Selected problems of index theory in international comparisons of GDP

The article presents issues of the theory of price and quantum indices used in the international multilateral comparisons of GDP at purchasing power parities carried out by the World Bank in accordance with the decision by the UN Statistical Commission. It applies to the following indices: Fisher, EKS, Geary-Khamis and Walsh. Relative advantages and limitations of these indices have been discussed for decades on different forums and on pages of special literature including SNA 1993 and SNA 2008. However, this discussion can hardly be considered finished due to the complexities of these problems and the need to dig deep into the essence of somewhat opposite points of view of the experts (R.Stone,I.Krevis,P.Hill, E.Dievert). The author reviews the major tests of axiomatic theory of indices such as: transitivity, additivity, factor reversal, base country invariance, etc., as well as the degree to which they are satisfied to the above mentioned indices. In this context it is noted that in international comparisons of GDP the difference between Laspeyres and Paashe indices are much larger as compared with traditional indices and this complicates economic interpretation of Fisher index (averaging Laspeyres and Paashe indices), which above all does not satisfy the requirements of additivity. For illustration purposes are presented the figures from international comparison of national income of the USSR and other countries of the Council of Mutual Assistance and Cooperation for 1988. The author also draws a conclusion that the difference in economic potentials between these countries was very substantial and therefore the span between Laspeyres and Paashe indices was very significant as well. The attractiveness of Geary-Khamis formula is argued. The basis of it is formed by the valuation of GDP of countries at average international prices; this formula is satisfied by the major tests of axiomatic theory of indices. One of the advantages of this formula, in the author's opinion, is that the use international prices in comparative analysis have clear economic interpretation.

аксиоматическая теория, транзитивность, аддитивность, тест, сопоставление, ограничение, индекс Фишера, axiomatic theory, transitivity, additivity, test, comparison, limitation, Fisher index

1. Ершов Э.Б. Ситуационная теория индексов цен и количеств. - М.: РИОР, 2011.

2. Сергеев С.М. Экономическая статистика: учебник для вузов. Глава по международным сопоставлениям ВВП. -М.: Инфра-М, 2016.

3. Diewert W.E. Axiomatic and economic approaches to international comparisons. A chapter in «International and Interarea Comparisons of Income, Output, and Prices», Alan Heston and Robert E. Lipsey editors; University of Chicago Press, 1999.

4. Kravis I.B., Heston A.W., Summers R. World Product and Income, International Comparison of Real Gross Product, Baltimore: John Hopkins University Press, 1982.

5. Krevis I., Heston A., Summers R., Kenessi Z. A system of international comparisons of gross product and purchasing power. World Bank, 1975.

6. Sergeev S. Aggregation methods on the basis of structural international price. Joint World Bank - OECD Seminar on PPPs «Recent Advances in Methods and Applications» (Woshington, D.C., 30.01-02.02.2001).

7. Stone R. Quantity and price indexes in national accounting, OEEC, 1956.

8. Hill P. Multilateral Measurements of Purchasing Power and Real GDP. SOEC, Luxembourg, 1982.