# Definition: Eltetö-Köves-Szulc method

## Purchasing power parities

The method used by Eurostat and the OECD to calculate PPPs (Purchasing power parities) for basic headings and to aggregate basic heading PPPs to obtain PPPs for each level of aggregation up to and including GDP (Gross domestic product). Strictly speaking, the EKS is a procedure whereby any set of intransitive binary index numbers are made transitive while respecting characteristicity. The procedure is independent of the method used to calculate the intransitive binary indices. But in the manual, EKS covers both the way the intransitive binary PPPs are calculated and the procedure to make them transitive and multilateral. Basically, the method used to obtain the intransitive binary PPPs for a basic heading or aggregate involves calculating first a matrix of Laspeyres type PPPs, then a matrix of Paasche type PPPs and finally, by taking the geometric mean of the two, a matrix of Fisher type PPPs. The Fisher type PPPs are made transitive and multilateral by applying the EKS procedure which involves replacing the Fisher type PPP between each pair of countries by the geometric mean of itself squared and all the corresponding indirect Fisher type PPPs between the pair obtained using the other countries as bridges. The resulting EKS PPPs provide real expenditures that are not subject to the Gerschenkron effect but nor are they additive. Within the context of Eurostat and OECD comparisons, EKS results are considered to be better suited to comparisons across countries of the price and volume levels of individual aggregates. EKS results are the official results of Eurostat and OECD comparisons. See also "Laspeyres type PPP" and "Paasche type PPP" because their formulation depends on whether they are being used to calculate basic heading PPPs or to aggregate basic heading PPPs. Note that there are two versions of the EKS at the basic heading level: one that takes account of the representativity of the products priced and one that does not. Throughout the manual, unless stated otherwise, EKS refers to the version that takes the representativity of products into consideration (2012 Methodological manual on purchasing power parities). The Eltetö-Köves-Szulc method (EKS method) is the method used by Eurostat and the OECD to calculate PPPs for basic headings and to aggregate basic heading PPPs to obtain PPPs for each level of aggregation up to and including GDP. Strictly speaking, the EKS is a procedure whereby any set of intransitive binary index numbers are made transitive while respecting characteristicity. The procedure is independent of the method used to calculate the intransitive binary indices. But in the manual, "EKS" covers both the way the intransitive binary PPPs are calculated and the procedure to make them transitive and multilateral. Basically, the method used to obtain the intransitive binary PPPs for a basic heading or aggregate involves calculating first a matrix of Laspeyres type PPPs, then a matrix of Paasche type PPP and finally, by taking the geometric mean of the two, a matrix of Fisher type PPPs. The Fisher type PPPs are made transitive and multilateral by applying the EKS procedure which involves replacing the Fisher type PPP between each pair of countries by the geometric mean of itself squared and all the corresponding indirect Fisher type PPPs between the pair obtained using the other countries as bridges. The resulting EKS PPPs provide real final expenditures that are not additive, nor subject to the Gerschenkron effect. Within the context of Eurostat-OECD comparisons, EKS results are considered to be better suited to comparisons across countries of the price and volume levels of individual aggregates. EKS results are the official results of Eurostat-OECD comparisons. See also "Laspeyres type PPP" and "Paasche type PPP" because their formulation depends on whether they are being used to calculate basic heading PPPs or to aggregate basic heading PPPs (2005 Methodological manual on purchasing power parities).

**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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