21
(E P ) $/€ EU
4. Real exchange rate: depreciation and appreciation
(E P ) $/€ EU
– If EU basket costs €100, U.S. basket costs $120, and nominal exchange rate is $1.20 per euro, then real exchange rate is 1 U.S. basket per 1 EU basket.
– Depreciation of real exchange rate means:
• A fall in dollar′s purchasing power of EU products relative to dollar′s
purchasing power of U.S. products.
• U.S. goods become less expensive and less valuable relative to EU goods.
The University of 22
4. Real exchange rate: the determinants of nominal exchange rate
– According to PPP, exchange rates are determined by relative average prices:
– According to more general real exchange rate approach, exchange rates may also be influenced by real exchange rate:
– What influences real exchange rate? The University of 23
4. Real exchange rate: the determinants of real exchange rate
– Nominal exchange rate affected by
– realoutputfactors:changerelativedemandandrelativesupplyof
US product output (e.g. increase in US productivity) – monetaryfactorssuchasmoneysupply
– When economic changes are influenced only by monetary factors and nominal exchange rates determined by PPP, real exchange rates stay constant.
– When economic changes are caused by real output factors, nominal exchange rates are determined by PPP and real exchange rate.
The University of 24
5. Real interest parity
– Differences in nominal interest rates across countries can be derived expected change in real exchange rate = expected change in nominal rate
(qe −q)(Ee−E)
US/EU US/EU = $ / € $ / € − ( e
qE US/EU $/€
− e ) EU
– expected inflation
Combining with
Interest parity condition:
and rearranging: The University of Sydney
(Ee −E) $/€ $/€
R −R = US/EU US/EU +(e −e ) $ € q US EU
5. Real interest parity
– Real interest rates are inflation-adjusted interest rates: re =R−e
where erepresents expected inflation rate and R represents a measure of nominal interest rates.
Combine with identity from previous slide:
We obtain:
re −re =(R −e )−(R −e ) US EU $ US € EU
US/EU US/EU +(e
(qe −q ) US/EU US/EU
qUS/EU – The last equation is called real interest parity.
The University of 26
– Output, exchange rates, earnings growth and stock markets (I)
The University of 27
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