VI Purchasing Power Parity Based Weights for the World Economic Outlook Anne Marie Guide and Marianne Schulze-Ghattas1 lobal economic analyses generally involve the This study provides background information on Gaggregation of economic indicators across the new set of weights introduced in the May 1993 countries. In many instances, aggregates are World Economic Outlook. It reviews GDP weights defined as weighted averages of indicators for indi- based on market (or official) exchange rates and vidual countries, with the weights reflecting the rel- weights based on available estimates of PPPs and ative size of countries.2 A widely employed examines their impact on indicators of aggregate approach is to define countries' weights as their real GDP growth. The first section, which deals shares in total GDP of the group considered.3 To with exchange rate based GDP weights, provides a ensure that GDP weights reflect each country's brief summary of the empirical evidence on the share in real output, differences in price levels relationship between exchange rates and PPPs and across countries need to be taken into account. The discusses the implications of aggregating growth conversion factors used to convert data expressed in rates of real GDP with different sets of exchange national currencies into a common numeraire cur- rate based GDP weights. The study then examines rency should thus reflect each currency's purchasing an alternative weighting scheme derived from PPP- power relative to the numeraire currency.4 based GDP data generated by the International 5 For practical reasons, GDP data expressed in Comparison Program (ICP). It briefly summarizes problems of PPP index construction and the main national currencies are usually converted at market 6 exchange rates. Such conversions may be accept- features of the ICP approach. It also discusses able as long as differences between market rates and issues relating to the intertemporal extension of purchasing power parities (PPPs) are likely to be PPP-based GDP data that are available only for small and transitory. However, if market exchange individual benchmark years, and issues relating to rates diverge substantially and for extended periods the estimation of PPPs for nonbenchmark countries. from PPPs, conversion at market exchange rates Aggregate growth rates of real GDP derived from may yield biased GDP weights and, hence, biased PPP-based GDP weights are then compared with indicators of aggregate economic activity in groups aggregates derived from exchange rate based GDP of countries. weights. The concluding section contains a sum- mary of the main findings. 'Ms. Guide was a summer intern in the Research Department The PPP-based GDP weights used in this study of the IMF when an earlier draft of this study was prepared; she are derived from the Penn World Tables prepared by is now an economist in the European I Department. The authors are indebted to Prof. Robert Summers at the University of Summers and Heston (1991), which combine data Pennsylvania for valuable comments and for making available from four ICP benchmark studies covering 80 coun- the Penn World Tables, which contain national income data tries with estimates for a large number of non- based on purchasing power parity for more than 130 countries. benchmark countries. These estimates for non- They also wish to acknowledge comments and suggestions from other IMF departments, and to thank Peter Clark, David benchmark countries were supplemented by World Bank and IMF staff estimates and an independent T. Coe, Flemming Larsen, and Kenneth S. Warwick for com- 7 ments, and Sheila Bassett, Mandy Hemmati, and Prem Pillai estimate for China. The authors wish to emphasize for research assistance. indicators that are additive and expressed in a common unit 5The ICP is coordinated by the United Nations and is sup- of account, such as current account balances, can readily be ported by a number of other international agencies. aggregated by summing up individual country data. 6A detailed review of methodological problems encountered 3 Other weights can be used to aggregate economic indica- in the construction of PPP indices is beyond the scope of this tors. Weights based on population shares, for example, are paper. See United Nations, Statistical Office (1991), Kravis and discussed in World Bank (1991), Appendix B. The choice others (1975), and Kravis, Heston, and Summers (1982) for a among alternative weighting schemes depends ultimately on discussion of these issues. the focus of the analysis. 7Summers and Heston (1991), World Bank (1992), Guide 4Comparisons and aggregation of economic data across and Schulze-Ghattas (1992), and Taylor (1991). Professors countries are also complicated by other problems, such as dif- Summers and Heston have been associated with ICP for nearly ferences in definition and coverage. two decades. 106 ©International Monetary Fund. Not for Redistribution GDP Weights Based on Exchange Rates that the following review of PPP estimates focuses If all goods are tradable, the PPP rate can be on their use as conversion factors and does not bear defined as on issues relating to equilibrium exchange rates. GDP Weights Based on Exchange Rates Exchange Rates and Purchasing Power Parities Comparison and aggregation of real GDPs across countries would pose less of a problem if market (or assuming that the arbitrage condition described by official) exchange rates were equal to the ratios of equation (1) holds. According to equation (2), the the weighted averages of prices (at the level of market exchange rate s is equal to the PPP rate, GDP) in the respective countries relative to a base Sppp, if at = af; that is, if the weights are the same country. In this case, price levels, defined as the in both countries. weighted average of prices (at the level of GDP) In the presence of nontradables, assuming that expressed in a common unit of account, would be the law of one price holds for all tradable goods, the the same in all countries. Converting GDPs in PPP rate can be defined as terms of current domestic prices and national cur- rencies 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 where 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.8 PPP theories of exchange rate determination describe an equilibrium relation- ship between prices and exchange rates without and similarly for P% and Pf. The share of nontrad- specifying the mechanisms that bring about this ables in total output is represented by a. If some 9 goods are nontradable, the market exchange rate s is relationship. They are based on the notion that in a the absence of transportation cost and trade bar- only equal to the PPP rate, sPPP, if (PN/PT) = (P$/P$)a*, that is, if the relative prices and shares riers, the law of one price ensures that the prices of 10 homogeneous goods are equalized across countries: of nontradables are the same in both countries. Not all PPP theories of exchange rate determina- tion refer to the concept of PPP described by equa- tion (3). PPP theories can be formulated in absolute form, as in equation (3), relating the level of the where where exchange rate to relative price levels, or in relative form, relating changes in exchange rates to changes Pi = Pi = the price of good /; and 11 = in relative price levels. Also, PPP theories differ s the market exchange rate defined as units in the definition of the price level and the time hori- of domestic currency per unit of foreign zon for which the equilibrium relationship between currency. prices and exchange rates is expected to hold. Empirical tests of these various forms of PPP pro- Variables relating to the foreign country are marked vide useful information about the relationship with an "*." between prices and exchange rates. However, mar- ket (or official) exchange rates would be appropriate conversion factors for GDPs only if there was evi- 8See, for example, Officer (1976b), Levich (1985), Dorn- 10McKinnon (1979) discusses the conditions that must be met busch (1989), Isard (1988), and Mussa (1990) for surveys of for PPP to hold for the overall price level. the literature. 11 See Officer (1976b) for a discussion of various forms of 9This point is emphasized in Frenkel (1981). PPP theories. 107 ©International Monetary Fund. Not for Redistribution VI PURCHASING POWER PARITY BASED WEIGHTS FOR WORLD ECONOMIC OUTLOOK dence that PPP holds for broadly defined price nontradables are fully offset by differences in their indices and in the absolute form described by equa- respective weights in total output.18 tion (3). Direct empirical tests of PPP are generally based A number of empirical and theoretical studies on time-series data, with prices in each country suggest that the conditions for s = sPPP are likely expressed in the form of intertemporal indices to be violated frequently.12 Although the law of rather than ratios of weighted averages of prices as one price is believed to hold for a subset of inter- in equation (3). Unless the market exchange rate is nationally traded goods, such as primary com- known to be equal to the PPP rate in the base modities, Isard (1977, p.942) concludes that it is period, such tests cannot ascertain whether s = "flagrantly and systematically violated" for manu- SpPP\ they only test whether there is a one-to-one factured goods.13 Moreover, there is evidence that relationship between the index of s and the ratio of the ratio of the price levels of traded and nontraded the corresponding price indices over time (absolute goods differs systematically across countries and PPP), or between the changes in the index of s and changes over time.14 the changes in the corresponding price indices (rela- tive PPP).