PPP Calculation and Estimation


 

Elementary PPP calculation

Reference PPPs

PPP aggregation

PPP linking

Imputing PPPs for non-benchmark countries

Extrapolating PPPs to non-benchmark years

 

Elementary PPP calculation

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

At the regional level, these prices are used to calculate regional PPPs. PPPs are first computed at the individual item level within each basic heading for each pair of countries being compared. Basic headings are the lowest aggregation level in the ICP national accounts expenditures classification for which explicit expenditure weights can be estimated. 

Suppose three countries—A, B, and C—price three kinds of rice for the basic heading rice. For each kind of rice, there are three PPPs: 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 PPPs between them for the three kinds of rice, which is a bilateral comparison. The PPP between economies B and A can also be computed indirectly: PPPC/A × PPPB/C = PPPB/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 each other country. A change in the mix of economies included in the comparison will also change the PPPs between any two countries.

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 country.

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Reference PPPs

For basic headings for which no price or other data were collected, PPPs were imputed in three different ways. In the first approach, most missing PPPs were imputed using price-based reference PPPs. This simply means that the PPPs from a similar basic heading or headings became the PPP for the missing value. The second approach was the reference volume method used for housing and described earlier. Finally, exchange rates were used for the two basic headings exports of goods and services and imports of goods and services and the two basic headings expenditures of residents abroad and expenditures of nonresidents on the economic territory.

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PPP aggregation

The regional basic heading PPPs are further aggregated using national account expenditures as weights, in order to derive intraregional measures of price and volume relatives for the countries participating in the regional comparison.

A property underlying the aggregation of basic heading PPPs is that countries are treated equally regardless of the size of their GDP. In order to achieve this, PPPs are first weighted using country A’s weights (Laspeyres index), and then weighted again using country B’s weights (Paasche index). Each index provides a weighted average of the PPP between country A and country B. To maintain symmetry, the geometric mean is taken of the two aggregated PPPs for every pair of country in the comparison. The result is a Fisher index. For each pair of economies, the multilateral PPP is the geometric mean of the direct and indirect Fisher indexes.

This method, however, 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 countries. As a result, the real expenditures of poor countries become artificially larger and move closer to the real expenditures of rich countries. This is known as the Gerschenkron effect. For uses of ICP PPPs such as poverty analysis, non-additive methods that avoid the Gerschenkron bias are preferred.

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PPP linking

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

The resulting linked basic heading PPPs are subsequently weighted and aggregated, and finally adjusted to maintain the fixity of the regional results. The fixity concept means that the relative volume—the ratio of real expenditures—between any pair of countries in a region remains the same after the region has been combined with countries in other regions. In order to maintain the fixity of regional and global results, the total regional expenditure volumes from the global aggregation are redistributed according to the countries’ expenditure volumes shares in the regional comparisons. This allows subsequently calculating the global PPPs indirectly, that is, by dividing countries nominal expenditure volumes by the real expenditure volumes.

The above listed properties of the PPPs apply for each computational step: computing basic heading PPPs between countries, aggregating basic heading PPPs within the region, linking basic heading PPPs across the regions, and finally computing aggregated global PPPs.

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Imputing PPPs for non-benchmark countries

199 economies participated in the 2011 round of the ICP. Even so, coverage of the world economy was not exhaustive. Some economies did not participate in the comparison for a variety of reasons, including civil unrest, lack of resources, or lack of national interest. Although these 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 world’s economic size or of world poverty. Thus, to provide a more complete set of PPPs for the world economy, the ICP imputed PPPs for 15 of the economies that did not participate in ICP 2011.

For its 2005 round, the ICP imputed PPPs for 42 nonparticipating economies. The drop in the number of nonparticipants in ICP 2011 was the result of the improved coverage in the Latin America region and the introduction of two new regions, the Caribbean region and the Pacific Islands region. Four of the nonparticipants in ICP 2011 participated in ICP 2005: Argentina, Lebanon, South Sudan (as part of Sudan), and the Syrian Arab Republic. Eight of the nonparticipants in ICP 2011 were also nonparticipants in ICP 2005: Afghanistan, Eritrea, Guyana, Libya, San Marino, Timor-Leste, Turkmenistan, and Uzbekistan.

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Extrapolating PPPs to non-benchmark years

The most common method used to interpolate PPPs and real expenditures between ICP benchmarks and to extrapolate from the latest set of benchmark PPPs for each economy is a time series of price deflators at a broad level (typically GDP but sometimes a handful of major components of GDP). The process involves comparing changes in national accounts deflators for an economy with those in a base economy and using these comparative movements to extrapolate from the latest ICP benchmark.

For the current method used in WDI, please refer to the WDI page “How do you extrapolate the PPP conversion factors estimated by the ICP?

Also, please refer to Agenda Item 2 and 3 under Research agenda section of this website for topics on refining the extrapolation method for non-benchmark years.

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