Journal Issue

Estimating Yen/Dollar and Mark/Dollar Purchasing Power Parities

International Monetary Fund. Research Dept.
Published Date:
January 1990
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The purpose of this paper is to present an economical way of estimating purchasing power parity (PPP) exchange rates under the present floating exchange rate regime. The new technique, which will be called the price pressure method, takes advantage of the property that relative prices between two countries are systematically affected as the exchange rate deviates from PPP as defined by a broad basket of tradable goods. The methodology was developed as a technical complement to the PPP criterion for stabilizing exchange rates proposed by Ronald McKinnon,1 and is therefore most naturally interpreted in its context.

However, its validity also extends beyond the controversy surrounding fixed versus floating exchange rate regimes. The price pressure method offers a statistically more satisfactory way of estimating PPP exchange rates than the currently available methods.

The paper is organized as follows. Following a survey of current techniques for solving the “base-year” problem associated with PPP estimation in Section I, Section II introduces the price pressure methodology. Section III reports the empirical results of actual estimations using data for the United States and Japan and for the United States and the Federal Republic of Germany. Section IV discusses caveats in estimation, and Section V provides conclusions.

I. Estimating PPP: An Overview

This section summarizes the problem involved in estimating PPP exchange rates and briefly describes the currently available methodology to solve it. Later sections will introduce an entirely new technique of estimation based on price pressure exerted by the exchange rate.

When nominal exchange rates have been fixed for a long time and trade is fairly free, international commodity arbitrage should tend to align individual as well as average national price levels of goods that are subjected to international competition, although the prices of nontradable goods could diverge across countries. However, under a floating exchange rate regime where exchange rates move much faster than sticky prices do, there is no presumption that the same tradable goods would cost the same in different countries, and, in fact, under normal circumstances their prices are different (Isard (1977), Krugman (1987), Hooper and Mann (1987), and Ohno (1989a)). In estimating PPP exchange rates under the present system, one faces the problem of extracting the hypothetical rate of exchange at which prices of tradable goods would be equalized on average across countries from the data of the 1970s and 1980s when PPP did not generally hold. Because of dispersion of tradable goods prices (see below), there is no single exchange rate that would preserve the law of one price for each individual tradable good under the current exchange arrangement.

The “Base-Year” Problem

The problem of estimating the PPP exchange rate between, say, Japan and the United States can be summarized as follows. Ideally, one would like to have the absolute yen and dollar prices for the common broad basket of tradable goods whose components are prescribed in appropriate physical quantities: Pa and , respectively. Then the absolute PPP exchange rate can be simply computed as

Unfortunately, however, there is no such comparable absolute price data among major industrial countries on a systematic basis.2

In the absence of this information, one could still estimate PPP using the technique of relative PPP. Existing official producer price indices (PPIs) are price relatives, such that

where θ is an unknown scale factor that links the price relatives, Pand P*. These indices represent domestic currency prices of commodity baskets that are similar in composition but of arbitrary size—for example, 100 in the year 1967 or 1980. The approximate equality (≈) reflects the fact that the two commodity baskets may not have exactly the same weights. With θ unknown, equation (2) is a correct formula only up to a positive multiplicative factor. The base-year problem in estimating PPP is equivalent to that of assigning an appropriate value to θ.

Cassel-Keynes Method

In estimating PPP exchange rates after the turbulence of World War I, both Cassel (1922) and Keynes (1923) solved this problem with a simple method that is still practiced widely. Their method amounts to choosing a base year (“time 0”) when one can reasonably assume that PPP actually held, and then using the subsequent movements of relative prices for updating the base period's exchange rate to get the new estimate of PPP at time t:3

where E0 is the actual and PPP exchange rate at time 0, and the θ in equation (2) is

This methodology was well suited for the historical circumstances witnessed by the two economists. Because of unparalleled exchange rate stability and active and largely unrestricted international trade under the gold standard, the presumption that PPP held among principal countries in the early twentieth century is a justifiable one (see Triffin (1964) and McCloskey and Zecher (1976)). Thus, 1913 was a natural base year from which to project PPP exchange rates after World War I (1914–1918).

However, the Cassel-Keynes method is hardly useful for the last quarter of the twentieth century. After a long period of fluctuating exchange rates and constant violation of PPP, there is no single (not-too-distant) base year for which one could confidently assert that PPP held among the yen, dollar, and deutsche mark. Various authors have made the case for this or that base year—for instance, 1973 because of the inception of general floating; 1975 because of international convergence of inflation rates; 1978 because the yen was thought to be at the “correct” level reflecting Japan's competitiveness; or 1980 because U.S. trade was roughly in balance in the previous year—but these choices lead to a distressingly wide dispersion of estimates for what current PPP exchange rates might be.

Long-Run Averaging

One way to circumvent the problem is to use the long-run average of past relative prices, rather than a single base year, as the benchmark for estimating current PPP exchange rates. Assume that, in the long run of a decade or two, the exchange rate is overvalued and undervalued (by the criterion of PPP in tradable goods) with equal probabilities. Furthermore, although the exchange rate may remain overvalued or undervalued for a few years, such persistent misalignment will, through international arbitrage, exert pressure on national price levels to re-establish PPP in several years. Unless one has a reason to believe that deviating movements of the exchange rate from PPP always occur in the same direction, one may assume that the average nominal exchange rate stays close to PPP in the long run.

Table 1 reports some estimates of PPP yen/dollar and mark/dollar exchange rates for the first quarter of 1990 (the reference point throughout this paper). Although the main interest is PPP in tradable goods (that is, producer prices), PPP estimates based on other price indices are also listed where available.

Table 1.PPP Estimates for First Quarter of 1990
Yen/DollarMark. Dollar
Method and Base PeriodPP1ULCCPIGNP deflatorPPIULCCPIGNP deflator
Long-run averaging base 1975:1–1990:11751951801792.032.271.902.01
Long-run averaging base 1980:1–1990:11721881741742.142.322.022.11
Morrison-Hale method base 1985, updated using PPIa2002.33
Price pressure method sample period
1975:1–1988:2, updated using
PPI or ULCb1701862.042.19
Note: Indices used are producer prices (PPI), unit labor costs (ULC), consumer prices (CPI), and gross national product (GNP) deflator, all taken from Organization for Economic Cooperation and Development, Main Economic indicators, Exchange rates are from International Monetary Fund, International Financial Statistics, See text for a detailed account of each methodology.

Estimation in September 1989.

See Section III.

Note: Indices used are producer prices (PPI), unit labor costs (ULC), consumer prices (CPI), and gross national product (GNP) deflator, all taken from Organization for Economic Cooperation and Development, Main Economic indicators, Exchange rates are from International Monetary Fund, International Financial Statistics, See text for a detailed account of each methodology.

Estimation in September 1989.

See Section III.

Although the question of how far back one should look to calculate long-run averages remains, it is not unreasonable to include the entire period of the recent floating experience, except 1973–74, the years when the world economy was in transition to a new system. Thus, with the long-run base period of 1975:1—1990:1 and using producer price indices (PPIs), PPP exchange rates for the yen and the mark against the dollar as of the first quarter of 1990 are estimated to be ¥ 175/US$1 and DM2.03/US$1.

One potential problem of the long-run averaging method is the bias due to cumulative measurement error. Since each country uses different ways to correct for changing quality and shifting commodity weights, estimated PPP exchange rates may depend on the particular long-run base used. (If there were no bias, any reasonably long-run average should generate similar estimates.) In practice, however, such biases seem small in recent years. Table 1 shows alternative long-run averaging PPP estimates that omit from the base the last five years of the 1970s. Estimates are not dissimilar to the previous ones, especially for the yen against the dollar. It has also been suggested (McKinnon and Ohno (1989)) that biases are much smaller for PPI than for other price indices.

Morrison-Hale Method

Based on the methodology of absolute PPP, the Organization for Economic Cooperation and Development (OECD) estimates PPP exchange rates among major industrial countries every five years. However, the price data from which the OECD estimates are derived contain many nontradable components, since their computation is for the purpose of international comparison of income and living standards.

Morrison and Hale (1987) and Hale (1989) have devised a clever method of using the absolute domestic currency price data collected by the OECD to estimate PPP in tradable goods. They re-evaluated the OECD price data with a new set of weights reflecting the trade patterns of the United States, Japan, the Federal Republic of Germany, and the United Kingdom. The new weights were not reported, but statistical processing of the original and new PPP estimates reveals that the authors eliminated such nontradables as medical care, leisure and education, government consumption, and construction from the original data while increasing the weight attached to machinery, and so on. Using these weights adjusted for “tradability,” Hale (1989) calculated absolute PPP exchange rates for 1985 and updated them using relative PPIs. The resulting PPP estimates were ¥204/US$l and DM 2.36/US$1 in September 1989.

One serious drawback of the Morrison-Hale method was the inclusion in their price data of net indirect taxes. Some tradable goods, notably energy-related products, have considerably different tax and tariff structures across countries. Since energy is more heavily taxed in Japan and the Federal Republic of Germany than in the United States, it is likely that the Morrison-Hale estimates are biased upward, and in fact they are higher than other estimates.

Ideal Method

The ideal method of estimating PPP in tradable goods (although it has never been practiced) involves constructing a common and well-defined basket of internationally tradable goods that represents the trade patterns of major industrial countries, and expressing its value in currency units of dollars, yen, mark, and so forth. The basket will have similar contents to those of producer or wholesale price indices, but will differ from them on two accounts: the size of the basket is precisely determined in the physical quantity of each good, and the basket is identical for all countries. These “international tradable price indices” would provide the starting values for the McKinnon regime. They would also serve as the nominal anchor for monitoring worldwide inflationary or deflationary pressures.

Since such a project demands a considerable amount of time and resources, it is best undertaken by either governments or an international organization on a regular basis. Governments already collect a multitude of individual price data for the purpose of compiling existing price indices, so the technical difficulty in constructing the new index should not be insurmountable.

Price Dispersion and PPP Drift

Two complications in estimating PPP exchange rates under a floating exchange rate system should be noted.

First, no single PPP exchange rate immediately ensures the law of one price for all tradable commodities because of systematic price dispersion. Since tradable goods differ in tradability—from flex-price primary commodities to manufactured products with sticky prices—relative prices among them change with the movement of the exchange rate. Suppose the dollar depreciates rapidly from the position where PPP initially held. Primary commodity price indices (say, gold or oil) would lead one to pick the new value of the dollar as the “ρρρ” exchange rate, because these prices are always aligned internationally through electronic arbitrage. Indices containing a broader basket of producer prices would suggest a somewhat higher value of the dollar for PPP; and those based on unit labor costs, a higher value yet. Thus, PPP estimates under the floating exchange rate are highly dependent on the precise content of the commodity basket.

Another salient characteristic of the PPP estimates when exchange rates float is the possibility of persistent drift. Unlike a regime with irrevocably fixed exchange rates, floating allows one of the countries in the system to intentionally drive down its currency to gain export competitiveness. However, any country that adopts currency depreciation as a long-term strategy would have a higher inflation in tradable goods—and with it a higher nontradable inflation as well—than its trading partners. This is not only because the resultant increase in import prices will eventually be passed through to domestic prices but, more important, because a depreciation policy requires that monetary policy be consistently easy relative to the rest of the world, fueling domestic inflation with a lag. When this happens, the PPP exchange rate of the undervalued currency tends to depreciate as if to partially restore the violated law of one price. Similarly, the PPP exchange rate of the overvalued currency appreciates over time to catch up with the actual exchange rate. Such movements in relative prices, while statistically significant, are small relative to typical swings in the exchange rate, as will be seen below.

II. The Price Pressure Model

In this section an empirical model is introduced for estimating PPP exchange rates using price relatives—that is, officially published price and cost indices for two countries with arbitrary choices of the base year; these indices are nonetheless comparable because the contents of the commodity baskets they represent are similar. The price pressure model is particularly suitable for estimating PPP exchange rates in the McKinnon sense, where PPP is defined as the hypothetical exchange rate that would equate the absolute price levels of the same broad basket of tradable goods (manufactured goods in particular) internationally.

The primary aim is to endow estimation of PPP with a structural content. The price pressure method is a way of systematically estimating the absolute level of PPP from the information contained in the entire sample period, rather than guessing that this or that year would be a good base year. The structure imposed is a relatively simple one, which could be summarized in two equations: the relative price equation and the relative cost equation. The relative price equation assumes that any deviation from PPP in the McKinnon sense prompts adjustment in the price of tradable goods in both countries, which tends to partially (but not completely) offset the initial deviation of the real exchange rate. Implicit in this adjustment of relative prices is the pricing behavior of profit-maximizing export firms responding to changes in international competitiveness. The relative cost equation, in turn, assumes that, when such price adjustment occurs, the domestic cost of production responds in the same direction as output prices to ameliorate the excess profit or loss of export firms. Behind this response is the wage-setting behavior of workers, which depends on the expected long-run productivity gain as well as the short-run profitability of the firm.

The price pressure method takes advantage of differential speeds of adjustment to exchange rate shocks in a model with two types of goods: tradable output (mainly manufactured goods), and nontradable input (labor). When the nominal exchange rate deviates from the PPP level, thereby upsetting the international law of one price, the price of output adjusts more quickly than the price of input to re-establish PPP. Because of the divergent movements of the prices of output and input, firms experience variation in profitability—excess profit when the home currency is undervalued and profit-squeeze or even loss when the home currency is overvalued (by the PPP criterion). Assuredly, this price pressure phenomenon is temporary, and PPP will eventually be restored for all goods in the very long run. The evidence will show, however, that “temporary” price pressure typically lasts several or more years.

The price pressure model adopts the working definition of PPP where the PPP exchange rate is that path of the exchange rate that, on its own, would exert no price pressure on the two countries (the price neutrality of the exchange rate).


The model assumes two countries—say, Japan and the United States—producing tradable manufactured goods that are similar, but imperfect substitutes. These goods are produced in each country with a single nontradable input (labor) under the assumption of constant returns to scale.

Define competitiveness between Japan and the United States in terms of production costs. In other words, competitiveness is defined as the real exchange rate where relative costs of producing manufactured goods are used as the deflator:

where et, is the log of the nominal yen/dollar rate, and and are the logs of unit labor costs in the United States and Japan, respectively. A rise in σt associated with an increase in et, (yen depreciation) or an increased U.S. unit cost tips competitiveness in Japan's favor, while an increase in Japanese cost lowers σtand makes U.S. firms relatively more competitive.

Equation (4) defines competitiveness solely in terms of relative costs and independently of firms’ pricing behavior, given the cost differential. An alternative way to define competitiveness would be to deflate the nominal exchange rate by the relative prices of output, rather than the relative costs of producing it. However, this method tends to confuse the change in cost advantages due to technology, relative factor costs, and exchange rate movements, on the one hand, and export firms' pricing behavior in response to these fundamental forces, on the other. As will become clear, the distinction between these two causes of export price changes is important in building a structural model of exchange rate fluctuation and resultant price pressure.

Relative Price Equation

Recent theoretical research in export pricing strategy, where imperfect competition prevails and each firm sets rather than takes the price, has emphasized the importance of market structure in determining to what degree exchange rate changes are passed through to foreign prices.4

Following Feenstra (1987) and Marston (1989), assume that an oligopolistic export firm is faced with a downward-sloping demand curve denominated in foreign currency, and the cost of production is denominated in domestic currency. Given foreign income, foreign rival firms' prices, and domestic wages, Feenstra and Marston show that the simple framework of static profit-maximization gives the pricing rule where the pass-through coefficient (that is, the elasticity of the foreign-currency-denominated export price with respect to the exchange rate) depends on the elasticity of marginal revenue with respect to price and the slope of the marginal cost curve. More generally, the pass-through coefficient is a function of the shapes of both the demand and supply curves denominated in different currencies. The coefficient is not necessarily equal either to zero (no pass-through) or unity (complete pass-through), but it is normally between these two extreme cases.5

Firms' pricing behavior as described above can be represented by a markup over unit labor cost, where the markup rate depends on the competitiveness as defined in equation (4):

where and are logs of unit prices of Japanese and U.S. goods, each measured in the respective domestic currency; and and are error terms reflecting other factors affecting firms' pricing behavior. These error terms may be serially correlated individually, and mutually correlated contemporaneously.6

Firms and workers set output prices and labor wages one period in advance. Thus, the current unit price reflects the competitiveness of the previous period and the unit cost that is in effect today but was set in the last period.

In equations (5) and (6), αJand αUSare simply unity minus the corresponding pass-through coefficients, and thus normally take values between zero and unity. These parameters, which in turn depend on various demand and supply parameters, represent firms' pricing strategy with respect to changes in competitiveness.7Empirical studies of export pricing behavior suggest that αJ(for Japan) is different either from zero or one, whereas αUS(for the United States) is not statistically different from zero for many manufacturing industries. In other words, U.S. firms tend to price to domestic cost while Japanese firms are more sensitive to the exchange rate (Mann (1986). Krugman (1987), Baldwin (1988), and Ohno (1989a)).

In the next step, denote relative variables, parameters, or error terms by the same symbols as the original ones but without superscripts:

and so on. (Note that α is defined as the sum of α and αUS, rather than the difference.) Then equations (5) and (6) can be rewritten as

where the new error term is assumed to be serially correlated:

where ε1t, is white noise.

Equation (7) says that relative prices (measured in respective domestic currencies) between Japan and the United States systematically deviate from the underlying relative costs of production as competitiveness—defined in equation (4)—changes. Suppose, for instance, that Japanese firms become low-cost producers of manufactured goods relative to U.S. firms, either because of a change in cost trends or because the yen depreciates against the dollar. Equation (7) predicts that Japanese firms will increase their profit margin (or U.S. firms will shave their profit margin), which tends to offset part of the change in competitiveness.

The left-hand side of equation (7), pt–ct, is the price pressure that is exerted by the departure of the exchange rate from PPP in tradable goods.

Relative Unit Labor Cost Equation

Assume that changes in labor productivity in each country, denoted and are characterized by the following equations:

where and are constants representing drift, and and are shocks to labor productivity. These shocks can be correlated across countries, and they may be serially correlated as well. (However, see footnote 6.) Expressed in relative terms, from (9) and (10):



where ε2t is white noise.

Next are the following assumptions about the evolution of nominal wages. Workers demand a wage increase in each period (which becomes effective in the next period) based on both the competitive position (that is, profitability) of the firm in the previous period and expectations of long-run gain in labor productivity:

Note the twice-lagged competitiveness in these equations. It is presumed that ωi is positive, meaning that a higher rise in wages is realized when firms are internationally competitive and therefore profitable; and that δiare between zero and unity, because workers demand a gradual pay increase reflecting part of—but not necessarily all of—the productivity gain that is expected over the long run.

As before, using the notation the relative wage equation corresponding to (13) and (14) is obtained:

The change in relative unit labor costs is simply the change in relative wages minus the change in labor productivity. This can be written, from (7), (11), (12), and (15), as


Equation (16) is the unit labor cost equation; β measures the lagged elasticity of relative wages with respect to the price pressure exerted by the deviation of the exchange rate from PPP.

Equation (16) will be coupled with equation (7) to form the two key equations in the price pressure method of estimating PPP exchange rates.

The Empirical Adaptation

The price pressure model for PPP estimation requires a few more steps in order to be applicable to actual data. The first remaining step is to express the model in terms of observable price and cost indices.

Recall that officially published price and cost data have arbitrary base periods, which causes the base-year problem, as discussed in Section I. In particular,

where the tilde indicates the use of official price or unit labor cost indices, unadjusted for the necessary but unknown constants—θ1and θ2, respectively. (See equation (2).)

The two key equations are reproduced below; the relative price equation (7):

and the relative unit labor cost equation (16):

Using (17) and (18), these equations can be rewritten so that only observable variables remain:

The next step deals with serial correlation in the error terms. The error terms of these equations have the following structure due to equations (8), (12), and (16):

However, it is presumed that the twice-lagged cross term is sufficiently small and therefore could be safely ignored empirically. The somewhat simplified assumption about the error terms is thus a first-order vector autoregression:

where ρl2is expected to be insignificantly different from zero.

Finally, the model is summarized in vector-matrix form. Equations (19), (20), and (22) provide the basis of the estimation. Let

Then the price pressure model can be compactly expressed as follows:

where (IRL)ut, = εt, (Lis the lag operator and I is the identity matrix).

Premultiplying this equation by (IRL) and rearranging yields

where εt, is bivariate white noise. This is the system of equations that is actually estimated.

V. Empirical Results

The two important bilateral PPP exchange rates—yen/dollar and mark/dollar—are estimated using quarterly average data for the first quarter of 1975 to the second quarter of 1988, with 54 observations. Nominal bilateral exchange rates are taken from line rf of the International Monetary Fund's (IMF) International Financial Statistics and PPIs and unit labor cost indices (seasonally adjusted) are taken from the OECD's Main Economic Indicators. In the estimation of the mark/dollar PPP exchange rate, the Federal Republic of Germany replaces Japan in the model presented in the previous section.

The parameter γ¯, the long-run trend in relative unit labor costs, is obtained separately by regressing the logarithm of actual relative unit labor costs on a constant and a time trend over the sample period. The estimated values of γ¯ turn out to be—0.0081 for the yen/dollar data and—0.0042 for the mark/dollar data. In annualized terms, this implies that Japanese unit labor costs tended to decline 3.3 percent relative to those in the United States, while German unit labor costs fell 1.7 percent, on average, relative to those in the United States.

The price pressure model, with two key equations compactly expressed in equation (24), is estimated by the maximum-likelihood method with orthogonalized error terms to ensure efficiency.8 The results of estimation are reported in Tables 2a and 2b for the yen/dollar data, and in Tables 3a and 3b for the mark/dollar data.

Table 2a.Price Pressure Method: Yen/Dollar
Note: The sample period is from the first quarter of 1975 to the second quarter of 1988. Indices used are producer prices (PPI) and unit labor costs (ULC) taken from Organization for Economic Cooperation and Development, Main Economic Indicators. The exchange rate is from International Monetary Fund, International Financial Statistics. The asterisk indicates significance at the 5 percent level.

The estimated value depends on the base year of the original price or cost indices used, in this case 1980 = 100.

Note: The sample period is from the first quarter of 1975 to the second quarter of 1988. Indices used are producer prices (PPI) and unit labor costs (ULC) taken from Organization for Economic Cooperation and Development, Main Economic Indicators. The exchange rate is from International Monetary Fund, International Financial Statistics. The asterisk indicates significance at the 5 percent level.

The estimated value depends on the base year of the original price or cost indices used, in this case 1980 = 100.

Table 2b.Price Pressure Method: Yen/Dollar, Summary Statistics
EquationR¯2SEDWQ -statistic
Relative price equation0.8480.0201.6712.7
Relative cost equation0.2110.0171.928.4
Note: The Q-statistic is distributed asymptotically as x2(8). The critical value for the 5 percent significance level is 15.5; R¯2 denotes the adjusted coefficient of determination; SE is the standard error of the equation; and DW is the Durbin-Watson statistic.
Note: The Q-statistic is distributed asymptotically as x2(8). The critical value for the 5 percent significance level is 15.5; R¯2 denotes the adjusted coefficient of determination; SE is the standard error of the equation; and DW is the Durbin-Watson statistic.
Table 3a.Price Pressure Method: Mark/Dollar
Note: The sample period is from the first quarter of 1975 to the second quarter of 1988. Indices used are producer prices (PPI) and unit labor costs (ULC) taken from Organization for Economic Cooperation and Development, Main Economic Indicators. The exchange rate is from International Monetary Fund, International Financial Statistics. The asterisk indicates significance at the 5 percent level.

The estimated value depends on the base year of the original price or cost indices used, in this case 1980 = 100.

Note: The sample period is from the first quarter of 1975 to the second quarter of 1988. Indices used are producer prices (PPI) and unit labor costs (ULC) taken from Organization for Economic Cooperation and Development, Main Economic Indicators. The exchange rate is from International Monetary Fund, International Financial Statistics. The asterisk indicates significance at the 5 percent level.

The estimated value depends on the base year of the original price or cost indices used, in this case 1980 = 100.

Table 3b.Price Pressure Method: Mark/Dollar, Summary Statistics
EquationR¯2SEDWQ -statistic
Relative price equation0.7490.0212.007.3
Relative cost equation0.0850.0192.105.7
Note: The Q-statistic is distributed asymptotically as x2(8). The critical value for the 5 percent significance level is 15.5; R¯2 denotes the adjusted coefficient of determination; SE is the standard error of the equation; and DW is the Durbin-Watson statistic.
Note: The Q-statistic is distributed asymptotically as x2(8). The critical value for the 5 percent significance level is 15.5; R¯2 denotes the adjusted coefficient of determination; SE is the standard error of the equation; and DW is the Durbin-Watson statistic.

More important, the price pressure model imposes six nonlinear constraints, compared with the unconstrained version of the same model.9


The overall fit of the model is fairly satisfactory. The corrected R2 of the relative price equation is quite high for both the yen/dollar (0.848) and the mark/dollar (0.749). The corrected R2 of the relative cost equation is not as high for either the yen/dollar (0.211) or the mark/dollar (0.085). But these results are not surprising, because the dependent variable in the relative cost equation is the rate of change, rather than the level, of relative unit labor costs (see equation (20), for instance). The residual terms in the equations (ε's) are very close to bivariate white noise. The estimation method used here forces them to be contemporaneously uncorrelated with each other. In addition, the Durbin-Watson and Q-statistics both suggest that, for each currency pair, there is no evidence of serious serial correlation in the residual terms. In light of this, the specification of serial correlation in the original error terms seems appropriate. Estimated values of ρ's are all plausible as well.

Whether these constraints are consistent with the data can be checked by the log-likelihood ratio test. With the test statistics distributed asymptotically as χ2 with 6 degrees of freedom, neither the yen/dollar data (11.46) nor the mark/dollar data (9.16) reject these constraints at the significance level of 5 percent. This further confirms that the model is correctly specified.

Estimates for α and β

Estimated values of α, which measures the price response of firms to the exchange rate, are positive fractions and statistically significant. In the case of Japan and the United States, relative prices move to offset 10.5 percent of the initial deviation of the exchange rate from PPP after one quarter. In the case of the Federal Republic of Germany and the United States, the corresponding price adjustment is 6.2 percent of the initial divergence. The difference in the price sensitivity to the dollar exchange rate may reflect the relative importance of the dollar exchange rate to Japanese trade compared with German trade.

In contrast, German wages are more responsive to price pressure than Japanese wages, as can be seen from the estimated values of β. When output prices deviate from the cost of production (indicating that firms are making unusual profits or losses in the short run), the cost of production itself tends to adjust, so that excess profit or loss is partially offset. This tendency is more prominent in Germany, where relative cost movement offsets 52.5 percent of price pressure after one quarter, than in Japan, where only 28.4 percent of such pressure is relieved.

These values of α and β raise a few interesting points. First, since Japanese prices are more responsive to the exchange rate but Japanese wages are less responsive to the resultant price pressure, compared with Germany, it follows that the profitability of Japanese firms is much more seriously affected by dollar exchange rate fluctuations than that of German firms—provided that variability of the exchange rate is the same. In other words, short-term exchange risks are borne mainly by firms, rather than by workers, in Japan. Second, with these parameter values, the speed of reversion to a new PPP level following an initial shock in the exchange rate is excruciatingly slow. Simple iterative calculation shows that it takes as many as 20 quarters for relative prices to close half of the initial deviation from PPP, regardless of whether Japanese or German prices are involved. This evidence supports the well-known hypothesis of sticky prices. It further implies that PPP for tradable goods—at any rate, for most manufactured goods—is in practice rarely observed under a floating exchange rate regime. McKinnon suggests that slowness of adjustment may be attributed to the great exchange rate uncertainty. If changes in the exchange rate were unidirectional, one would expect prices and cost to respond more quickly.

PPP Estimates

The terms In θ1and In θ2are the logarithms of the hitherto unknown constant terms that would reveal the absolute level of the PPP exchange rate (see equations (17) and (18)): In θ1is associated with PPP measured in terms of actual output price (and thus inclusive of firms' profits), and In θ2relates to PPP measured in terms of production cost (and thus exclusive of firms' profits). Note that In θ1 and In θ2are dependent on the base years of price or cost indices used in estimation (in the case here, all indices take the value 100 in 1980). Therefore, the estimated In θ1and In θ2—and their t-statistics—are neither unique nor easily interpreted. They become meaningful when used to compute the estimated paths of PPP exchange rates in absolute yen/dollar or mark/dollar terms. These estimated paths are unique, regardless of the base years of the indices used.

However, the estimated standard errors of In θ1and In θ2are independent from the scaling of indices, and provide the valuable information about the accuracy of the PPP estimates. The asymptotic standard errors are given below.

In θ10.0640.033
In θ20.0470.024

For example, the standard error of 0.064 in In θ1 for the yen/dollar implies that (applying the two-sigma rule) the chance of the true PPI-based PPP exchange rate lying above or below 12.8 percent of the estimated PPP yen/dollar path is roughly 1 in 20. Notice that the mark/ dollar PPP estimates are considerably “sharper” than those for the yen/ dollar by the factor of 2 to 1. In addition, the estimators of In θ1and In θ2are highly correlated.10 This is hardly surprising given the methodology used to estimate them.

Figures 1 and 2 report the final results of PPP estimation graphically. In each figure, the solid line represents the actual yen/dollar or mark/ dollar exchange rate. Superimposed on it are the estimated PPP exchange rates: the one based on PPI and the other based on unit labor costs (ULC).

Figure 1.Actual and PPP Yen/Dollar Rates

Figure 2.Actual and PPP Mark!Dollar Rates

It is immediately apparent that the actual exchange rate is far more volatile than the movement of either relative prices or relative costs of production, with the result that PPP holds only momentarily and by chance under a freely floating exchange rate regime. (At such points, “actual” and “ppp” exchange rates cross.) This phenomenon was also evident from the estimated coefficients of α and β. In the long run, however, the actual exchange rate does not diverge indefinitely from the PPP exchange rate of either variety. Indeed, the actual exchange rate comes back to the PPP level from an over- or undervalued position every few years, only to overshoot it in the other direction.

Furthermore, the price pressure model predicts certain relationships among the three exchange rates plotted in each figure. When the actual exchange rate is above PPP (the dollar is overvalued), profits of U.S. firms are squeezed and profits of foreign firms become fatter. This tends to push the PPI-based PPP above the ULC-based PPP. Conversely, when the actual exchange rate is below PPP (the dollar is undervalued), PPI-based PPP is expected to lie below the ULC-based PPP. Although lags and serial correlation in the model complicate the matter somewhat, this general rule seems to be confirmed for both currency pairs (especially for the yen/dollar). The only exception is the earlier period of 1975—77 where no such tendency exists for either yen/dollar or mark/ dollar exchange rates. This may suggest that the specification of a linear trend in relative unit labor costs may not be appropriate for the mid-1970s—although the assumption seems acceptable for the remainder of the period.

For the comparison with other methods of PPP estimation, Table 1 also shows the PPP exchange rates for the second quarter of 1988 estimated by the price pressure method and updated to the first quarter of 1990 using relative PPI or ULC movements. These are fairly close to the other estimates. The fact that different methods yield similar estimates of PPP is highly encouraging. Finally, it is observed that in the first quarter of 1990, the PPl-based PPP exchange rate was lower than the ULC-based PPP exchange rate for both the yen/dollar and mark/dollar. This is as it should be, because the dollar was undervalued against both the yen and the mark in that quarter by the criterion of PPP. The actual exchange rates were ¥ 148/US$1 and DM 1.69/US$1.

Although one may agree or disagree with the policy of targeting nominal exchange rates so as to achieve PPP, one could hardly deny the technical proposition that such PPP exchange rates are estimable with reasonable confidence. As long as it remains clear which price indices should be the basis of PPP estimation, estimates derived from different methods tend to coalesce within a narrow margin.

IV. A Few Caveats

Although the price pressure methodology provides a more structural approach to PPP estimation than other methods, its limitations should also be recognized. First, although suitable for well-diversified industrial economies, the method cannot be used for either a small monoculture economy or an economy in which price controls proliferate; in either case, exchange rate fluctuations would have little influence on internal relative prices. Second, there is the data problem associated with the ULC time series, which is derived from wage, labor, and output data. Unlike producer prices, ULC series compiled by different institutions are not identical, and may also be revised considerably over time. Using ULC indices of the IMF instead of the OECD, for example, would increase the standard errors of α and β, although the estimated PPP exchange rates were not dissimilar. (In passing, the price pressure methodology seems fairly robust against addition of a few observations.) Third, the time trend of relative unit labor costs should be endogenized within the model. The present model somewhat naively assumes that this is directly related to the linear trend in relative productivity and the long-run share of labor, both of which are determined outside the model.

V. Concluding Remarks

Purchasing power parity is an old doctrine, dating back to the days of Hume and Ricardo, which still survives and even thrives in the economic literature and in policy discussions. The concept of PPP, the international version of the law of one price, embraces so many important yet diverse facets of open economies that each generation of economists reinterprets it or finds a new meaning to it. This study has approached PPP along the path prepared by McKinnon, who regards it as a criterion for conducting monetary and exchange rate policies in an integrated world economy.

The main contribution of this paper has been the presentation of the price pressure model, where PPP exchange rates are calculated using an entirely new procedure. This is one technical aspect of the McKinnon proposal that has not been formally presented in his own writing. It has been shown that estimating PPP, while not a trivial exercise, can be performed with scientific accuracy, and, hence, agnosticism about PPP exchange rates can be dispelled, subject to the caveats spelled out in the previous section.

International Price Comparison

In 1989, a number of Japanese ministries and agencies investigated absolute price levels in Japan vis-à-vis its trading partners in response to the criticism that Japanese prices were too high. The typical procedure was as follows: (1) select a common basket for comparison, (2) sample individual prices comprising the basket in each country, (3) convert collected price data into a common currency unit using the actual exchange rate, and (4) average the outcome using various weights. The final output was cost of living indices for individual countries. Whatever the motivation or purpose of these studies, the exercise is essentially that of absolute PPP estimation (see equation (1)), and it is quite easy to rearrange the results as such.

Table 4.International Price Comparison
Price Level (Tokyo = 100)aImplied PPP Rate against Dollar
ItemNew YorkHamburgyenmark
All items72681781.66
Clothing and footwear67711911.86
Other commodities79891621.98
Energy and water44702912.79
Transportation and
Medical services106241210.40
Land-intensive services37693463.28
Other services118781091.16
Source: Economic Planning Agency, Bukka Report '89 (October 1989).

Conversion rates are ¥ 128.15 = US$1 and ¥72.97 = DM 1 (1988 averages).

Source: Economic Planning Agency, Bukka Report '89 (October 1989).

Conversion rates are ¥ 128.15 = US$1 and ¥72.97 = DM 1 (1988 averages).

The most frequently quoted among these studies is the Economic Planning Agency's Bukka [Price] Report '89 (October 1989). The accompanying table (Table 4) shows the cost of living indices for New York and Hamburg estimated by the Report (p. 33), with Tokyo = 100 in the left columns, and PPP exchange rates implied by them in the right columns, for various categories of goods and services. PPP exchange rates differ substantially, depending on tradability and government intervention (including regulations, indirect taxes, and subsidies). But it is noteworthy that PPP exchange rates defined by “durables,” which mainly contain tradable manufactured products, are very close to those estimated by the price pressure method (¥170/US$1 and DM 2.04/USS1).


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Kenichi Ohno is an Economist in the Middle Eastern Department. He holds a doctorate from Stanford University as well as degrees from Hitotsubashi University, Tokyo. The author thanks Ronald McKinnon for his advice and encouragement and Howard Handy and Camille Baulant for useful comments.

Apart from the conventional interpretation of PPP as a theory of exchange rate determination, McKinnon in recent years has advanced the idea of using PPP as a policy criterion to stabilize exchange rates and price levels among the industrial economies, which are becoming increasingly integrated through trade and finance. His version of PPP encompasses a sweeping reform of the international monetary system. The key ingredients of his proposal are (1) commitment to permanently fixed nominal exchange rates; (2) use of the price of a broad basket of internationally tradable goods as the nominal anchor of the system; and (3) the relative price adjustment mechanism based on absorption control and divergent price movements of various nontradable goods (McKinnon (1984, 1988a, 1988b, 1989), McKinnon and Ohno (1988, 1989), and Ohno (1989b)).

The Organization for Economic Cooperation and Development (OECD) and the World Bank calculate absolute PPP exchange rates for broader baskets including nontradables (see below). Recently, a number of Japanese ministries launched international price comparison studies on a limited number of commodities and services (see Appendix).

“When two currencies have been inflated, the new normal rate of exchange will be equal to the old rate multiplied by the quotient between the degrees of inflation of both countries” (Cassel (1921, p. 37)).

Although most authors agree that pass-through is generally different from unity, underlying reasons for this conclusion differ from one model to another. For example, Knetter (1989), Krugman (1987), Mann (1986), and Yamawaki (1988) attribute various degrees of pass-through to dissimilar conditions of demand or supply in each country (in static profit-maximization). Baldwin (1988), Baldwin and Krugman (1986), Foster and Baldwin (1986), Dixit (1987, 1989), and Froot and Klemperer (1989) stress the role of hysteresis in dynamic pricing behavior, Daniel (1987), Klein (1988), and Murphy (1988) contend that different shock structures in the macroeconomy lead to different optimal price responses to the exchange rate signal.

The pass-through coefficient could exceed unity in certain special cases. One sufficient condition (in Feenstra's model) is that the elasticity of demand is decreasing in price and marginal costs are declining.

However, for simplicity it is assumed that both error terms are individually ARMA (1,0) with the same autoregressive coefficients. This assumption permits a simple structure of the error term in relative form, as in equation (8) below. A similar assumption is made for bilateral productivity shocks below.

For example, aJ = 0 in equation (5) implies that Japanese firms are pricing their exports to domestic cost irrespective of the exchange rate. In contrast, if aJ= 1, then

In the steady state where the exchange rate and costs remain constant, and ignoring the error term, one has pJ= e + cUS; that is. Japanese firms are pricing to foreign cost (converted to yen), irrespective of domestic cost of production. This is the closest analogue of the concept of “pricing to market” in the model. Furthermore, consider the special case where αJUS=1 and again assume the steady state. Then, equations (4), (5), and (6) reduce to pJ= ρUS+ e, which implies that PPP holds constantly (except for random errors). However, empirical evidence convincingly shows (Isard (1977), Ohno (1989a)) that PPP does not hold for manufactured goods under a floating exchange rate system, owing to sticky prices. Thus, previous empirical evidence suggests 0 #x003C;αJ #x003C;1, αUS≈0, and αJ + αUS< 1.

The LSQ procedure of the TSP statistical package is used.

The model estimates 8 parameters, including those associated with serial correlation. In the unconstrained version, the relative price equation and the relative cost equation would each have free parameters on a constant, 2 lagged dependent variables, 2 concurrent independent variables, and 2 lagged independent variables—14 free parameters in all.

From the asymptotic variance-covariance matrix of the estimated parameters, the correlation between In θ1and In θ2is estimated to be 0.96 for the yen/ dollar and 0.86 for the mark/dollar.

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