PPP Calculation and Estimation

Imputing PPPs for non-benchmark economies

Price relatives are first computed for individual items within each basic heading for each pair of economies being compared. Basic headings are the lowest aggregation level in the ICP expenditure classification for which explicit national accounts expenditure weights can be estimated. Elementary purchasing power parities (PPPs) are then calculated for each basic heading based on these price relatives. They are subsequently aggregated to calculate PPPs for each classification aggregate.

Suppose three economies—A, B, and C—price two kinds of rice under the rice basic heading. For each kind of rice, there are three price relatives: PB/PA, PC/PA, and PC/PB. The basic-heading PPP for each pair of economies can be computed directly by taking the geometric mean of the price relatives between them for the two kinds of rice. This is a bilateral comparison. The PPP between economies B and A can be computed indirectly: PPP C/A × PPP B/C = PPP B/A. The use of both direct and indirect PPPs is a multilateral comparison. This means that the PPPs between any two economies are affected by their respective PPPs with other economies in the comparison. As a result, a change in the mix of economies included in the comparison will also change the PPPs between any two economies.

Different methods can be used to compute multilateral PPPs. The choice of method is based on two basic properties: transitivity and base country invariance. PPPs are transitive when the PPP between any two economies is the same whether it is computed directly or indirectly through a third economy. PPPs are base country invariant if the PPP between any two economies is the same regardless of the choice of base economy.

Another property underlying the computational steps to obtain International Comparison Program (ICP) PPPs is that economies are treated equally regardless of the size of their gross domestic product (GDP). However, this property does not satisfy the additivity requirement. Additivity occurs when the sum of the real expenditures of the basic headings constituting an aggregate equals the real expenditures based on the PPPs for the aggregate. Additive methods have the disadvantage of giving more weight to the relative prices of the larger, more developed economies. As a result, the real expenditures of poor economies become artificially larger and move closer to the real expenditures of rich economies. This is known as the Gerschenkron effect. For the uses of ICP PPPs, such as for poverty analysis, non-additive methods that avoid the Gerschenkron effect are preferred.

Fixity is yet another concept that determines the methods used. The fixity concept means that the relative volume—the ratio of real expenditures—between any pair of economies in a region remains the same after the regional results have been combined into a set of global results including all economies.

Elementary PPP calculation

The PPP estimation process begins with the participating economies collecting prices for items chosen from a common list of precisely defined items. These common lists include both regional items, priced in a specific region, as well as global items, priced in all ICP regions. These two sets of prices cover the whole range of final goods and services included in GDP: household consumption expenditures, government consumption expenditures, and gross capital formation expenditures.

Two basic methods are used in the ICP to calculate basic-heading PPPs. The first approach is based on the Jevons index made transitive by the Gini-Éltető-Köves-Szulc (GEKS) method, which transforms bilateral PPPs into multilateral PPPs. The other method uses a regression model known as the country product dummy (CPD) method, which directly estimates PPPs that are transitive and base-country invariant in one step. The results obtained by both methods are the same if every economy prices every item. Both methods can be modified to include weighting at the item level.

Reference PPPs

For some basic headings, expenditure data exist, but price collection is considered too expensive or time-consuming or the price data are unreliable. For these basic headings, reference PPPs are used, and they can be categorized as follows:

Price-based reference PPPs, specific or neutral
Market exchange rate reference PPPs.

Price-based reference PPPs form the majority of all reference PPPs used. They are based on the PPPs of other basic headings for which prices were collected. These PPPs are referred to as specific reference PPPs. They may be the PPPs for a single basic heading or an average of the PPPs for several basic headings.

Market exchange rate reference PPPs are used for the following four basic headings: net purchases abroad, acquisitions less disposals of valuables, exports of goods and services, and imports of goods and services.

PPP aggregation

Once PPPs are computed for each basic heading for all participating economies within a region, they are used as inputs for the higher levels of aggregation using the GEKS method. Basic heading PPPs are first weighted using economy A’s weights (Laspeyres index), and then weighted again using economy B’s weights (Paasche index). Each index provides a weighted average of the PPP between economies A and B. To maintain symmetry, the geometric mean is taken of the two aggregated PPPs for every pair of economies in the comparison. The result is a Fisher index. For each pair of economies, the multilateral GEKS PPP is the geometric mean of the direct and indirect Fisher indexes.

PPP linking

At the global level, regional PPPs are linked to form a global set of PPPs and measures of price and volume relatives. In order to link the regional basic-heading PPPs for each participating economy, interregional linking factors are calculated based on the prices of global items collected in all ICP regions.

The GEKS aggregation method, with further redistribution of regional volumes in accordance with an economy’s regional volume shares (known as the country aggregation with redistribution [CAR] procedure), is used to obtain real expenditures (hereafter referred to as volumes) and aggregated PPPs with regional fixity. All economies in the standard ICP regions participated simultaneously and equally in the global aggregation using the GEKS method.

Imputing PPPs for non-participating economies

Although non-participating economies account for a small share of the world economy and world population, it is important that they be included in any comprehensive measurement of the size of the world economy or of global poverty.

The method used for imputing PPPs for nonparticipating economies uses two regression models, one based on the price level index (PLI) for GDP and the other based on the PLI for individual consumption expenditure by households, including non-profit institutions serving households (NPISHs). The two regressions are estimated jointly using the “seemingly unrelated regression” method. The required explanatory variables are the following: GDP per capita in US dollars based on market exchange rates, imports as a share of GDP, exports as a share of GDP, and the age dependency ratio. Dummy variables are required for the Sub-Saharan African economies, the Eurostat-OECD PPP Programme participants, island economies, and landlocked economies. Interaction terms of GDP per capita in US dollars based on market exchange rates and the dummy variables are also required.

Interpolating annual PPPs

For the years between reference years, currently, between 2011 and 2017, PPPs are calculated based on an approach in which basic heading PPPs are first interpolated between the reference years and subsequently aggregated using the standard GEKS method. In addition, regional PPPs between the reference years, where available,6 are incorporated using the CAR procedure. The resulting annual PPPs uphold the same properties of base-country invariance and fixity as the PPPs from reference year comparisons.

The data required to construct annual PPPs included global PPPs for the two reference years; regional PPPs between the reference years, where available; national accounts deflators and consumer price indexes; national accounts expenditures at current prices in local currency units; market exchange rates; and population.

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