Aggregation of Economic Indicators Across Countries
Exchange Rate versus PPP Based GDP Weights

Relative GDP shares are frequently used as weights in aggregations. In order to ensure that these weights reflect countries’ shares in real output, GDP data in national currencies should be converted into a common numeraire currency at purchasing power parity (PPP) rates. A review of the empirical evidence on the relationship between exchange rates and prices suggests that market (or official) exchange rates are generally poor proxies for PPP rates. The paper examines the PPP-based GDP data generated by the International Comparison Program and compares aggregations with PPP- and exchange rate-based GDP weights.

Abstract

Relative GDP shares are frequently used as weights in aggregations. In order to ensure that these weights reflect countries’ shares in real output, GDP data in national currencies should be converted into a common numeraire currency at purchasing power parity (PPP) rates. A review of the empirical evidence on the relationship between exchange rates and prices suggests that market (or official) exchange rates are generally poor proxies for PPP rates. The paper examines the PPP-based GDP data generated by the International Comparison Program and compares aggregations with PPP- and exchange rate-based GDP weights.

I. Introduction

Global economic analyses generally involve the aggregation of economic indicators across countries. In many instances, aggregates are defined as weighted averages of indicators for individual countries, with the weights reflecting the relative size of countries. 1/ A widely employed approach is to define countries’ weights as their shares in total GDP of the group considered. 2/ In order to ensure that GDP weights reflect each country’s share in real output, differences in price levels across countries need to be taken into account. Data expressed in national currencies should thus be converted into a common numeraire currency using conversion factors that reflect each currency’s purchasing power relative to the numeraire currency. 3/

For practical reasons, GDP data expressed in national currencies are usually converted at market exchange rates. The use of market exchange rates for conversion purposes may be an acceptable approach as long as differences between market rates and purchasing power parities (PPPs) are likely to be small and transitory. However, if market exchange rates diverge substantially and for extended periods from purchasing power parities, conversion at market exchange rates may yield biased GDP weights and hence biased indicators of aggregate economic activity in groups of countries.

This paper compares GDP weights based on market (or official) exchange rates with weights based on available estimates of PPPs. The comparison focusses on conversion factors and does not bear on issues relating to equilibrium exchange rates. The paper reviews alternative weighting schemes and examines their impact on indicators of aggregate real GDP growth. Section II deals with exchange rate based GDP weights. It provides a brief summary of the empirical evidence on the relationship between exchange rates and PPPs and discusses the implications of aggregating growth rates of real GDP with different sets of exchange rate based GDP weights. Section III examines an alternative weighting scheme derived from PPP-based GDP data generated by the International Comparison Program (ICP). The section briefly summarizes problems of PPP index construction and the main features of the ICP approach. 1/ It discusses issues relating to the intertemporal extension of PPP-based GDP data that are available only for individual benchmark years, and issues relating to the estimation of PPPs for non-benchmark countries. The section then compares aggregate growth rates of real GDP derived from PPP-based GDP weights with aggregates derived from exchange rate based GDP weights. Section IV summarizes the main conclusions of the paper.

II. GDP Weights Based on Exchange Rates

1. Exchange rates and purchasing power parities

Comparison and aggregation of real GDPs across countries would pose less of a problem if market (or official) exchange rates were equal to the ratios of the weighted averages of prices (at the level of GDP) in the respective countries relative to a base country. 2/ In this case price levels, defined as the weighted average of prices (at the level of GDP) expressed in a common unit of account, would be the same in all countries. Converting GDPs in terms of current domestic prices and national currencies at market (or official) exchange rates into a common unit of account would then yield GDP data that reflect cross country differences in real output rather than price differences. Over time, changes in the weighted average of prices in any given country relative to the numeraire country would be offset by changes in the exchange rate and would not affect the country’s GDP relative to the numeraire country or any other country.

The relationship between prices and exchange rates has been the subject of numerous theoretical and empirical studies. 3/ PPP theories of exchange rate determination describe an equilibrium relationship between prices and exchange rates without specifying the mechanisms that bring about this relationship. 4/ They are based on the notion that in the absence of transportation cost and trade barriers, the law of one price ensures that the prices of homogeneous goods are equalized across countries:

Pi=spi*(1)

with

pi = the price of good i;

s = the market exchange rate defined as units of domestic currency per unit of foreign currency.

Variables relating to the foreign country are marked with an “*”.

If all goods are tradable, the PPP rate can be defined as

spppΠi=1mpiaiΠi=1mpi*ai*=sΠi=1mpi*aiΠi=1mpi*ai*(2)

assuming that the arbitrage condition described by equation (1) holds. According to equation (2), the market exchange rate s is equal to the PPP rate, sppp, if ai=ai*, i.e., if the weights are the same in both countries.

In the presence of nontradables, assuming that the law of one price holds for all tradable goods, the PPP rate can be defined as

sPPPPNαPT(1α)PN*a*PT*(1a*)=s(PN/PT)α(PN*/PT*)α*(3)

with

PN=Πd=1hpNdbd
PT=Πi=1mpTiai

and similarly for PN* and PT*. The share of nontradables in total output is represented by α. If some goods are nontradable, the market exchange rate s is only equal to the PPP rate, sPPP, if (PN/PT)α=(PN*/PT*)α*, i. e., if the relative prices and shares of nontradables are the same in both countries. 1/

Not all PPP theories of exchange rate determination refer to the concept of PPP described by equation (3). The theories differ in the definition of the price level and the time horizon for which the equilibrium relationship between prices and exchange rates is expected to hold. Also, PPP theories can be formulated in absolute form as in equation (3), relating the level of the exchange rate to relative price levels, or in relative form, relating changes in exchange rates to changes in relative price levels. 2/ Empirical tests of these various forms of PPP provide useful information about the relationship between prices and exchange rates. However, market (or official) exchange rates would only be appropriate conversion factors for GDPs if there was evidence that PPP holds for broadly defined price indices and in the absolute form described by equation (3).

A number of empirical and theoretical studies suggest that the conditions for s=sPPP are likely to be violated frequently. 3/ While the law of one price is believed to hold for a subset of internationally traded goods such as primary commodities, Isard (1977) concludes that it is “flagrantly and systematically violated” for manufactured goods. 4/ Moreover, there is evidence that the ratio of the price levels of traded and nontraded goods differs systematically across countries and changes over time. 5/

A well known explanation for differences in the relative prices of tradables and nontradables across countries is the “productivity difference model,” which dates back to Ricardo and was developed mainly by Balassa. 6/ This model assumes that international productivity differences tend to be larger in the tradables than in the nontradables sector and that prices for tradables are determined in international markets. 7/ With marginal cost pricing, intercountry differences in factor prices reflect productivity differences in the tradables sector, while unrestricted factor mobility within each country ensures equalization of factor prices across sectors. Under these conditions, relatively high productivity in the tradables sector translates into relatively high wages and prices in the nontradables sector. 1/ The market exchange rate of a country with higher productivity than the numeraire country is thus likely to be more appreciated than the PPP rate, unless the differences in the relative prices of tradables and nontradables are fully offset by differences in their respective weights in total output. 2/

Direct empirical tests of PPP are generally based on time series data, with prices in each country expressed in the form of intertemporal indices, rather than ratios of weighted averages of prices as in equation (3). Unless the market exchange rate is known to be equal to the PPP rate in the base period, such tests cannot ascertain whether s=sPPP; they only test whether there is a one-to-one relationship between the index of s and the ratio of the corresponding price indices over time (absolute PPP), or between the changes in the index of s and the changes in the corresponding price indices (relative PPP). The evidence from these tests is mixed. 3/ There is evidence of significant short-run deviations from PPP, which are generally attributed to differences in the degree of price flexibility in goods and asset markets. 4/ Moreover, while several empirical studies confirm the validity of absolute PPP in the long run for major currencies during the 1920s, 5/ there is evidence of long-run PPP only in its relative form for major currencies during the 1970s and 1980s. 6/

To sum up, the direct empirical evidence on PPP theory indicates that market exchange rates differ frequently and for extended periods from PPP rates. Moreover, there is indirect evidence suggesting that the conditions for PPP to hold in its strong, absolute form for broadly defined price indices are generally violated. In these circumstances, market exchange rates are unlikely to be good proxies for the conversion factors that are required to offset international differences in price levels and derive real GDP data that are comparable across countries.

2. Aggregation with exchange rate based GDP weights

Notwithstanding their shortcomings, market exchange rates are widely used in comparisons and aggregations of GDPs and related economic data. The weighting system used to aggregate time series such as GDP growth rates, investment ratios, and consumer price inflation in the World Economic Outlook is based on three year moving averages of nominal GDPs converted into U.S. dollars at market or official exchange rates, which are adjusted on a case by case basis to account for apparent anomalies in levels or changes such as large discrete changes in official exchange rates or large spreads between official and secondary market rates. In the World Bank’s Global Economic Prospects and the Developing Countries 1/, growth rates of real GDP are aggregated on the basis of constant 1987 GDP weights, with GDPs in national currencies converted into U.S. dollars at the period average market exchange rate of the base year. Constant GDP weights based on market exchange rates are, in principle, also used to aggregate time series of consumer price inflation and money growth in International Financial Statistics (IFS), but weights for a given base year are applied to sub-periods of about 5 years, which are spliced to create a continuous time series. 2/

There are no well established criteria for choosing between alternative forms of exchange rate based weights; choices of base years or certain averaging procedures are thus generally based on pragmatic considerations. 3/ These largely arbitrary choices can have a significant impact on the weighting system and thus on the derived aggregates.

Table 1 illustrates how alternative exchange rate based weighting systems affect aggregate real GDP growth rates for major country groups during 1982-91. The table shows mean deviations and mean absolute deviations between the aggregates published in the World Economic Outlook of October 1991 and aggregate growth rates based on the same set of country data but alternative weighting schemes. While the differences between the aggregate growth rates at the world level and for the industrial countries are relatively small, there are considerable discrepancies between the aggregate growth rates for the developing countries as a group and, in particular, the growth rates for certain developing regions, such as the Middle East, Africa, and the Western Hemisphere. For example, the aggregate growth rate for the developing countries based on real GDP weights with 1987 as base year differs, on average, by almost one half of a percentage point from the corresponding aggregate published in the World Economic Outlook of October 1991; for the developing countries in the Middle East, these two weighting systems produce aggregate growth rates that differ on average by more than 2 percentage points. Nominal GDP weights, which are conceptually the same as current WEO weights but do not include the averaging and the case by case adjustments of the latter, yield aggregate growth rates that are significantly different from the WEO aggregates, particularly for Africa and the Middle East. With the exception of the aggregates for the Middle East, there is little evidence of systematic deviations in one direction, with most discrepancies canceling out over time. The comparison suggests, however, that the choice among alternative exchange rate based weighting systems can have significant implications for the interpretation of developments in output growth in a number of groups of developing countries.

Table 1.

Effects of Alternative Exchange Rate Based Weighting Schemes on Aggregate Real GDP Growth

(In percentage points)

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Difference between aggregate growth rates of real GDP from World Economic Outlook. October 1991, and aggregates based on the same data set and the weights indicated in the table. Mean deviations in the table refer to the arithmetic average of the deviations for the period 1982-91; means of absolute deviations refer to the arithmetic averages of the absolute deviations. The weights used in the World Economic Outlook are 3-year moving averages of U.S. dollar GDPs derived from nominal GDFs converted at market exchange rates, adjusted on an ad hoc basis, and lagged one period.

Nominal GDPs in national currencies converted into U.S. dollars at period average market exchange rates, lagged one period.

Real GDPs in national currency converted into U.S. dollars at the period average exchange rate of the base year, lagged one period,

Real GDPs of the base year converted into U.S. dollars at the average market exchange rate of the base year.

Aggregate growth rates in the World Bank’s Global Economic Prospects and the Developing Countries. May 1991 are based on constant 1987 GDP weights.

IFS aggregates of changes in consumer prices are based on constant GDP weights for subperiods (1980 weights for the period 1978-83, and average 1984-86 weights for the period 1983 onward), which are spliced at overlapping years. See, for example, International Financial Statistics. September 1991, p. 15 for a description of this weighting system.

III. GDP Weights Based on Purchasing Power Parities

1. Problems of PPP index construction

a. The international comparison program

Widespread interest in international comparisons of national incomes and the recognition that conversion factors based on market exchange rates are poor substitutes for PPPs led to the creation of the International Comparison Project, later renamed International Comparison Program (ICP), whose task was to estimate PPPs on the basis of price surveys for certain benchmark years. ICP started in the late 1960s as a joint venture of the United Nations and the International Comparison Unit of the University of Pennsylvania, with initial support from the Ford Foundation and the World Bank. 1/ Phases I and II of ICP focused on methodological issues and produced PPP-based comparisons of national incomes for a small number of industrial and developing countries for the reference years 1967, 1970, and 1973. Beginning with phase III, ICP became a regular exercise which has generated benchmark estimates of PPPs in five-year intervals for an increasing number of countries. Interest in intra-regional comparisons led to a growing regionalization of ICP during the 1980s, with regional organizations assuming a central role in ICP-related statistical work. ICP has now entered phase VI, which is to produce estimates for the reference year 1990. Current work on PPP estimation in various regional centers, including the OECD and the Statistical Office of the European Communities, is based on the methodological foundations developed in the context of ICP.

b. Desired properties of a PPP index

A PPP index is essentially a type of international price index with a particular set of desired properties. 1/ At the disaggregated level, PPP for a given pair of countries j, k refers to the ratio of prices for a well defined item i:

PPPijk=PijPik(4)

In order to determine the overall purchasing power of country j’s currency relative to that of country k, a large number of prices for individual items have to be aggregated to yield a ratio of weighted averages of prices. PPP at the level of GDP is thus a function of prices and weights:

PPPjk=f(P,W).(5)

Evidently, the resulting PPP depends on the composition of P and W, as well as on the functional form of (5). For example, if PPP is derived from weighted arithmetic averages of prices in countries j and k, weights based on quantities in country j (which would correspond to a Paasche formula) will normally yield a lower PPPjk than weights based on quantities in country k (corresponding to a Laspeyres formula). This is due to substitution effects, which typically result in widely observed negative correlations between prices and quantities, and is a well-known problem in the literature on index numbers. 2/

The core problem in constructing a PPP index is to choose the appropriate sets of prices and weights and to determine the precise form of f (P, W). In order to evaluate solutions to this problem, it is useful to consider the desired properties of a PPP index. 1/ In general, a PPP index should meet the following requirements:

-- Base country invariance. All countries included in a comparison should be treated in such a way that the resulting PPPs will be independent of the country that is chosen as the base (or numeraire) country. 2/

-- Transitivity. In a multilateral comparative study involving (at least) three countries (j, k, m), an index PPPjm multiplied by another index PPPmk should equal the index PPPjk, if this one had been calculated directly.

-- Additive (matrix) consistency. Derived quantities (in value terms) for subaggregates should be stated in such a way as to allow for comparisons across subaggregates (within one country) and across countries (within any subaggregate).

-- Characteristicity. The quantity weights used for PPP index construction should be characteristic in the sense that they should reflect the actual quantities consumed in the countries involved.

Unfortunately, it is not possible to construct a single index that satisfies all requirements simultaneously. In practice, for example, there is a tradeoff between transitivity and characteristicity. 3/ If PPPs are estimated to derive internationally comparable real GDP data, base country invariance and transitivity seem to be important properties because they ensure a unique ordering of countries according to their PPP-based GDPs. 4/ Characteristic weights are very desirable, but in worldwide comparisons characteristicity is constrained by the transitivity requirement.

In principle, a multilateral system of PPP indices can be derived from individual bilateral comparisons. To fulfill the transitivity requirement, all bilateral comparisons must be calculated using the same weights from a given base country. This approach, which has been termed the “star country method,” will result in indices that are not invariant to the choice of the base country. As a general rule, base country invariance and transitivity can only be achieved if each bilateral comparison in a multicountry framework uses information on prices and weights for all countries included in the comparison.

c. The methodology of the International Comparison Program

The approach to multilateral PPP index construction chosen by the ICP is the Geary-Khamis (GK) method 1/ which is conveniently summarized in the following sets of simultaneous equations:

πi=Σj=1nPijPPPj[qijΣj=1nqij]i=1,...,m(6)
PPPj=Σi=1mpijqijΣi=1mπiqijj=1,...,n(7)

where i denotes each of m categories of goods and j each of n countries included in the comparison, pij the price of good i in country j, qij the quantity of good i in country j, πi the international price of good l and PPPj the PPP of country j.

The basic idea of the GK approach is to express PPP for a given country j as the ratio of total expenditure valued at country j’s own prices pij to total expenditure valued at international prices πi. These international prices are in turn a weighted average of the domestic prices of all countries included in the comparison, with domestic prices converted into the currency of the numeraire country at the country’s PPP, and the weights reflecting the share of each country in the total quantity of each good. 1/ PPPs and πs can be derived simultaneously from the above system of m + n equations, using prices and quantities in individual countries as inputs. Only m + n - 1 equations of the system described by (6) and (7) are independent, and PPP for the numeraire country is set equal to 1.

In order to keep the system manageable, the number of prices included in the calculation of the PPPs needs to be limited. The ICP solution to this problem was to divide the main sub-aggregates of GDP into approximately 150 detailed categories of goods and services, 2/ and to derive prices for these categories as simple geometric averages of the prices of several well defined items. 1/ The approach may be illustrated by a matrix (M) of prices of items representing a given category: 2/

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The main problem with the derivation of a transitive system of category prices is that they should be based on the same set of items in each country, i.e., the matrix M should have no empty cells. One possible solution is to exclude all items that cannot be priced in all countries. However, this would greatly reduce the number of items considered in each category and would unduly limit the characteristicity of the results. To overcome this difficulty, the ICP developed the Country-Product-Dummy (CPD) method, which is a regression procedure for estimating the missing observations from the available price data. 1/

For certain service categories, such as general government services and education, direct price comparisons are generally not possible because market prices are not observed. In these cases, ICP has employed indirect estimation methods based on input cost, or, in some instances, on output related quantity information that has been used to derive implicit price comparisons. These methods are clearly less reliable than direct price comparisons but it is worth noting that they are also used in intertemporal comparisons where similar problems with “comparison resistant services” are encountered. 2/

With category prices and derived “notional quantities” as inputs, 1/ the GK method described by equations (6) and (7) above can be used to derive PPPs. 2/ These PPPs are expressed in terms of the numeraire country’s currency, which is usually the US dollar, but they are invariant to the choice of the base country. In addition, they fulfill the requirements of transitivity and matrix consistency. 3/ Dividing the sum of all expenditure categories valued at national prices and in national currencies by these PPPs yields expenditure valued at constant international prices (in terms of US dollars).

As noted above, beginning with the 1980 benchmark study, ICP became increasingly regionalized. 4/ While the emphasis on intra-regional comparisons (covering the European Community and the OECD area in particular) helped to enhance the characteristicity of the comparisons within a given group of countries, it was, inevitably, achieved at the cost of the quality of inter-regional comparisons. As the international prices used for the estimation of PPPs in regional comparisons are only based on prices of countries in a particular region, GDP for a given country valued at international prices can vary considerably depending on the specific region for which the analysis is carried out. 5/ In order to avoid the proliferation of conflicting results, ICP has accepted the principle of “fixity” which states that a result published for a regional comparison must remain unchanged in any other comparison including a larger set of countries. 1/ However, fixity cannot be achieved without cost. The methods developed to ensure fixity either produce the desired result only at the aggregate GDP level or result in subaggregates which meet the fixity requirement but are non-additive in the sense that the components of GDP may not add up to total GDP.

2. Intertemporal extension of benchmark data

In view of the considerable cost of benchmark studies, which require collection and processing of a large amount of price and expenditure data, it is generally not feasible to produce benchmark data on an annual basis. Time series of PPP-based real GDP thus have to be derived from extrapolated benchmark data.

GDP at constant international prices can, in principle, be extrapolated using growth rates of real GDP in national currency. However, since these growth rates represent domestic rather than international price weights, they may lead to distortions in the time series for GDP at constant international prices. In order to minimize such distortions, Summers and Heston (1988) have suggested a method that extrapolates the principal components of GDP at constant international prices on the basis of the corresponding real growth rates from national sources; these components are then aggregated to GDP at constant international prices.

A special problem arises in the case of countries for which multiple benchmark studies are available. In theory, the rate of change of GDP at constant international prices derived from two benchmark studies should be equal to the rate of change over the same period derived from the corresponding national accounts series in constant prices. In practice, this is frequently not the case, even when allowance is made for differences in methodology between individual benchmark studies. 2/ As international comparisons and national accounts data are both subject to error, Summers and Heston argue that there is no a priori reason for considering one system to be more reliable than the other. Instead of discarding information from multiple benchmark studies in favor of national accounts growth rates, they therefore applied a special procedure that ensures the consistency of the data from both sources. This procedure is based on a general errors in variables model that produces adjustment factors for national accounts growth rates as well as for benchmark data. 3/

3. Estimation of PPPs for non-benchmark countries

Cost constraints have not only precluded benchmark studies on an annual basis, they have also limited the sample of countries for which benchmark comparisons have been undertaken. Extension of the scope of PPP-based GDP data to a global system thus depends on the quality of possible “short-cut” methods for estimating PPPs for those countries that have not yet been included in benchmark studies.

One approach to generating PPPs for non-benchmark countries is to estimate a simple model of the relationship between PPPs and exchange rates for those countries for which benchmark data on PPPs are available and to use this “bridging equation” to predict PPPs for non-benchmark countries. The theoretical arguments outlined in section II.1 suggest that structural characteristics, such as relative productivity levels, may play an important role in explaining differences in the ratio of PPP to the exchange rate (real price level) across countries. In the empirical literature, real per capita GDP has been widely used as a proxy for productivity levels and indeed much of the empirical research has focused on the relationship between real per capita GDPs and real price levels. 1/ In order to use these price level equations as bridging equations, PPP-based per capita GDP has to be replaced by exchange rate based per capita GDP as the explanatory variable. Alternatively, bridging equations that include real PPP-based per capita GDP as the dependent variable and exchange rate based per capita GDP as the explanatory variable can be estimated directly. This approach was adopted in several studies by the ICP team. 2/ Estimation results for both types of bridging equations are reported in the Appendix.

In order to improve the quality of PPP estimates for non-benchmark countries, Summers and Heston have developed an approach using price data from post-adjustment surveys. 1/ While post-adjustment indices, which are based on price surveys for a special consumer basket (expatriates) in special areas (usually capital cities), are not a perfect substitute for PPPs, they are probably more closely correlated with “true” PPPs than market exchange rates. Summers and Heston estimated PPP-based GDPs for non-benchmark countries on the basis of bridging equations that include PPP-based domestic absorption as the dependent variable and absorption based on the conversion factors implicit in the post-adjustment data as explanatory variables. 2/

Table 2 examines the out-of-sample prediction properties of alternative bridging equations. For a set of countries that were included in the 1985 but not in the 1980 benchmark study, benchmark values of PPP-based per capita GDP for 1985 are compared with predictions from alternative bridging equations that were estimated for the sample of 1980 benchmark countries. 3/ Mean deviations between exchange rate based per capita GDPs and the ICP benchmark values are included for comparison. In addition, the table shows the results from an evaluation by Kravis and Lipsey (1990) of the prediction properties of bridging equations that include as explanatory variables exchange rate based data and data based on post-adjustment indices.

Table 2.

Prediction Properties of Alternative Bridging Equations

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Percentage deviations were calcuated as: ((predicted-actual)/actual)*100. Means refer to arithmetic averages for a sample of 13 developing countries that were included in the 1985 benchmark study but not in the 1980 benchmark study. The bridging equations yield predictions for 1980 PPP-based per capita GDP which were extrapolated to 1985 using the growth rates of real per capita GDP from Summers and Heston (1991).

Based on equation 1, Table 6 in the Appendix. The price level is defined as the ratio of the PPP rate to the market exchange rate. Predicted values for the price level were used to derive PPPs which then were used to convert per capita GDP in national currency.

Based on equation 6, Table 6 in the Appendix.

Based on equation 1, Table 7 in the Appendix.

Based on equation 5, Table 7 in the Appendix.

The mean absolute deviations reported here are taken from Kravis and Lipsey (1990), Table 3, who specified alternative bridging equations with PPP-based domestic absorption as the dependent, variable. These bridging equations were estimated for two subsets of the 1980 (Phase IV) benchmark countries and the results were used to predict PPP-based domestic absorption for the other subset. GDP was derived by adding the foreign balance (converted at the market exchange rate) to domestic absorption.

Three main conclusions emerge from Table 2. First, while predictions from bridging equations are subject to substantial errors, these errors are considerably smaller than the errors resulting from approximating PPPs by exchange rates. Second, while per capita GDPs converted at market exchange rates entail a marked downward bias, there is no strong bias in the predictions derived from the bridging equations with PPP-based per capita GDP as the dependent variable. Third, the information incorporated in the post-adjustment data improves the prediction properties of the bridging equations.

4. Aggregation with PPP-based GDP weights

With 5 benchmark studies completed to date, ICP has produced estimates of PPP-based GDP for 80 countries for at least one, and in most cases several, benchmark years. Extended over time and to non-benchmark countries according to the methods described above, these data represent a possible alternative to exchange rate based GDP weights.

As a result of the regionalization of ICP, worldwide comparisons have unfortunately lagged behind. In 1986, the UN Statistical Office and the EC published an international comparison based on linked regional comparisons of the 1980 benchmark study. 1/ There is, to date, no similar comparison based on the 1985 benchmark results. However, Summers and Heston have produced a worldwide comparison based on ICP’s detailed price and expenditure composition data. 2/ They have extrapolated the benchmark values according to the procedures described in section III.2 using growth from national accounts sources. In addition, they have estimated PPPs for non-benchmark countries on the basis of information on post-adjustment indices. These data are included in the Penn World Tables (PWT), the most recent of which is the Penn World Table Mark 5 (PWT5). PWT5 contains data on GDPs at constant international prices (PPP-based GDP) for 138 industrial and developing countries, with data for 80 countries based on ICP benchmark studies, including in some cases the 1985 benchmark data.

Estimates of GDP in terms of U.S. dollars, or any other common foreign currency, are particularly difficult to obtain for the formerly centrally planned economies. These countries typically used a large variety of exchange rates and special conversion factors, which made the conversion of national data into foreign currency virtually impossible. 3/ Given the difficulties of choosing among a large number of conversion factors, which bear no resemblance to market exchange rates, most attempts to derive GDPs in terms of a common foreign currency for the formerly centrally planned economies have relied on some approximation of PPPs. 4/

ICP benchmark data are available only for Hungary, Poland, and Yugoslavia for 1980. In addition, there are data for Romania from the 1975 ICP benchmark study. For Bulgaria, the Czech and Slovak Federal Republic (Czechoslovakia), and the former U.S.S.R., estimates of U.S. dollar GDP are available from a study published in 1980 by the United Nation’s Economic Commission for Europe, which is based on the physical indicators global (PIG) method. 1/ The estimates of U.S. dollar GDP for the Eastern European countries and the former U.S.S.R. in PWT5 2/ are derived from these sources, and are thus broadly similar to other published estimates for these countries, which are based on the same sources. 3/

PWT5 does not provide data for all countries but relatively few and mainly small countries are excluded. For these countries, PPP-based GDPs were estimated on the basis of equation 1, Table 7 in the Appendix. All time series on PPP-based GDPs were extended using growth rates of real GDP from the WEO data base. 4/

Table 3.

Comparison of PPP-Based GDP Weights and WEO Weights

(In percent of world GDP)

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Table 4.

Aggregate Real GDP Growth Rates Based on PPP Weights 1

(Annual changes, in percent)

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Weights based on GDPs in terms of constant international prices.

Table 5.

Differences Between Aggregate Real GDP Growth Rates Based on PPP Weights and on WEO Weights

(In percentage points)

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The resulting set of PPP-based GDP weights is complete but not perfect. Estimates derived from ICP benchmark studies cover between three quarters (PPP-based GDPs) and 90 percent (exchange rate based GDPs) of world output, but only the estimates for the industrial countries are likely to be very reliable. The estimates for the developing countries are probably subject to much larger errors, reflecting the paucity of the data in many countries, and possibly also the effects of a potential bias in the structure of the estimated international prices toward the prices of large and/or rich countries. Errors are likely to be even larger for those countries whose PPP-based GDPs are derived from relatively simple bridging equations. 1/ However, while the errors for individual countries can be substantial, there is no indication that the estimates are systematically biased. Moreover, it appears that the available estimates for the developing countries are much closer to the “true” PPP-based GDPs than data converted at market (or official) exchange rates.

Table 3 compares, for illustrative purposes, the shares in world GDP based on PPP and WEO weights for major country groups in the World Economic Outlook. The most striking difference between the two weighting schemes is that PPP-based GDPs imply a substantial increase in the weight for the developing countries. In interpreting this result it is helpful to recall the “productivity difference model” discussed briefly in Section II.1, which suggests that GDP data converted at market exchange rates generally understate the position of countries with relatively low productivity and hence low per capita income, because the market (or official) exchange rates in these countries tend to be more depreciated than the PPP rates that would eliminate differences in price levels across countries. The difference between PPP-based GDP weights and WEO weights is particularly pronounced for the developing countries in Asia, whose share in world GDP in 1990 based on PPPs is more than three times larger than in the WEO weighting system. 2/ Between 1982 and 1990, the share of the developing countries in Asia in world GDP based on PPPs increased by 6 percentage points, reflecting the fact that real GDP growth during that time was well above the world average in many countries in East and Southeast Asia. By contrast, WEO weights, which are strongly influenced by movements in real exchange rates, suggest that the share In world GDP of the developing countries in Asia actually declined during 1982-90. 1/ To illustrate the impact of PPP-based weights on aggregate real GDP growth for major country groups in the World Economic Outlook, the country data underlying the World Economic Outlook of October 1991 were re-aggregated using the set of PPP-based GDP weights described above. The results from this aggregation are summarized in Table 4. Table 5 presents the differences between these aggregates and the aggregate growth rates that were published in the World Economic Outlook of October 1991. For the years 1989-91, there is almost no difference between world real GDP growth derived from PPP-based weights and the growth rates based on current WEO weights. However, for the years 1982-88, PPP-based GDP weights yield world GDP growth rates that are generally higher than the growth rates derived from current WEO weights, with deviations averaging one half of one percentage point over the whole period 1982-91. This increase in average world GDP growth is due to the larger PPP-based GDP weight for the developing countries and the fact that these countries grew more rapidly than the industrial countries during 1982-88. In 1989-91, the growth differential between the industrial and the developing countries disappeared, and the impact of different weighting schemes on world GDP growth became negligible.

For the industrial countries as a group, the impact of PPP-based GDP weights on aggregate real GDP growth is marginal, with the exception of 1990-91. In these years, average GDP 2/ growth in the G7 countries derived from PPP-based weights is almost one half of one percentage point lower than the aggregate growth rates derived from current WEO weights, reflecting mainly differences in the relative weights of the United States and Japan. While the relative shares of both countries in total industrial country GDP are relatively stable over time when PPPs are used as conversion factors, there are large shifts in the corresponding shares in the current WEO weighting system, which is based on exchange rate conversion. In the WEO weighting system, the share of the United States in industrial country GDP declines by nearly 10 percentage points between 1986 and 1991, while the corresponding share of Japan increases by 5 percentage points. As a result, the current WEO weighting scheme implies a larger weight for Japan in 1990-91 and a lower weight for the United States than PPP-based GDP weights. As growth slowed significantly in the United States and remained strong in Japan in 1990-91, PPP-based GDP weights result in lower aggregate growth rates for both years for the G7 countries and, consequently, for the industrial countries as a group. 1/

For the developing countries as a group, PPP-based GDP weights result in substantial increases in aggregate GDP growth rates, averaging well over one percentage point in 1982-91. These increases reflect mainly a larger weight for the developing countries in Asia, many of which have been growing at considerably faster rates than the countries in other developing regions during 1982-91. Even though PPP-based GDP weights imply larger shares in world GDP for all developing regions, they only imply a larger share in total developing country GDP for Asia. For all other developing regions, the corresponding shares in total developing country GDP are smaller than in the current WEO weighting system.

IV. Conclusions

The available evidence on the relationship between exchange rates and PPPs suggests that exchange rates are poor proxies for the PPPs that are required to derive internationally comparable national income data. Even so, exchange rate based GDP weights in a variety of forms are widely used in aggregations of output growth and related economic data. The choice among these various sets of exchange rate based GDP weights is largely arbitrary, but it can have a significant impact on aggregate indicators of economic activity.

Estimates of PPP-based GDPs are a valuable alternative to conventional exchange rate based weighting systems and have been used for several years by institutions such as the EC Commission and the OECD, albeit only for industrial countries where relatively reliable PPP estimates have been available for some time. PPP estimates for many developing countries are no doubt considerably weaker, and deviations from “true” PPPs are likely to be even larger for the countries where benchmark studies are not available. However, notwithstanding these shortcomings, the PPP-based GDP weights considered in this paper are probably a better measure of real output shares than exchange rate based GDPs, which are likely to be biased due to systematic discrepancies between PPPs and exchange rates.

The PPP estimates discussed in this paper are conversion factors for GDP and related economic data. As such they are broadly defined for a whole range of prices of tradables and nontradables. They are unrelated to and should not be confused with the concept of equilibrium exchange rates. Also, PPPs are not necessarily the right conversion factors for all purposes. Conversion and aggregation of international transactions valued at current market prices, such as current account and capital flows, require conversion factors that reflect the actual price at which one currency is exchanged against another currency in foreign exchange markets, i.e. market exchange rates.

APPENDIX Bridging Equations for Non-Benchmark Countries

This appendix summarizes the results from cross section estimations of equations that relate the price level, defined as the ratio of PPP to the market (or official) exchange rate, and PPP-based per capita GDP to a few readily observable explanatory variables. These equations can be used as “bridging equations” to derive PPPs or PPP-based GDPs for countries that were not included in ICP benchmark studies. The selection of explanatory variables is based on the theoretical arguments and the empirical research summarized in section 111,3. The following variables were included:

-- Real per capita GDP, which is frequently used as a proxy for the productivity level, the main variable explaining cross country differences in price levels according to the productivity difference model. 1/ Its coefficient is expected to be positive.

-- Openness, which is defined as the ratio of exports and imports of goods and services to GDP. This variable has been found significant in explaining price levels in several studies by members of the ICP team. 2/ Kravis and Lipsey (1983) argue that, ceteris paribus, a high degree of openness tends to raise the price of the abundant factor and thus implies higher prices for non-tradables in relatively labor-abundant countries and lower prices for non-tradables in capital-abundant countries. As countries’ price levels are generally expressed relative to the price level of the United States, one of the most capital-abundant countries, the effect of the degree of openness on the price level is expected to be positive. 3/

-- Money growth, which can be relatively easily identified among the various transitory factors influencing price levels. 4/ In the context of models of exchange rate overshooting, relatively high money growth is expected to lower the ratio of PPP to the exchange rate due to a depreciation of the nominal exchange rate which is not immediately matched by a corresponding change in prices. 5/

In order to allow for the possibility of different intercepts for the industrial and the developing countries, a dummy variable for the developing countries was included in the equation that were estimated for the full sample of industrial and developing countries. Moreover, results from earlier empirical studies suggest that price levels are on average higher- - and spreads between PPP-and exchange rate-based GDPs consequently smaller- - in Africa than in other developing regions. Ideally, this phenomenon should be explained by the bridging equations, and attempts were made to incorporate variables representing factors such as exchange regimes and structural characteristics of the external sector. 1/ However, possibly due to the paucity of the data, these variables contributed much less to the overall explanatory power of the equations than a simple dummy variable for Africa.

Estimation results for the price level equations are summarized in Table 6. The equations were estimated for the two samples of countries covered by the 1980 and 1985 ICP benchmark studies, and for two samples that include only the developing countries in each benchmark study. The estimated equations explain more than two thirds of the cross country variation in price levels, somewhat less if only developing countries are considered. The coefficients of per capita GDP are significant and have the expected sign in all equations. They are also relatively stable for the majority of the equations. 2/ By contrast, the intercept is generally smaller in the equations that were estimated for the sample of developing countries only--an effect that is not fully captured by the dummy variable in the equations for the full sample. The coefficients of the variable representing openness are significant but negative, while differences in money growth do not appear to contribute to the explanation of cross country variation in price levels. 3/ The results confirm the finding of earlier studies that African countries tend to have relatively high price levels given their per capita GDPs.

Table 6.

Bridging Equations for the Price Level

(Dependent variable: In (PL))

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Notes: T-values are indicated in parentheses below the coefficients. The variables are defined as follows:PL: Price level, defined as the PPP rate divided by the market exchange rate (national currency per U.S. dollar), multiplied by 100.GDPPC: Per capita GDP in terms of U.S. dollars, derived by converting GDP in national currency at the market (or official) exchange rate.OP: Openness, defined as the ratio of exports and imports of goods and nonfactor services to GDP.M2: Annual rate of change of M2 (in percent) minus trend growth of M2, where the latter is a three-year moving average of annual rates of change of M2.DD: Dummy variable for developing countries.DA: Dummy variable for African Countries.Data sources: Price level data from Summers and Heston (1991); all other data from WEO data bank.

Table 7 summarizes estimation results for a set of equations that include PPP-based per capita GDP directly as the dependent variable. The results suggest a close relationship between exchange rate based and PPP-based per capita GDPs, but a 10 percent difference in the former would only correspond to a 6-7 percent difference in the latter, confirming earlier findings that cross country differences in per capita GDPs tend to be smaller when PPPs are used to convert GDPs into a common unit of account. The coefficient of the openness variable is only significant in the equations that were estimated for the samples of 1985 benchmark countries; its positive sign is consistent with the negative sign in the price level equations. The dummy variable for Africa is again significant in most equations. A comparison of equations with similar specifications across samples (for example, equations 2 and 6, and equations 1 and 3) suggests that the coefficients of the main explanatory variable do not vary significantly.

Table 7.

Bridging Equations for PPP Based per Capita GDP

(Dependent variable: In (RGDPPC))

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Notes: T-values are indicated in parentheses below the coefficients. RGDPPC is PPP-based per capita GDP from Summers and Heston (1991), defined as per capita GDP valued at constant 1985 international prices. For definitions and sources of all other variables see notes to Table 6.

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