5. Purchasing Power Parity and the Balassa-Samuelson Effect

(See handouts no.5 & supplement to no.5; chapters 5 & 6)

Prof. Gustav Cassel

Karl Gustav Cassel, 1866-1945

The previous lecture discussed interest parities, namely the relationship between the exchange rate (e) and interest rates (i, i*). This lecture discusses the relationship between the exchange rate (e) and prices (p, p*), another key relationship in international economics. This should really be called "price parity" (equality between prices). But it is now called "purchasing power parity" (equality between the buying powers of monies) for the following historical reason.

Before World War I, thanks to free trade and fixed exchange rates under the Classical Gold Standard, price levels were equalized among major countries. When WW1 began, however, the gold standard broke down, international trade was suspended, and each country printed money at different speeds to finance the war effort. As a result, different inflation rates emerged across countries.

Professor Gustav Cassel of Sweden argued that exchange rate movements follow a certain law even under floating, and it was possible to calculate the "correct" rate. According to him, money was valuable because it purchased goods. The conversion ratio between two national monies should therefore be the one that equalized their "purchasing powers." The purchasing power of money, in turn, was measured by the inverse of the general price level (1/P). The higher are the prices, the lower is the purchasing power of money, and vice versa. He called this the "purchasing power parity" or PPP.

Prof. Cassel and John Maynard Keynes were both interested in computing the new correct exchange rates after WW1. Their method (arrived separately) was to use the original exchange rate multiplied by the relative movement of price levels.

[Correct rate] = [Old rate] x [Price increase in country A] / [Price increase in country B]

or

EPPP(t) = E(0) x [Pa(t)/Pa(0)] / [Pb(t)/Pb(0)]        (assuming that EPPP(0) = E(0))

They argued as follows:

(1) Let us assume that in 1913 (immediately before WW1), UK prices and US prices were equalized (the assumption of the base period--see below).

(2) After 1913, UK inflation was higher than US inflation, and the cumulative difference was 10%.

(3) Thus, the new correct rate should be the one in which the UK pound is 10% more depreciated against the US dollar, relative to 1913.

This method has become very popular because it is very easy. Even today, many people use this method to calculate the "correct" exchange rate. When the IMF advises currency devaluation, it is often based on this kind of calculation (when I was an economist at IMF, during 1987-91, we used this method to ask the Egyptian government to devalue the Egyptian pound).

PPP, real exchange rate, and naigai kakakusa

The three concepts of PPP, the real exchange rate, and naigai kakakusa (literally, domestic-foreign price gap) are mutually related. Let

P: domestic price
P*: foreign price
E: actual exchange rate
EPPP: PPP exchange rate

(1) The PPP exchange rate is defined as follows:

EPPP = P/P*

In words, PPP is the hypothetical exchange rate that equalizes domestic and foreign prices. [A]

(2) The real exchange rate (RER) is defined as follows:

RER = (E P*)/P

In words, RER measures the deviation of the actual exchange rate from PPP. That is, RER = E/EPPP. The adjective "real" means "inflation-adjusted."

(3) The concept of naigai kakakusa asks the following question:

Is it    E P* < P    or     E P* > P  ?

In words, are domestic prices higher or lower than foreign prices? In the 1980s this became a political problem between Japan and the US. The US claimed that Japanese prices were too high because of excessive regulation and inefficiency (E P* < P, where P is the Japanese price). The US trade negotiators demanded that Japan open up its economy quickly (especially to US goods).

It is clear that the three concepts are closely related. In fact, (2) and (3) are derivative ideas of PPP. In light of this, we can add the following statements:

PPP is the hypothetical exchange rate that stabilizes RER. [B]

PPP is the hypothetical exchange rate that eliminates the domestic and foreign price gap. [C]

Note that the converse of [B] does not hold because of the way RER is normally computed (see below for the base year problem) as an index with some base year (with the index value of 100). Even if RER is stable, it does not necessarily mean that PPP is holding. (The related concept of REER (real effective exchange rate) will be discussed later in lecture 13.)

<Warning> an exchange rate can be quoted in both ways: (i) foreign currency per domestic currency (its rise means appreciation of the domestic currency); or (ii) domestic currency per foreign currency (its rise means depreciation of the domestic currency). In Japan, as in many other countries, the yen-dollar rate is quoted as 115 yen/dollar etc, using the second method. But we cannot guarantee that all exchange data are expressed in this form. The British pound is traditionally quoted by the first method. You must always check which currency is the denominator and which one is the numerator. Even though I have been studying and teaching exchange rates for long, I am still sometimes confused.

Different uses of PPP

PPP (and its derivative concepts) are typical cases of the law of one price (LOOP--see lecture 4). It has many applications other than IMF conditionality for currency devaluation. The main uses include the following:

(1) Theory of exchange rate determination: PPP can explain why the actual exchange rate moves in a certain way. Typically, high inflation countries have depreciating currencies and low inflation countries have appreciating currencies (especially during hyperinflation or in the long run). [This is called the "positive" (factual) use of PPP.]

(2) Pointer of the correct level: PPP can indicate the "correct" or "desirable" exchange rate, when the actual rate deviates from it. The government and the central bank may try to narrow the gap between the actual and the desirable rate, either by devaluation or domestic adjustment (macroeconomic austerity). When the government wishes to stabilize the exchange rate, PPP can provide the appropriate target level. [This is called the "normative" (policy) use of PPP.]

(3) Indicator of competitiveness: the real exchange rate (RER) is frequently used as an indicator of international price competitiveness. When RER rises (domestic currency depreciates in real terms, E > EPPP), the home country gains competitiveness because domestic prices become relatively lower. This is called undervaluation. By contrast, when RER falls (real appreciation, E < EPPP), the home country loses competitiveness because domestic prices are relatively higher. This is called overvaluation. [But please recall the warning above: sometimes, RER is quoted with the numerator and the denominator reversed].

(4) International income comparison: international organizations like the World Bank must compare GDP size and per capita GDP of each member country, for statistical or policy purposes. Sometimes, the salaries of professional workers or the stipends of foreign students in different countries are adjusted using such data. PPP information is necessary to determine the relative costliness of living in each country. But there is a serious bias--see the Balassa-Samuelson issue below.

(5) Pressure of Imported inflation: in macroeconomic modeling, deviation from PPP is often considered as the determinant of imported inflation. For example, [Inflation] = k [E - EPPP] + [other factors], where 0<k<1. In this case, LOOP is assumed to hold gradually at the speed proportional to the size of domestic and foreign price gap. This may hold in a small open economy but maybe not in China or the United States.

Different types of PPP

Apart from different uses, there are different types (analytical concepts) of PPP.

(1) Tradable PPP versus nontradable PPP: if we use the prices of "tradable goods" (those that are actually traded internationally or whose prices are strongly affected by foreign prices: oil, wheat, steel, cars, electronics, industrial parts, etc), we have tradable PPP. If we use the prices of "nontradable goods" (those which are not traded or not affected by foreign prices: house rents, taxi rides, school fees, etc), we have nontradable PPP.

Whether a good is tradable or not depends on its physical character (portability) as well as policy (tariffs, quotas, trade bans). Haircut service is naturally nontradable because it is too costly to invite hairdressers from abroad, so people go to local shops. On the other hand, agricultural products are transportable but governments often prevent free importation, so they are artificially nontradable. 

Obviously, PPP holds (E = EPPP) more readily for tradables than nontradables because, by definition, arbitrage is easier for the former than the latter.

(2) Absolute PPP versus relative PPP: PPP has absolute and relative versions. Absolute PPP compares price levels, while relative PPP compares price changes (or movements). The former assures that prices are equalized across countries, but the latter only assures that the exchange rate moves by the same amount as the bilateral inflation gap (without asking whether the original prices were equal). Clearly, relative PPP is a weaker condition than the absolute one. Examples:

Absolute PPP statement: "A motorbike costs 110,000 yen (=$1,000) in Japan and 15,000,000 dong (=$1,000) in Vietnam. It costs the same between these two countries." [assuming $1 = 110 yen = 15,000 dong]

Relative PPP statement: "Japanese inflation was 0% and Vietnamese inflation was 5%. Meanwhile, the dong depreciated 5% against the yen. Thus, relative cost comparison remains the same between the two countries."

(3) Short-term PPP versus long-term PPP: it is empirically known that PPP does not hold (actual and PPP rates are different) within a day, a week, a month, a year, and even within a few years. But it is often observed that PPP is more firmly established as a long-term tendency (decades or even centuries). For prices, LOOP is assumed to work better in the long run.

[OPTIONAL: Testing PPP] In time-series analysis, there is a technique called "co-integration analysis" (and a related concept of the error-correction model estimation) which checks if two (or many) variables have a tendency to share similar long-term movements. This technique is often used to test long-run PPP, that is, whether exchange rates and prices are "co-integrated" (i.e., share the same trend). A more crude technique is to run regressions of exchange rates on relative prices (in absolute or relative version). Another way to check PPP is to use frequency-domain, such as spectrum analysis.

Causality and pass-through

One big issue associated with PPP is the question of causality. Generally speaking, all economic variables are mutually dependent, so there is no unilateral causation. But for practical purposes, it is possible to argue and empirically determine which causation is dominant: P => E, or E => P ? It is very important to know, but people sometimes forget to ask this question.

(1) If the exchange rate moves because of differential inflation in two countries (causality runs from P to E), we have a theory of exchange rate determination. In this case, domestic and foreign prices are the driving force. This is what Prof. Cassel and J. M. Keynes had in mind.

(2) But if domestic prices are changing because of exchange rate undervaluation or overvaluation (causality runs from E to P), we have a theory of price determination. In this case, the independent behavior of the exchange rate is the cause and the inflation or deflation is the result.

These two cases have very different policy implications. In the first case, the exchange rate is an adjusting variable and its movement is welcome (although there may be short-term disturbances). But in the second case, the exchange rate is a destabilizing factor for the domestic economy and we can no longer say its fluctuation is always desirable.

In the second case above, the passive movement of domestic prices in response to an exchange rate shock is called the "pass-through" effect. If the exchange rate depreciates 30% and domestic prices rise 15% as a result, we say the pass-through coefficient is 0.5 (or pass-through is 50%) [assuming that global prices are stable].

For big and complex economies like the US and EU, pass-through may be small. Domestic inflation is hardly affected by exchange rate movement. But for small open economies, it may be very high. In such a case, currency devaluation for the purpose of gaining competitiveness may not work, because exchange rate changes are immediately offset by domestic inflation. Japan, although it is a large economy, has a relatively high pass-through coefficient compared with the US or EU.

Pass-through is generally greater for primary commodities (oil, minerals, farm products, etc) than for manufactured products which are highly differentiated and carry brand names. Obviously, pass-through is smaller for regulated goods and countries with many trade restrictions than for free trade commodities and externally open countries.

Estimating PPP

The actual exchange rate is easy to know as it is reported daily in the newspaper. But how do we know the PPP exchange rate? We must estimate it statistically, and it involves methodological problems and measurement errors. As a result, different economists and organizations have different estimates of PPP. The central bank research department, university economists, investment bankers, and IMF may disagree as to whether the domestic currency is overvalued or undervalued, and by how much.

Basically, there are only two ways to estimate PPP. For details, see handout no.5.

<1. Cassel-Keynes method>

The first way is to use readily available statistical data (exchange rates and price data from IFS CD-ROM or annual statistical yearbooks). You can use an EXCEL spreadsheet to calculate PPP (no need for any statistical software). This method corresponds to the concept of relative PPP. We have already explained it above, as the method that Cassel and Keynes employed after WW1. Prof. McKinnon and I call it the "Cassel-Keynes method" but this is not a generally accepted term.

But there is the "base-year problem" (this term is generally accepted) inherent in this method.

Since price data are expressed as an index with some arbitrary base year (say, 100 in the year 1995, it contains movement information but not level information (by how much Japanese prices were higher than US prices in 1995, for example). If we calculate PPP with 1995 as the base year, this is equivalent to assuming that PPP held in 1995. The validity of this assumption is unproven (in fact, the yen was clearly overvalued against the dollar in 1995). Any such PPP estimate will have an unspecified error which is equal to the difference between the actual and PPP rates in 1995.

<2. Price survey>

In order to avoid the base-year problem, the better way to estimate PPP is to check actual prices. For a very limited number of goods, even you can do it. If a bowl of noodles is 10,000 dong in Hanoi and 700 yen in Tokyo, the PPP exchange rate is 14.3 dong/yen (=10,000/700). Since the actual rate is about 138 dong/yen (=15,900/115), the Japanese yen is grossly overvalued (about 10 times) against the Vietnamese dong according to the "noodle PPP."

But if we are to compare many prices, this method is very costly and time consuming (you must travel to many places and stay for many days). A graduate student can hardly afford it, and even professors with research budgets cannot easily do it. If you work at a statistical bureau of the government, you may be able to get many domestic prices, but how do you get similar foreign prices (with matching classification)?

Another big technical problem is that products with the same name are often actually different across countries. Thai rice is different from Chinese rice. Even the same model of Toyota car (say, Corolla) is equipped with different specs and options in USA and EU. With respect to noodles, ramen in Roppongi is not exactly the same as pho bo in Hanoi. So how do we compare these products? We must select goods as similar as possible, but the gap inevitably remains.

There is also the weight problem. The content (shares of individual products) of a typical consumption basket is different from country to country. Japanese eat more fish but less beef than Australians. So how do you construct "internationally common" consumption weights? Should we give a greater weight to fish or beef? (Admittedly, this problem can also occur under the Cassel-Keynes method.)

So, not many organizations can do price surveys due to technical difficulties as well as time and budget constraints. The World Bank-OECD international price comparison program once did it. The Japanese Ministry of International Trade and Industry (MITI--now called METI) also conducted such surveys regularly for Tokyo, New York, Paris and Berlin for political purposes (recall the US criticism against high Japanese costs. Due to US pressure, Japan had to monitor naigai kakakusa every year).

I once conducted a price survey with a research organization under MITI. Based on our price survey, the calculated PPP yen/dollar exchange rate is shown below (semi-log scale). Note that the tradable PPP falls gradually because Japanese inflation is lower than US inflation. Moreover, PPP moves more smoothly than the actual exchange rate, which is highly volatile.

Note: Tradable PPP is based on the price survey of manufactured goods conducted by the Research Institute for International Price Mechanism (1993). In the fourth quarter of 1992, the estimated tradable PPP was 150.5 yen per dollar. This benchmark was updated and backdated using the Japanese overall wholesale price index and the US producer price index to obtain the PPP levels for the entire period.

The Balassa-Samuelson effect

The problem that I would like to discuss is as follows (for more details, please read the supplement to handout no.5).

When we compare GDP or per capita income across countries, the use of actual exchange rates as conversion factors often yield biases. One bias comes from temporary exchange rate fluctuation. When the home currency is overvalued, domestic prices and income are artificially boosted. Conversely, when the home currency is undervalued, they look too low. Annual movements in per capita income (at actual exchange rates) mostly reflect exchange rate instability, and not growth in real wage or productivity. The volatility of the yen/dollar exchange rate in the figure above clearly illustrates this problem.

However, there is another source of systematic error which is more permanent. Using actual exchange rates, we tend to overestimate the GDP of a high-income country and underestimate the GDP of a low-income country. In other words, the income gap between rich and poor countries is exaggerated.

This occurs because goods and services in high-income countries are generally more expensive than those in low-income countries. Remember the calculation of noodle PPP above, which indicated that the Japanese price is about 10 times higher than the Vietnamese price. In other words, the purchasing power of one US dollar (its domestic currency equivalent) is lower in developed countries. If you have the same dollar income, you can live a better material life in Lusaka than in Osaka. I am sure you (as a foreign student) are experiencing how high Japanese prices are. But the real question is: why developed countries have systematically higher prices than developing countries, when international trade is relatively free and LOOP holds?

The Balassa-Samuelson effect explains why. There are also the Scandinavian model of inflation and the theory of "productivity growth gap" inflation, which employ similar ideas. All of these models assume that the economy consists of two sectors: (i) the tradable sector which enjoys high productivity growth as industrialization proceeds; and (ii) the nontradable sector whose productivity is stagnant. The typical tradable sector is the manufacturing industry, and the nontradable sector can be represented by low-tech services and family farming.

If the factor market (typically the labor market) is integrated within a rapidly industrializing country, the cost of employing that factor must be the same across different industries. All producers in that country must pay the same wage to workers. But if productivity in the manufacturing sector rises much faster than the service and agriculture sector, the price of manufactured products can be reduced much faster than the price of services and non-traded farm products (productivity growth translates into lower prices).

By assumption, international price arbitrage works only for the tradable sector, so tradable prices are equalized across countries, but not nontradable prices. I checked the prices of similar air-conditioners or digital cameras in Hanoi and Tokyo, and they were about the same. But haircut is far more expensive in Japan (I pay 3,800 yen or $33) than in Vietnam (I pay 40,000 dong or $2.5). [These days I always cut my hair in Vietnam, because of this price gap and also because I want to check the hairdresser shops I have helped to create]

Industrialization occurs with a rapid improvement in manufacturing productivity while productivity in the traditional sector rises much more slowly. Because the internal productivity growth gap between manufacturing and services/farming is much greater in more developed countries, nontradable prices in those countries are much higher than in developing countries. If we use a general price index containing both tradable and nontradable prices, we still conclude that prices are higher in high-income countries, on average, because of higher nontradable prices.

In addition, we can also argue that the average quality (of the same product) is generally higher in developed countries than in developing countries. I feel that this is true for TV, air-con, computer, haircut, taxi, cashew nuts, and so on (maybe Japanese quality is sometimes unnecessarily high--do we really need an automatic toilet or an automatic door for taxi?) But after adjusting for such quality difference, there is still a large price gap which must be explained by the Balassa-Samuelson effect.


<References>

Cassel, Gustav, "Abnormal Deviations in International Exchanges," Economic Journal, December 1918.

Cassel, Gustav, Money and Foreign Exchange after 1914, Macmillan, 1922.

McKinnon, Ronald I., and Kenichi Ohno, Dollar and Yen: Resolving Economic Conflict between the United States and Japan, MIT Press, 1997 (Japanese translation, Nihon Keizai Shimbunsha, 1998).

Ohno, Kenichi, "Export Pricing Behavior of Manufacturing: A U.S.-Japan Comparison," IMF Staff Papers 36:3, 1989, pp.550-579.