Definition: Additivity

Purchasing power parities

The values of the national accounts aggregates of countries participating in a comparison are equal to the sum of the values of their components when both aggregates and components are valued at current national price levels. Additivity requires this identity to be preserved when the values of the aggregates and their components are valued at international price levels. An aggregation method is additive if, for each country being compared, it provides real values for aggregates that are equal to sum of the real values of their constituent basic headings. An additive aggregation method provides volumes that satisfy the average test for volumes but are subject to the Gerschenkron effect (2012 Methodological manual on purchasing power parities).

The values of the national accounts aggregates of countries participating in a comparison are equal to the sum of the values of their components when both aggregates and components are valued at current national prices. Additivity requires this identity to be preserved when the values of the aggregates and their components are valued at international prices. An aggregation method is additive if, for each country being compared, it provides real values for basic headings that sum to the real values of the aggregates of which they are components. An additive aggregation method provides volumes that satisfy the average test for volumes (2005 Methodological manual on purchasing power parities).

A very similar definition is applied in the Consumer Price Index Manual (2004):

At current prices, the value of an aggregate is identical to the sum of the values of its components. Additivity requires this identity to be preserved for the extrapolated values of the aggregate and its components when their current values in some period are extrapolated using a set of interrelated quantity indices; or, alternatively, when the current values of an aggregate and its components in some period are deflated using a set of interrelated price indices.
Source:
Eurostat, Organization for Economic Cooperation and Development (OECD), "Eurostat-OECD Methodological Manual on Purchasing Power Parities", Publications Office of the European Union, Luxembourg, 2012
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