The World Bank Atlas method - detailed methodology
In calculating gross national income (GNI—formerly referred to as GNP) in U.S. dollars for certain operational and analytical purposes, the World Bank uses the Atlas conversion factor instead of simple exchange rates. The purpose of the Atlas conversion factor is to reduce the impact of exchange rate fluctuations in the cross-country comparison of national incomes.
The Atlas conversion factor for any year is the average of a country’s exchange rate for that year and its exchange rates for the two preceding years, adjusted for the difference between the rate of inflation in the country and international inflation; the objective of the adjustment is to reduce any changes to the exchange rate caused by inflation.
A country’s inflation rate between year t and year t-n is measured by the change in its GDP deflator http://databank.worldbank.org/data/download/site-content/kb/formula-2.png:
http://databank.worldbank.org/data/download/site-content/kb/formula-3.png
International inflation between year t and year t-n is measured using the change in a deflator based on the International Monetary Fund’s unit of account, special drawing rights (or SDRs). Known as the “SDR deflator,” it is a weighted average of the GDP deflators (in SDR terms) of China, Japan, the United Kingdom, the United States, and the euro area, converted to U.S. dollar terms; weights are the amount of each currency in one SDR unit.
http://databank.worldbank.org/data/download/site-content/kb/formula-5.png
The Atlas conversion factor (local currency to the U.S. dollar) for any country for year t http://databank.worldbank.org/data/download/site-content/kb/formula-6.png is given by:
http://databank.worldbank.org/data/download/site-content/kb/formula-7.png
where http://databank.worldbank.org/data/download/site-content/kb/formula-7a.png is the average annual exchange rate (local currency to the U.S. dollar) for year t.
GNI in U.S. dollars (Atlas method) for year t is calculated by applying the Atlas conversion factor to a country’s GNI in current prices (local currency) http://databank.worldbank.org/data/download/site-content/kb/formula-9.pngas follows:
http://databank.worldbank.org/data/download/site-content/kb/formula-10.png
The resulting GNI in U.S. dollars can then be divided by a country’s midyear population to derive GNI per capita (Atlas method).
Worked example
Variable | t-2 |
t-1 |
t |
||
GDP deflator http://databank.worldbank.org/data/download/site-content/kb/formula-11.png (NY.GDP.DEFL.ZS) | 100 |
125 |
150 |
||
Calculate rate of inflation | 1.50 |
1.20 |
- |
||
SDR deflator http://databank.worldbank.org/data/download/site-content/kb/formula-12.png | 100 |
105 |
110 |
||
Calculate rate of inflation | 1.10 |
1.05 |
- |
||
Calculate local inflation relative to international inflation (a)/(b) |
1.36 |
1.15 |
- |
||
Annual average market exchange rate http://databank.worldbank.org/data/download/site-content/kb/formula-14.png (PA.NUS.FCRF) | 3 |
4 |
5 |
||
Simple 3-year average exchange rate (for comparison) | 4 |
||||
Calculate Atlas method exchange rate http://databank.worldbank.org/data/download/site-content/kb/formula-15.png | 4.56 |
||||
GNI, current local currency, billions http://databank.worldbank.org/data/download/site-content/kb/formula-15a.png(NY.GNP.MKTP.CN) | 90 |
120 |
150 |
||
GNI, average market exchange rate, current US$ billions | 30.00 |
||||
GNI, 3-year average market exchange rate, current US$ billions | 37.50 |
||||
Calculate GNI, Atlas method conversion factor, current US$ billions http://databank.worldbank.org/data/download/site-content/kb/formula-16.png | 32.91 |
||||
Mid-year population, millions http://databank.worldbank.org/data/download/site-content/kb/formula-17.png (SP.POP.TOTL) | 10 |
12 |
15 |
||
GNI per capita, average market exchange rate, current US$ | 2,000 |
||||
GNI per capita, 3-year average market exchange rate, current US$ | 2,500 |
||||
Calculate GNI per capita, Atlas method conversion factor, current US$ http://databank.worldbank.org/data/download/site-content/kb/formula-18.png | 2,194 |
Notes:
- For countries with multiple exchange rate systems, the practice has been to apply a weighted average of the exchange rates, with shares of foreign exchange transactions subject to the different exchange rates used as weights. The weighted-average exchange rate is then used in the Atlas formula.
- When official exchange rates are deemed to be unreliable or unrepresentative of the exchange rate effectively applied to domestic transactions of foreign currencies and traded products during a period, an alternative estimate (PA.NUS.ATLS) of the exchange rate is used. While each case is judged on its merits, one case is when there is a significant change in the nominal exchange rate compared to with the relative rate of inflation (the ratio of domestic to international inflation, measured by the SDR deflator– for instance, more than 30% over three years. Typically, an alternative conversion factor is estimated by extrapolating a “normal” period’s exchange rate using the change in relative inflation. These alternative local currency conversion factors are applied as single-year rates, and are used for only a small number of countries.
- In the special case of countries in transition to a market-based economy, much of their international trade was carried out at exchange rates that differed markedly from official rates. In these cases, official exchange rates could not be used to convert GNI from local currency to U.S. dollars. The alternative approach used for market economies of selecting a past exchange rate as a basis for forward extrapolations was not feasible, given the history of managed price and exchange rate regimes in these countries. In view of these problems, an alternative method, known as the synthetic Atlas-type conversion factor, was developed. The synthetic Atlas-type conversion factors were used for the first time to convert 1990 per capita income for 16 transition economies. From 2002 onward, the synthetic Atlas-type conversion factors have not been applied to any economy.