In calculating gross national income (GNI—formerly referred to as GNP) and GNI per capita in U.S. dollars for certain operational purposes, the World Bank uses the Atlas conversion factor. 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 (or alternative conversion factor) 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 through 2000, that in the G-5 countries (France, Germany, Japan, the United Kingdom, and the United States). For 2001 onwards, these countries include the Euro Zone, Japan, the United Kingdom, and the United States. A country’s inflation rate is measured by the change in its GDP deflator.
The inflation rate for G-5 countries (through 2000, and the Euro Zone, Japan, the United Kingdom, and the United States for 2001 onwards), representing international inflation, is measured by the change in the SDR deflator. (Special drawing rights, or SDRs, are the IMF’s unit of account.) The SDR deflator is calculated as a weighted average of the G-5 countries’ (through 2000, and the Euro Zone, Japan, the United Kingdom, and the United States for 2001 onwards) GDP deflators in SDR terms, the weights being the amount of each country’s currency in one SDR unit. Weights vary over time because both the composition of the SDR and the relative exchange rates for each currency change. The SDR deflator is calculated in SDR terms first and then converted to U.S. dollars using the SDR to dollar Atlas conversion factor. The Atlas conversion factor is then applied to a country’s GNI. The resulting GNI in U.S. dollars is divided by the midyear population to derive GNI per capita.
When official exchange rates are deemed to be unreliable or unrepresentative of the effective exchange rate during a period, an alternative estimate of the exchange rate is used in the Atlas formula (see below).
The following formulas describe the calculation of the Atlas conversion factor for year t:
and the calculation of GNI per capita in U.S. dollars for year t :
where et* is the Atlas conversion factor (national currency to the U.S. dollar) for year t, et is the average annual exchange rate (national currency to the U.S. dollar) for year t, pt is the GDP deflator for year t, pt S$ is the SDR deflator in U.S. dollar terms for year t, Yt $ is the Atlas GNI per capita in U.S. dollars in year t, Yt is current GNI (local currency) for year t, and Nt is the midyear population for year t.