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5 Purchasing power parity – the facts at a glance

5 Purchasing power parity – the facts at a glance

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The international setting

Figure 2.1  Real exchange rates, 1970–2011 (consumer prices) (1999 = 100)

Figure 2.2  Real exchange rates, 1970–2011 (producer prices) (1999 = 100)


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Prices in the open economy: purchasing power parity

Figure 2.3  Purchasing power parity exchange rates, 1970–2011 (consumer prices) (1999 = 100)

markedly), and then depreciated sharply in the 1980s as the dollar rose to a peak in 1985.

The dollar then declined as rapidly in the second half of the 1980s. The 1990s have seen

far less volatility, helped by the convergence of European economies. What we see in the

graphs, then, is the outcome of developments specific to each country with, at the same

time, developments affecting the relative value of the dollar.

Second, and most important of all, note the amplitude of the fluctuations in what should,

under PPP, be flat graphs. For example, the pound appreciated (in other words, UK competitiveness fell relative to the USA) by nearly one-third in real terms between 1976 and

1980, and then fell by around 60%, recovering much of the ground at the end of the 1980s,

only to lose it again on exit from the ERM. Since its initial post-exit fall, however, it has more

than made up the lost ground. The other currencies have been only a little less volatile.

In fact, Figures 2.1 and 2.2 could almost be said to track the movements in nominal

exchange rates shown in Figure 1.3, a feature that serves merely to illustrate the point made

earlier on that, except for highly deviant inflation rates, exchange rates fluctuate to an

extent that swamps variations in relative price levels.11

Figures 2.3 and 2.4 present the facts in a different form. What is labelled there the PPP

exchange rate is the nominal exchange rate against the US dollar required to preserve the

same real exchange rate (that is, the same level of competitiveness) as in 1980. In other

words, it is the (1980) nominal exchange rate adjusted for changes in the price ratio. In

Figures 2.3 and 2.4, the PPP exchange rate is shown as a ratio of the average spot rate


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The international setting

Figure 2.4  Purchasing power parity exchange rates, 1970–2011 (producer prices) (1999 = 100)

Exhibit 2.1  The Big Mac index

12 January 2012, 16:53 by The Economist online

Burgernomics shows Switzerland has the most overvalued currency

The Economist’s Big Mac index is based on the theory of purchasing-power parity: in the

long run, exchange rates should adjust to equal the price of a basket of goods and services

in different countries. This particular basket holds a McDonald’s Big Mac, whose price

around the world we compared with its American average of $4.20. According to burgernomics the Swiss franc is a meaty 62% overvalued. The exchange rate that would equalise

the price of a Swiss Big Mac with an American one is SFr1.55 to the dollar; the actual

exchange rate is only 0.96. The cheapest burger is found in India, costing just $1.62. Though

because Big Macs are not sold in India, we take the price of a Maharaja Mac, which is made

with chicken instead of beef. Nonetheless, our index suggests the rupee is 60% undercooked. The euro, which recently fell to a 16-month low against the dollar, is now trading at

less than €1.30 to the greenback. The last time we served up our index in July 2011, the euro

was 21% overvalued against the dollar, but it is now just 6% overvalued. Other European

currencies have also weakened against the dollar since our previous index, notably the

Hungarian forint and Czech koruna, which have fallen by 23% and 16% respectively. Six

months ago both currencies were close to fair value, but they are now undervalued by 37%

and 18%.


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Prices in the open economy: purchasing power parity

Source: http://www.economist.com/blogs/graphicdetail/2012/01/daily-chart-3, 12 January 2012.


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The international setting

actually observed over the year in question (multiplied by 100). Thus, when this ratio is

above 100, the exchange rate is overvalued relative to the dollar – assuming it was at its PPP

level in the base year, 1980.

It may be tempting to view Figures 2.3 and 2.4 as reflecting a protracted convergence on

current equilibrium levels of competitiveness. There are at least two problems with this

optimistic interpretation. First, it is to some extent an optical illusion. If we use a different

base year, we end up with a very different picture. In the first two editions of this book, for

example, the base year was taken as 1980, which resulted in the currencies seeming to converge smoothly on an equilibrium level of 100 in that year, subsequently diverging without

any apparent limit. Second, there is no reason to suppose that fluctuations in the value of

the pound, yen and Swiss franc in years to come will not take them far from their present

levels.12 Why should we believe that the real exchange rate will now settle down to its longrun level? The graphs can be more plausibly read as implying that although the cycles of

over- or undervaluation do tend to reverse themselves eventually, there is no sign that the

process of correction stops when equilibrium has been reinstated, a fact that has led some

economists to conclude that exchange rates have an inbuilt tendency to overshoot, as we

shall see in Chapter 7.

One final point worth noting is the effect of the 2008 crisis. Given the cataclysmic scale

of the crisis in the world’s banking system, the effect on exchange rates was relatively

modest and was almost entirely confined to a fall of over 30% in the real value of the pound

and a somewhat smaller appreciation in the yen.

We can summarise the evidence by saying that, on the face of it, there appears to be no

obvious tendency towards PPP. It is not even clear that producer prices fit the hypothesis

any better than retail prices, which may be a sign that the distinction between traded and

non-traded goods emphasised by some researchers is not very important in practice.

Notice that, in terms of volatility (about which we shall have a lot more to say in Chapters

5, 7 and 11–13), it is unquestionably true that exchange rates have varied far more than

prices. Look back at Equation 2.8, which shows how an exchange rate moves according to

the relative PPP doctrine. On the left-hand side is the relative inflation rate. Now relative

inflation rates between industrialised countries vary somewhat from year to year. A 5% gap

may narrow to, say, 3% or 4%, or possibly widen to 6% or 7% or even 10% by the time a

year has elapsed. But when we look at exchange rates, we find fluctuations of this magnitude, 1% or 2% or more, within the space of a single day’s trading. In fact, even looking at

monthly data, the volatility of exchange rates is often twice as great as the volatility of price


Any summary of the evidence needs, however, to mention one broad class of exceptions

to these otherwise negative conclusions. If we look at situations of very rapid (‘triple-digit’)

inflation, notably in Brazil, Argentina, Chile and Israel in the 1980s, we find PPP maintained

to within fairly narrow margins. Not surprisingly, the same is even truer of hyperinflations,

that is, inflation at astronomic rates (Germany in 1923–24 being the classic case). The

reason seems to be that in this type of hothouse environment, the cost of being wrong about

any price is potentially so great that agents are forced to invest considerable effort and

expense in gathering information. Furthermore, there tends to be a progressive collapse in

the kind of institutional and legal arrangements that in normal times serve to make prices

sticky, such as long-term contracts, price controls, and so on. In particular, attempts to fix

the exchange rate are soon swamped. The end result is that both prices and the exchange

rate move smoothly along their PPP paths.


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Prices in the open economy: purchasing power parity

A more scientific approach to testing PPP might of course yield different conclusions and

over the past 20 or 30 years researchers have investigated PPP in great depth. Their results

of that research programme will be summarised in Section 2.7, but first we examine some

of the explanations offered for the apparent failure of the law of one price and/or PPP.


Purchasing power parity extensions*

If ever there were a theory that ought to work, PPP – or the law of one price, at least – should

do so. That is the feeling of many economists. Its evident failure has motivated a number of

extensions of basic PPP theory, in addition of course to the numerous data-related explanations already mentioned. Notice, however, that it is purely a matter of semantics whether

we regard these extensions as ‘fixes’, allowing us to maintain PPP as a viable working

hypothesis, or as theoretical explanations of why PPP fails.

2.6.1 Traded versus non-traded goods: Balassa–Samuelson

As long ago as the 1960s, Balassa and Samuelson offered an explanation that sounded plausible then and still does, although the evidence is actually rather mixed.

Their analysis is based on the observation that, at least in the industrialised world, productivity increases are far more rapid in the traded than in the non-traded goods sectors of

the economy. One may speculate about the reasons for this bias in technical progress, but

identifying traded goods with manufactures and agricultural products, and non-traded

goods with the service sector of the economy, it does seem that the benefits of automation

are exploited more easily in the former than in the latter. In any case, if this observation is

correct, then wages in the traded goods sector will tend to rise more rapidly than in the

non-traded goods sector, as employers seek to exploit the benefits of higher productivity

per worker by expanding output, in the process competing for labour and driving up the

wage rate. If there is an integrated labour market, then, in the long run at least, wages will

be bid up to the same level in the services sector, even though productivity growth there has

been slower. This in turn means that prices in the services sector will have to rise relative to

those in the traded goods sector, so as to maintain profitability, other things being equal.14

The implication is that the price index, a weighted average of goods and services prices,

will make the country’s output look more overpriced (and hence less competitive) than is

actually the case.

2.6.2 Trade costs and adjustment to purchasing power parity*

Although the cost of actually moving goods around the world might seem an obvious place

to look for an explanation of deviations from PPP, the details are more problematic. In practice, there are many costs that are either fixed or at least unrelated to the value of the goods

being shipped – freight costs are normally based on weight or volume, management and

administrative expenses are largely fixed, and so on. To this extent, the effect is likely to be

the creation of a neutral zone in international price differentials, within which deviations

from the law of one price can persist more or less indefinitely. On this view, only when

deviations exceed the ‘threshold’ do prices finally react.


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The international setting

Now consider the implications as we move from individual prices to indices and from the

law of one price to PPP. Bear in mind that the fixed costs of trade will vary from product

category to category. Starting from a hypothetical PPP equilibrium, a shock that causes a

sudden jump in the exchange rate will generate deviations from the law of one price – and

hence arbitrage opportunities – in some product markets and not others. In general, the

larger the shock to the exchange rate, the greater the number of arbitrage opportunities

created. In the absence of barriers to arbitrage, therefore, the larger the shock to the

exchange rate, the more likely it is to be rectified. This type of logic has motivated a number

of researchers to test models that relate movements in the exchange rate nonlinearly to the

previous period’s deviation from its equilibrium level, with the relationship being stronger

the larger the size of the deviation. The result is a model of the form:



qt − rt−1 = ∑ aj(qt−j − rt−j−1) + Γ[γ; qt−d − rt−d−1]∑ βj(qt−j − rt−j−1)

j  =1  

j  =1  


In this equation, qt−j is the log of the real exchange rate at t − j (i.e. j months, quarters or

years back) and a bar over the top denotes an equilibrium level, which is often taken to be

simply the mean level of qt over the data period.

Equation 2.9 makes the disequilibrium real exchange rate, i.e. the gap between the

current level of the real exchange rate and last period’s equilibrium, qt − rt−1, depend on the

sum of two sorts of process. The first is simply an autoregression15 on the disequilibrium gap

for the last p periods (qt−1 − rt−2), (qt−2 − rt−3) . . . (qt−p − rt−p−1), where each period’s dis­

equilibrium gap is weighted by a coefficient aj j = 1 . . . p. The second term contains the

same sort of autoregression – we allow for different weights, bj j = 1 . . . p – but in this case

the autoregression is multiplied by the term Γ[γ; qt−d − rt−d−1], which is the key to the whole

model. This is a nonlinear function of the disequilibrium d periods back (d is most often set

to one) and it is parameterised by the most important coefficient to be estimated, γ.

Usually, a functional form is chosen to make Γ[ ] take values between 0 and 1 in each

period, so that it can be regarded as measuring the extent to which a gap between rt−1 and

qt−1 is eliminated by the next period’s change in the exchange rate. The greater is the function Γ [ ], the more rapidly the gap is closed and, since Γ[ ] is assumed to be increasing in

the gap itself, the implication is that larger deviations cause the exchange rate to react more.

In other words, small deviations from PPP equilibrium are eliminated slowly, and large

deviations rapidly. In fact, when the nonlinear component Γ[ ] = 0, which typically occurs

when the PPP gap (qt−d − rt−d−1) is zero, the real exchange rate is driven exclusively by the

first autoregressive component, which often turns out to be statistically indistinguishable

from a random walk. At the other extreme, when (qt−d − rt−d−1) is very large, the function Γ[ ]

approaches unity, and the real exchange rate process is an autoregression with coefficients

equal to the sum of the α’s and the β’s, which we expect will turn out to imply far faster

convergence on the equilibrium.16 One of the attractive features of this model is that it is

consistent with the contrasting evidence from low- and high-inflation countries, where

adjustment to PPP seems to be extremely rapid. If PPP is very quickly reinstated under

hyperinflation, deviations may never be observed, at least at the monthly or quarterly data

frequency typically available. On the other hand, for low-inflation countries, sluggish

adjustment may mean that even a period of a century or more may cover very few

completed cycles of return to PPP.

Moreover, by allowing for different speeds of adjustment depending on how far a

country is from its PPP equilibrium, this sort of nonlinear model does tend to yield more


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Prices in the open economy: purchasing power parity

plausible results. For example, one well-known paper estimates the half-life of disturbances

to the dollar–sterling exchange rate at as little as 10 months for large shocks of 40%

or more, rising to 32 months for only 1%. This looks like a substantial improvement on

the sort of estimates in the range 3–7 years which emerge from simpler linear models of


2.6.3 Trade costs: the iceberg model*

If transaction costs are related linearly to the value of the goods shipped, then it might

appear that the outcome is more straightforward. Even here, however, there are still complications to overcome, which will come as no surprise to anyone who has ever worked with

balance-of-trade statistics. For example, is the value of a country’s exports to be understood

as including or excluding shipping costs? In any case, is the exporter or the importer

assumed to pay?

Assuming importers pay for transportation, insurance, wastage, and so on, a possible

formulation is the so-called iceberg model, which assumes that a proportion τ of every unit

of goods shipped internationally is lost or consumed in the form of shipping costs, so that

the importer only receives the remaining 1 − τ that survives the voyage. This means that

goods will sell at different prices, depending on where they originate. Consider first the case

of a foreign product imported into the home country. If its price in its country of origin is P*F

and its price at home is PF, then the two prices will be related as follows:

PF = P*F /(1 − τ)


To understand why, imagine the product is a perishable foodstuff, for example feta

cheese imported from Greece into France. If τ = 0.25, it is as if 25% of the cheese goes rotten

en route and is unsaleable in France. The French importer therefore has to buy 1/(1 − 0.25)

= 1.33 kilograms in order to have 1 kilogram available for sale. If he can get the cheese (or

similar) cheaper than P*F /(1 − τ) in another country, whether in the form of a lower basic

price for the produce or because of lower transport costs, then he will do so.

If, on the other hand, the cost of transporting Camembert to Greece involves a similar

degree of wastage, then its price will be lower in France than in Greece by 25%:

Figure 2.5  Iceberg costs


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The international setting

PC = (1 − τ)P*C


and so a kilo of Camembert will cost only 75% as much in France as in Greece.

Now consider the price of feta relative to Camembert. The mechanism just described

plainly drives a wedge between the relative prices of the two cheeses in France and Greece.

From the ratio of Equations 2.10 and 2.11, we can see that:



= (1 − τ)2 




so, relative to feta, Camembert will be only 56% as expensive in France as in Greece.

Notice that nothing has been said here about the exchange rate. As it happens, both

France and Greece currently use euros, but the preceding story would be essentially

unchanged if prices in the two countries were still quoted in francs and drachma. The only

change needed would involve converting to a common currency, for example by multi­

plying the right-hand side (Greek) prices by the franc price of drachma.

It has been claimed by some authors (notably Obstfeld and Rogoff (2000a)) that this

distortion of relative prices may have far-reaching consequences in a number of critical

areas of open economy macroeconomics, sufficient to explain some of the apparent anomalies in the pattern of international payments. For the moment, however, it is simply worth

noting that this is yet another possible explanation for the failure of PPP. In this scenario,

even if the index weights in the two countries are identical, price levels will still differ,

without necessarily representing any arbitrage opportunity.

2.6.4 Incomplete pass-through and pricing to market

In the past ten years or so, interest in international pricing has broadened out to cover issues

related to industrial structure, which according to standard closed economy microeconomics ought to have an important role to play in this context. In general terms, the conclusion

of this literature is easily stated: exchange rate movements will not necessarily be reflected

fully and instantaneously in the prices at which exports are sold in foreign markets. A 10%

devaluation will not necessarily cause exporters to cut their prices by 10%, at least immediately, and neither will a 10% revaluation make them raise prices at once by the full 10%.

In the standard jargon, we should not necessarily expect 100% pass-through, at least in the

short term. Instead, we might expect to witness something like, say, 30% immediate passthrough (i.e. a 3% fall in export prices following a 10% devaluation), 75% after six months

and 100% only after two years.

Why might there be less than 100% pass-through? To understand what is involved, take

the case of an importer buying goods from an exporter, for sale in the importer’s home market. It makes no difference whether the importer is an independent specialist whose only

business is importing and wholesaling products to local retailers, whether the importer is

itself a retailer, or whether, as is often the case nowadays, the importer is a local subsidiary

of the multinational company that originally produced the goods. Whatever the situation,

as far as the importer is concerned, exchange rates are a cost just like any other. When the

currency used to buy the imports rises in value, the importer’s costs rise, and vice versa

when the currency gets cheaper. Viewed from this angle, the question at issue is simply a

matter of judging how the typical importer deals with an increase in its costs – in other

words, a suitable case for microeconomic analysis.


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Prices in the open economy: purchasing power parity

Note the obvious point that, even if it is determined to keep its profit margin constant, a

firm need only adjust its export price in proportion to the net impact of an exchange rate

change. For example, suppose at some point the euro appreciates by 5% against the dollar.

In practice, the effect is to raise the cost of supplying French wine to the USA by somewhat

less than 5%, other things being equal, because the typical French winegrower will rely on

inputs – diesel fuel and spare parts for his tractors, fertiliser, possibly computing and telecommunications hardware and software, and so on – some or all of which may be priced in

dollars or dollar-linked currencies. If only 75% of costs are in euros, then the no-arbitrage

PPP price will only rise by 33/4 %, with the remaining 11/4 % accounted for by a fall in the euro


In practice there are a number of reasons why firms may be reluctant to adjust export

prices even to this extent in the short run. In the first place, exchange rate movements are

high-frequency events. They are certainly far higher frequency than changes in production

costs, such as wages, taxes and domestically produced raw materials and intermediate

inputs and probably higher frequency than demand fluctuations. Daily exchange rate

changes of 1% or 2% are not at all exceptional. It would plainly be ridiculous for firms

slavishly to adjust their export prices on a day-by-day basis in response to each day’s

exchange rate movement. Raising prices immediately may be difficult, especially where

customers either have a supply contract or believe they have an unwritten agreement

from the importer to keep prices fixed. Moreover, a firm may well have explicit long-term

contracts to supply products at fixed prices, in which case it must absorb currency volatility

in its profit margins unless it has hedged (i.e. insured) in the forward market or elsewhere

(see Chapter 3).17 Over and above all these considerations is the cost of actually publicising

price changes – costs of printing, advertising, informing customers, and so on.

In summary, changing prices is an activity that itself involves costs. These costs – menu

costs in the jargon of economics – may be greater or smaller, depending on the circumstances, but will in any case provide an incentive for importers at least to try to smooth price


In addition to these factors, a behavioural explanation for the stickiness of traded goods

prices is widely accepted by policymakers and many researchers. For example, suppose the

French winegrower has incurred heavy setup costs in establishing a presence in the US

market – perhaps recruiting sales staff and advertising in the USA, spending on public

relations, forging links with American importers, satisfying federal and state regulatory

requirements, and so forth. These costs can be regarded as an irreversible investment whose

payoff is the flow of future net profits the firm hopes to earn from US sales. Under these

circumstances, the French company may decide to keep the dollar price of its wine fixed

when the euro appreciates, rather than raise it and risk losing market share to such an

extent that, if the exchange rate returns to its previous level, it will be unable to re-establish

itself in the USA without incurring some or all of the setup costs all over again.18

All this presupposes that firms are actually able to sustain a policy of price discrimination,

at least in the short run. In other words, it requires that firms be in a position to set different

prices for their output in home and foreign markets. As is well known from elementary

microeconomics, any firm able to discriminate in this fashion will normally be able to profit

from exploiting the opportunity.19 But can firms actually seal off their export market from

their domestic market? Can they prevent arbitrage leakage of products from the cheaper to

the more expensive market? Obviously, the answer varies from country to country and from

case to case. In reality, we observe that the most effective barriers to prevent agents from


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The international setting

exploiting deviations from the law of one price are invariably created by governments for

one reason or another. Cars (especially in the minority of right-hand-drive countries), airline tickets and pharmaceuticals would be classic examples of industries where short-run

arbitrage is almost completely out of the question, although even in these cases recent

developments have made price discrimination far harder to sustain than a decade ago.20

Again, the question can be answered only by empirical research.


Empirical research

PPP is one of the most heavily researched topics in economics. In the first phase, through the

1970s and 1980s, the emerging consensus based on univariate regressions seemed to point

to the gloomy conclusion that, even in the long run, there was no evidence to support PPP.

On the contrary, the real exchange rate appeared to be what statisticians call a random

walk, in other words a process that changes only as a result of purely random disturbances:

qt = qt−1 + ut


where ut is a zero-mean random shock unrelated to any previous history.21

To understand the implications, consider the situation starting from a position of PPP

equilibrium. Now suppose that one Monday something happens to disturb the equilibrium,

for example some kind of political upheaval causing a 10% overnight depreciation and, of

course, having exactly the same impact on the real exchange rate, since the price level has

so far remained unchanged. So, for that Monday only, ut in Equation 2.13 is 10%, making

qt 10% higher at the start of the next day, Tuesday. However, since it is a random walk, on

Tuesday there is no reason to expect ut to be negative, let alone the −10% required to offset

the positive disturbance from the day before. In fact, Tuesday’s disturbance is just as likely

to be positive, taking the real exchange rate even further from equilibrium, as negative, taking it back towards equilibrium. Moreover, the same is true of Wednesday and Thursday. To

say that the real exchange rate is a random walk amounts to saying that there is no reason

to suppose that the 10% shock will ever be reversed. Instead, after absorbing Monday’s

shock, the best forecast is that the real exchange rate will remain at its new level indefinitely

– with no time limit on the domestic economy’s improved competitiveness.22

Of course, this is not to say that we expect no further change. It is simply saying that any

further change will be as unpredictable as was the original shock – equally likely to be

positive or negative, and equally likely to move the exchange back towards equilibrium or

even further away. In general, however overvalued relative to its PPP level a currency may

appear to be, it is as likely to rise as fall in subsequent periods.

Although this conclusion seems negative, it can be reconciled with a form of PPP under

certain circumstances, as we shall see at the end of the next chapter. Nonetheless, its

implications for the stability of a floating exchange rate system are far from encouraging.

Over the past decade, with the help of powerful new econometric methods and ever

faster computing, researchers have more or less rescued PPP as a theory of long-run

behaviour. In the first place, a number of ways have been found to remedy the problem of

a shortage of data points for estimation purposes.23 A number of researchers have used

panel data regressions, i.e. simultaneous analysis of a number of different countries over a

relatively short data period. Others have found sources of annual price and exchange rate

data for a few countries going back to the nineteenth century and beyond. Powerful new


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5 Purchasing power parity – the facts at a glance

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