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Part ⅡExchange-Rate Determination:

Theory, Evidence and Policy

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Chapter 6Purchasing Power Parity and Floating

Exchange-rate Experience

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6.1 IntroductionIn this chapter , we look at one of the

earliest and simplest models of exchange rate determination, known as PPP.

An understanding of PPP is essential to the study of international finance.

the theory has been advocated as a satisfactory model.

The theory provide a point of reference for the long-run exchange rate.

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Main contents of the chapter:1.Look at the PPP theory—6.2-6.4.2.Examine how well-suited it is to

explaining actual exchange-rate behavior—6.5-6.7.

3.Discuss some of the possible explanations for its failure—6.8,6.9.

4.The importance of PPP estimates—6.10.

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6.2 PPP Theory and the Law of One Price

PPP is generally attributed to Gustav Cassell’s writings in the 1920s.

The basic concept: arbitrage forces will lead to the equalization of goods prices internationally once the price of goods are measured in the same currency.

As such, the theory represents an application of the ‘law of one price’.

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The law of one price:1.This law simply states that in the

presence of a competitive market structure and the absence of transport costs and other barriers to trade, identical products which are sold in different markets will sell at the same price when expressed in terms of a common currency.

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2.the law of one price is based upon the idea of perfect goods arbitrage.

UK:£15000(P) S=£0.5/$(PPP) US:$30000(P*)

If S=£0.6/$, then: $30000=£30000*0.6 = £18000>£15000 UK car cheaper, buy UK car, sell in US, buy £ and sell $, £↑ & $↓ till S= £0.5/$.

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UK:£15000(P) S=£0.5/$(PPP) US:$30000(P*)

If S=£0.4/$, then: $30000=£30000*0.4 =£12000<£15000 US car cheaper, buy US car, sell in UK, buy $ and sell £, $↑ & £↓ till S= £0.5/$.

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6.3 Absolute and Relative PPP

PPP comes in two forms:Absolute PPP: based on a strict

interpretation of the law of one price;

Relative PPP: ‘weaker’ variation.

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1.Absolute PPP.Absolute PPP holds that if one takes a

bundle of goods in one country and compares the price of that bundle with an identical bundle of goods sold in a foreign country converted by the exchange rate into a common currency of measurement, then the prices will be equal.

It is expressed as: S=P/P* (6.1)

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2.Relative PPP.The absolute PPP is unlikely to hold

precisely (transport costs, imperfect information, tariffs and other forms of protectionism) a weaker form of PPP can be expected to hold even in the presence of such distortion.

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Relative PPP argues that the exchange rate will adjust by the same amount of the inflation differential between two economies.

It is expressed as: %∆S=%∆P-%∆P* (6.2)

That is, according to the relative version, the percentage variations in the exchange rate equal the percentage variations in the ratio of the price level of the two countries

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Note:The percentage variations in this

ratio are proximately equal to the difference between the percentage variations in the two price levels, or inflation differential.

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Example:£120(P0), $200(P0*), S0=£0.5/$(actual)

10% 6% ≠£0.6/$(PPP)£132(P1), $212(P1*), S1=£0.52/$

≠£0.622/$(PPP) (S1-S0)/S0=(S1-0.5)/0.5=10%-6%=4%

S1=£0.52/$

If the relative PPP holds, it does not mean that the absolute PPP necessarily holds.

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6.4 A Generalized Version of PPP

One of the major problem with PPP is that it is suggested to hold for all types of goods. However, PPP is more likely to hold for traded than non-traded goods.

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Traded goods: are goods that are susceptible to the rigours of international competition, be they exports or import-competing industries such as most manufactured goods.

Non-traded goods: are those that cannot be traded internationally at a profit, such as houses and certain services such as a haircut, or restaurant food.

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The price of traded goods will tend to be kept in line by international competition, while the price of non-traded goods will be determined predominately by domestic supply and demand considerations.

A more generalized version of PPP that provides some useful insights makes a distinction between traded and non-traded goods.

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Consider the importance of the tradables/ non-tradables distinction for PPP when aggregate price indices made up of both tradables and non-tradables are considered.

First, assume PPP hold for tradables: PT=SPT* (6.3)

The aggregate domestic price index: (6.4)

TNI PPP )1(

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The aggregate foreign price index:

(6.5)

Dividing equation (6.4) by (6.5):

(6.6)

*)1(** TNI PPP

*)1(*

)1(

* TN

TN

I

I

PP

PP

P

P

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Divide the numerator by PT and the denominator by SPT*:

(6.7)

Rearranged to give the solution for S: (6.8)

)1(*)/*(

)1()/(

*

TN

TN

I

I

PP

PPS

P

P

)1()/(

)1(*)/*(

*

TN

TN

I

I

PP

PP

P

PS

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From equation (6.8):1.it is an important modification to our

simple PPP equation because PPP no longer necessarily holds in terms of PI and PI* due to the multiplicative term on the right-hand side;

2.it suggests that the relative price of non-tradables relative to tradables will influence the exchange rate. That is:

If PN↑→S↓: PN↑→PT↓ to keep PI↕→S↓ to maintain PPP for tradables;

If PT↑→S↑.

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Implications: The tradable/non-tradable

distinction serves as a warning when testing for PPP. Testing for PPP using price indices based on tradable goods prices is likely to lead to better results than when using aggregate price indices made up of both types of goods.

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Exchange-rate movements induced by changes in relative prices between tradable and non-tradable goods represent real exchange-rate changes.

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6.5 Measurement Problems in Testing for

PPP1.To decide whether or not the theory is

supposed to be applicable to both traded and non-traded goods, or applicable to only one of these categories.

First: seems more readily applicable to traded goods;

However: the distinction is fuzzy and there are mechanisms linking both categories.

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The argument is important for the empirical testing for PPP theory:

If applicable only to tradables: the price index made up of only traded goods—wholesale or manufacturing price indices;

If applicable to both goods: a more general price index should be employed—consumer price index.

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2.An overall problem facing researchers whichever price index is used is that PPP is only expected to hold for similar baskets of goods with similar weights.

3.The base period for the test should ideally be one where PPP held approximately.

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4.there are divergences of view over the time-span during which PPP can be expected to assert itself:

Strong version: on a monthly basis;Progressively weaker version: on a

quarterly or six-monthly or yearly-and-beyond basis.

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6.6 Empirical Evidence on PPP

1.Graphical evidence on PPP. Figure 6.1(a)-(g) illustrate that

the exchange rate has diverged considerably from that suggested by PPP.

$/£ & DM/$ & JPY/$ & JPY/DM: PPP does not do at all well in tracking the actual rate.

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LIT/DM & FF/DM & £/DM: although there are deviations from PPP, that PPP does a reasonable work.

This is not that surprising since transport costs and trade barriers between France, Italy and Germany are small.

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It is noticeable that although the exchange rate is frequently far from PPP, it does have a tendency to go back to the PPP rate over the long run------PPP may be a useful guide for the determination of the long-run exchange rate.

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2.Econometric evidence on PPP.Testing for PPP by use of regression

analysis. In log form:Absolute PPP: Relative PPP: In both cases, for PPP to hold the

regression estimates would yield a1=0 and a2=1.

tttt uPPaaS *)ln(lnln 21

tttt uPPaaS *)lnln(ln 21

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The regression estimates provide additional support for the graphical analysis.

The overall evidence on the PPP hypothesis is not very supportive.

In sum, there is much more to exchange-rate determination than PPP.

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6.7 Summary of the Empirical Evidence on PPP PPP performs better for countries

that are geographically close to one another and where trade linkages are high;

There have been both substantial and prolonged deviations from PPP which have frequently been reversed over a number of years;

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Exchange rates have been much more volatile than the corresponding national price levels;

Empirically, PPP holds better in the long run than the short run;

PPP is the dominant force in determining their exchange rates in countries having very high inflation;

Overall, PPP holds for traded goods than non-traded goods.

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An influential paper by Rogoff(1996) shows that deviations from PPP are not speedily corrected, while Sarno and Taylor(2002) dispute the evidence reported by Rogoff.

PPP is much less likely to hold if one uses CPI, than if wholesale price indices(WPI) are used; significantly better is the use of a tradables price index(TPI).

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6.8 Explaining the Poor Performance of PPP Theory

1.Statistical problems: Different countries usually attach

different weightings to various categories of goods and services when constructing their price indices;

Differing consumption baskets are not of such significance, however, there is a problem posed by the differing quality of goods consumed.

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2.Transport costs and trade impediments.

To take the transport costs and trade impediments into account, the results of PPP theory will be changed.

Nonetheless, since transport costs and trade barriers do not change dramatically over time they are not sufficient explanations for the failure of the relative version of PPP.

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3.Imperfect competition.One of notions underlying PPP is that there

is sufficient international competition to prevent major departures of the price of a good in one country from its price in another. However, it is clear that there are considerable variations in the degree of competition internationally.

Because the conditions necessary for successful price discrimination are for the most part more likely to hold between rather than within countries.

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4.Differences between capital and goods markets.

PPP has nothing to say about the role of capital movements. However, in a world where capital markets are highly integrated and goods markets exhibit slow price adjustment, there can be substantial prolonged deviations of the exchange rate from PPP.

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5.Productivity differentials.Because the higher labor productivity in

the traded sector in developed countries compared to developing countries makes non-tradables goods prices are higher in developed than developing countries, the aggregate price indices tend to be higher in rich countries than in poor countries when prices of similar baskets of both traded and non-traded goods are converted into a common currency.

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6.9 The Balassa-Samuelson Model

Balassa and Samuelson argue that labor productivity in rich countries is higher than in poor countries. Furthermore, this productivity differential occurs predominately in the tradables rather than the non-tradables sectors.

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1.Analyze process: Assume:1.PN=WN/QN, PT=WT/QT (6.9)

PN*=WN

*/QN*, PT

*=WT*/QT

* (6.10)

2.WN=WT; WN*=WT

* (6.11)

3.QT*> QT, QN

*= QN (6.12)

4.S= PT/ PT* (6.13)

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Then:

Thus: PPP does not work for non-traded

goods.

SQP

QPS

QP

QP

W

W

W

Q

Q

W

P

P

TT

TT

TT

TT

T

T

N

N

N

N

N

N

**

*

**

**

*

*

*NN PSP

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2.Reason: low wages in the developing country due to low productivity in its traded sector also lead to a relatively low price for its non-traded goods,even though its productivity in this sector is the same as in developed countries.

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3.Significances:The Balassa-Samuelson model is helpful

in explaining: Why it is that rich countries tend to

have overall high price indices and poor countries low price indices;

Why the ratio of non-traded to traded price tends to be higher in developed economies than developing countries;

Why there are divergences from PPP in terms of aggregate price indices between developed countries.

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4.Limitation: It is only a partial explanation; It can not explain the failure of

PPP to hold for traded goods.

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6.10 Per capita income levels, the relative sizes of economies and the

importance of PPP estimates The World Bank keeps a very keen

eye on the per capita income levels of developing countries.

The fact that PPP tends not to hold is of considerable importance in this respect.

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It is well-documented that, in particular, the price of non-tradable goods and services is significantly lower in developing countries than in developed countries, simply because PPP is not holding.

In particular, the exchange rates of developing countries tend to be noticeably undervalued in terms of purchasing power for goods and services.

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The implications for calculations of GDP per capita.

United states: $35000; China: ￥ 8600.

If market exchange rate: $1= ￥ 8.6. Chinese GDP per capita(M)=$1000.If PPP exchange rate:

$1= ￥ 1.72(=8.6/5). Chinese GDP per

capita(PPP)=$5000.

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The GDP per capita based on PPP is therefore a more reliable guide to relative living standards in the two countries than using the market exchange rate which does not reflect PPP.

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The previous example calculation is by no means far from reality.

GDP per capita according to the World Bank using both the Atlas method and the PPP method shows that GDP per capita of developing countries are seriously undervalued using market exchange rate.

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Not only do PPP adjustments make a significant difference to GDP per capita estimates, they also make a big difference to the importance of the relative size of different economies.

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6.11 Conclusions The experience with floating rates

has shown that there can be substantial and prolonged deviations of exchange rates from PPP.

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There are many explanations for these deviations from PPP. Among the strongest candidates is that the theory has no role for the international capital movements.

The fact that PPP does not hold very well in the short to medium term does not mean that it has no role to play in exchange –rate determination.

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Further reading: 程伟，《基于双重法的经济规模的国际比较》，《当代财经》， 2008/05 。

魏佳，《巴萨效应在中国适用性的实证分析》，《特区经济》， 2008/05.

耿琳，《国际货币汇率是否符合购买力平价理论——一种计量经济学的分析视角》，《财经界》， 2008/01.