## World Comparison Real Gross Domestic Product and Purchasing Power

### GLOSSARY

Aggregates of basic headings: Any aggregation of groups of basic headings, like Bread and cereals, up to GDP Also termed summary or analytical categories.

Base-country invariance: The index-number property that involves the symmetrical treatment of all countries, with the result that the relative index-number standings of the countries are not affected by the choice of the reference (numeraire) country.

Basic headings: The subdivisions of final expenditure which correspond to the first aggregation of price (or quantity) ratios for individual specifications or items. Basic headings are sometimes referred to as detailed categories.

Binary comparison: A price or quantity comparison between two countries that draws upon data for only those two countries. Also called bilateral comparisons.

Bridge-country binary comparison: A price or quantity comparison between a pair of countries derived from the comparison of each country with a third country. For example, given Ij/k and Ii/k, the bridge-country method of obtaining Ij/1 is to divide Ij/k by litk where I is a price or quantity index and j, k, and I are countries. This is a common way of linking through a country, as in the case of the Group II countries in Europe, where Austria has served as the bridge country.

Characteristicity: The property whereby the sample of prices or quantities and the weights used in an international comparison conform closely to a representative sample of items and to the weights of each of the countries included in the comparison.

Circularity or transitivity: The property of indices when the price or quantity relationship among any two of three countries is the same, whether derived from an original-country comparison between them or from the comparison of each country with any third country. In the case of three countries, where I is a price or quantity index and j, k and I are countries, the circularity test is satisfied if Ij/k = Ij/i /Ik/i. When this test is satisfied, there is a unique cardinal scaling of countries with respect to relative quantities and prices.

Comparative price level: A comparative price level is defined as the purchasing-power parity divided by the exchange rate. (See Purchasing-power parity.) Expressed another way, the comparative price level for a bundle of goods is its cost in one country as a per cent of the cost of the same bundle in another country, when prices in both countries are expressed in a common currency, with the official exchange rate being used for currency conversions.

Consumption Expenditures of the Population (CEP): The ICP concept of "consumption", which includes both household expenditures and expenditures of government on such categories as health and education.

Country-product-dummy (CPD) method: A generalized bridge-country method in which regression analysis is used to obtain transitive price comparisons for each basic heading. The basic data for a given category consist of all the prices available for the various specifications for the entire collection of countries. The basic assumption is that within a given basic heading for a given country, the price of an item depends in a multiplicative way on a country factor and a price factor to be estimated from the sample of item-country prices in each heading. It follows from this that the logarithms of the prices are regressed against two sets of dummy variables: one set contains a dummy for each specification; the second set, a dummy for each country other than the numeraire country. The transitive price comparisons are derived from the coefficients of the country dummies.

Direct price or quantity comparison: Made by comparing for two or more countries the prices or quantities for a representative sample of equivalent commodities.

ECP: European Comparison Programme, the set of ICP comparisons for Europe carried out under the auspices of the Economic Commission for Europe. In the 1985 comparison the ECP was built on the EEC and part of the OECD comparisons and a group of Eastern European countries for which Austria served as the centre for a set of binary comparisons (referred to as "Group II").

EKS method: A multilateral method developed by Elteto, Koves and Szulc that computes the nth root of the product of all possible Fisher indices between n countries. It has been used at the detailed heading level to obtain heading parities, and also at the GDP level as a method of aggregation. EKS has the properties of base-country invariance and transitivity.

Fixity: The practice of fixing the results of an ICP aggregation for a country group when the country group is compared with a larger group. For example, the relation of France and Italy as given by Geary-Khamis or EKS for the 12 EEC countries would be fixed so that within the OECD, the France-Italy relationship would be preserved.

Geary-Khamis (G-K) method: An aggregation method in which category "international prices" (reflecting relative category values) and country PPPs (depicting relative country price levels) are estimated simultaneously from a system of linear equations. Has the properties of base-country invariance, matrix consistency and transitivity.

Government Final Consumption Expenditure (GFCE): The SNA concept of "government", which includes public expenditures on education, health and similar categories. The ICP uses a different approach; see Public Final Consumption Expenditure.

Gross capital formation (GCF): The ICP concept of gross capital formation includes fixed capital formation, change in stocks, and net exports. Definitions of these three components correspond to SNA concepts, although the SNA does not include net exports in its definition of the GCF.

Indirect price or quantity comparison: A comparison made by dividing the price or quantity ratio into the expenditure ratio. That is, the indirect quantity comparison between country j and country k for commodity i, qij/qik, is obtained from (pijqij/Pikqik)/ (Pij/Pik) = qij/qik, where the ps are the commodity prices.

International price (ni): The international price of basic heading i, is defined as a quantity-weighted average of the purchasing-power-adjusted parities at the basic heading level across the n countries.

Multilateral comparison: A price or quantity comparison of more than two countries simultaneously that

produces consistent relations among all pairs; that A, one that satisfies the circular test or the transitivity requirement.

Nominal expenditures: Expenditures in national currencies converted to a common currency at exchange rates.

Numeraire: Usually the currency unit of one country is chosen as numeraire for expressing real expenditures and PPPs. The CPD, EKS and Geary-Khamis procedures are all invariant as to which country is the numeraire or base. The numeraire may also be the average of a group, as has been the case in the EEC and the African comparisons.

Private Final Consumption Expenditure (PFCE): The SNA concept of "consumption", which excludes public expenditures on education, health and similar categories. The ICP uses a different approach; see Consumption Expenditure of the Population.

Public Final Consumption Expenditure (PFC): The ICP concept of "government", which excludes public expenditures for education, health and similar categories.

Purchasing-power parity (PPP): The number of currency units required to buy goods equivalent to what can be bought with one unit of the currency of the base country or with one unit of the common currency of a group of countries. Also referred to as Purchasing Power Standard. The PPP may be calculated over all of GDP, but also at levels of aggregation, like capital formation.

Real product or real quantity: The final product or quantity in two or more countries that is valued at common prices and, therefore, valued in comparable terms internationally.

Region alization: The practice of building up world ICP comparisons on the basis of comparisons carried out in various country groupings like the EEC or ESCAP.

Representativeness: A term used to describe how characteristic a particular item is of the types of goods and services included in a basic heading.

Specification: A description of an item for which a price comparison is to be made. The description is designed to ensure that goods of equivalent quality are compared. The terms "item" and "specification" are used interchangeably.

Transitivity requirements: See Circularity or transitivity.

United Nations Statistics Division - International Comparison Programme