AN INDEX NUMBER APPROACH TO THE INTERNATIONAL COMPARISON OF CONSUMPTION: WESTERN EUROPE AND THE UNITED STATES*

Yasushi Toda

Review of Income and Wealth, 1971, vol. 17, issue 4, 353-362

Abstract: The quantity index comparing the per capita consumption of one country vis‐à‐vis the other often gives widely different figures, depending on which country's prices are used as “weights”. In this paper, this gap between two quantity indexes is divided into a substitution effect and an income effect by assuming common tastes between nations. For this division, we estimate the points of over‐compensated variation and under‐compensated variation in income from Gilbert and Kravis’data. The results of our estimation show that the income effect is smaller than the substitution effect. But the sign of the income effect indicates that this effect is generally in the same direction as the difference between two quantity indexes. Translated into the Bortkiewicz covariance, this means that the income elasticities are inversely related to the relative prices; the higher the income elasticity of a good, the lower is its price in the high income country relative to the low income country. Since we only approximate the points of exactly compensated variation in income, we cannot estimate “true” quantity indexes. However, our result implies that the two indexes in Gilbert and Kravis’data do form the upper and lower boundaries to the true index‐numbers.

Date: 1971
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