M15: PPP Aggregation
Objectives of Module 15
By the end of this module, we will understand what PPP aggregation entails.
PPP Aggregation
Once the elementary PPPs are estimated, typically at the level of basic headings, the next step is the
aggregation to obtain PPPs above the elementary level.
Aggregation is done through averaging the elementary PPPs, or basic heading PPPs, and using the
national account expenditures as weights for each basic heading.
For example, the basic heading PPPs for “rice”, “cereals” and “bread” are aggregated to arrive at the
PPPs for the “bread and cereals” aggregate. Similarly, all household consumption-related basic heading
PPPs are aggregated to arrive at PPPs for household consumption.
In order to conduct the aggregation, a matrix of PPPs and a matrix of national accounts expenditures
weights are required.
The aggregation of basic heading PPPs is undertaken for each classification level separately, up to the
level of GDP.
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M15: PPP Aggregation
Methods for Aggregation of PPPs
Similar to the case of elementary PPPs, several methods exist to aggregate PPPs above the basic heading
level.
Commonly used methods are the GEKS method or “Gini-Éltető-Köves-Szulc”, the IDB method or
“Iklé‐Dikhanov‐Balk” and the GK method or “Geary‐Khamis”.
One of main differences between these methods is additivity. Additivity means that the total equals to
the sum of the components. GK and IDB methods are additive, while GEKS is not.
Additive methods such as GK, and to a lesser extent IDB, are subject the Gerschenkron‐effect. This
effect narrows the gap between high income countries and low income countries in terms of real
expenditures, and, as a result, poorer countries tend to have higher real expenditures in comparison to
methods that are free from the Gerschenkron‐effect.
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M15: PPP Aggregation
Choosing the Method
Selection of the aggregation method depends on the intended use of the estimates.
GEKS is preferred when comparison of real expenditures between the countries has priority.
IDB and GK methods are preferred when additive, internally consistent, real expenditures are needed.
The ICP uses the GEKS method as the official aggregation method.
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M15: PPP Aggregation
Knowledge Check
Let’s see how we are doing by answering this question and click submit.
Aggregation of PPPs Using GEKS Method
GEKS PPPs are obtained by taking a geometric mean of direct and indirect Fisher PPPs. Let’s break this
down to understand each step involved.
Fisher PPPs
Fisher PPPs are obtained by taking the geometric mean of the Laspeyres PPPs and Paasche PPPs.
Hence, in mathematical terms, for any two countries j and k, the Fisher PPPs are computed as shown.
The Laspeyres part of the formula is a weighted arithmetic average of basic heading PPPs, weighted by
expenditures of a country represented here as “k”.
The Paasche part of the formula is a harmonic average of basic heading PPPs, weighted by expenditures
of a country represented here as “j”.
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M15: PPP Aggregation
GEKS PPPs
It is important to note that the resulting Fisher PPPs are intransitive.
As we learned earlier, transitivity is the property where the direct PPP between each pair of countries is
equal to the indirect PPP derived via any third country. For example, in the case of the three countries A,
B and C, the ratio of the PPP between A and B and the PPP between C and B is equal to the PPP between
A and C.
A direct PPP is a PPP between two countries calculated using only the prices and weights for those two
countries. An indirect PPP is a PPP between two countries obtained by calculating it indirectly through a
third country.
In mathematical terms, the GEKS PPPs are calculated as shown here.
GEKS formula achieves transitivity by estimating the PPP between any pair of countries as a geometric
mean of direct Fisher type PPPs and indirect Fisher type PPPs.
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M15: PPP Aggregation
Aggregation of PPPs using GEKS Method (2)
The resulting GEKS PPPs are base country invariant, transitive and free of the Gerschenkron effect.
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M15: PPP Aggregation
Additional Resources
The following resources provide useful information for this module.
“Ch. 4 Methodologies Used to Calculate Regional and Global PPPs” in Purchasing Power
Parities and the Real Size of World Economies: A Comprehensive Report of the 2011
International Comparison Program“
“Elementary Aggregation Using the Country Product Dummy (CPD) Method” and “PPP
Aggregation above the Basic Heading Level Using the GEKS Method” in Operational
Guidelines and Procedures for Measuring the Real Size of the World Economy: 2011
International Comparison Program (ICP)
“Methods of Aggregation above the Basic Heading Level within Regions” in Measuring the
Real Size of the World Economy: The Framework, Methodology, and Results of the
International Comparison Program (ICP)
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