10.68 Comparisons of prices and volumes between countries have to overcome the difficulty in comparing different national currencies. Since exchange rates are neither sufficiently stable for this purpose nor do they reflect differences in purchasing power in a correct way, it is necessary to use a methodology similar to the one used for intertemporal comparisons between different periods within a single country. Price and volume indices have therefore to be compiled between pairs of countries, applying the same kinds of index number formulae as when measuring changes between time periods. Either of the two countries A and B can be used to give the weights and, viewed from the angle of country A, a Laspeyres-type index with weights from country A can be calculated as well as a Paasche-type using weights from country B.
10.69 If the economies of the two countries differ much from one another, the spread between these two indices may be quite large and the results would depend too much on which one is chosen. For binary comparisons the ESA therefore requires an average between the two, in the form of a Fisher index.
10.70 Direct quantitative comparisons between economic situations that have little in common with each other are inherently difficult and the method of deflation of current values with price indices is therefore the best alternative. This applies even more in international than in intertemporal comparisons. By careful specification and identification of products, price relatives can be calculated from information collected in price surveys in each country. As prices are quoted in national currencies, the interpretation of the price relatives introduces the concept of Purchasing Power Parity (PPP). For a given product the PPP between two currencies of countries A and B is defined as the number of units of country B's currency that are needed in country B to purchase the same quantity of the product as one unit of country A's currency will purchase in country A. PPPs for groups of products and successively higher levels of aggregation up to GDP are obtained by weighting PPPs for products by their share in expenditure. In order to arrive at a price level index between the two countries, the PPP index has to be divided by the current exchange rate between the two currencies concerned.
10.71 For non-market services, international comparisons face the same problem as intertemporal comparisons. This means that outputs are measured as the sum of inputs. The method used at present in interspatial comparisons is to obtain PPPs on the basis of price relatives for important elements in these inputs. This method, which implies volume comparisons of inputs, fails to take into account differences in productivity in non-market service production in the countries compared. It is important, therefore, to develop methods which instead lead to comparisons of the volume of output of non-market services. This should in principle be feasible for individual non-market services, in the same general way as when intertemporal comparisons are concerned.
10.72 The need to make international comparisons of prices and volumes between countries is recognised in the ESA. The main objective is volume comparisons of GDP and its uses and the condition of transitivity must be met. Transitivity means that the direct index for country C based on country A is equal to the indirect index obtained by multiplying the direct index for country B based on country A by the direct index for country C based on country B.
10.73 The approach adopted in the ESA to the calculation of a set of multilateral volume mea-sures and PPPs is to start from binary comparisons between all possible pairs of countries considered. The Fisher indices used for this purpose are not transitive, but it is possible to derive from them a set of transitive indices that resemble the original Fisher indices as closely as possible, using the traditional criterion of least squares for this purpose. Minimising the deviations between the original Fisher indices and the desired transitive indices leads to the so-called EKS formula.
10.74 The EKS index utilises all the indirect indices linking country i to country k as well as the direct index between them. Between countries i and k it is the geometric mean of the direct index between i and k and every possible indirect index connecting countries i and k. The direct index is given twice the weight of each indirect index. Transitivity is achieved by involving every other country in the EKS index for any given pair of countries.