The international dollar (int'l dollar or intl dollar, symbols Int'l$., Intl$., Int$), also known as Geary–Khamis dollar (symbols G–K$ or GK$), is a hypothetical unit of currency that has the same purchasing power parity (PPP) that the U.S. dollar had in the United States at a given point in time. It is mainly used in economics and financial statistics for various purposes, most notably to determine and compare the purchasing power parity and gross domestic product (GDP) of various countries and markets. The year 1990 or 2000 is often used as a benchmark year for comparisons that run through time. The unit is often abbreviated, e.g., 2000 US dollars or 2000 International$ (if the benchmark year is 2000). It is based on the twin concepts of PPP of currencies and the international average prices of commodities. It shows how much a local currency unit is worth within the country's borders. It is used to make comparisons both between countries and over time. For example, comparing the per capita GDP of various countries in international dollars, rather than based simply on exchange rates, provides a more valid measure to compare standards of living. It was proposed by Roy C. Geary in 1958 and developed by Salem Hanna Khamis between 1970 and 1982. Figures expressed in international dollars cannot be converted to another country's currency using current market exchange rates; instead, they must be converted using the country's PPP exchange rate used in the study.
Exchange rate by country According to the IMF, below is the implied PPP exchange rate of the international dollar to the local currencies of the following nations:
Short description of Geary–Khamis system This system is valuing the matrix of quantities using the international prices vector. The vector is obtained by averaging the national prices in the participating countries after their conversion into a common currency with PPP and weighing quantities. PPPs are obtained by averaging the shares of national and international prices in the participating countries, weighted by expenditure. International prices and PPPs are defined by a system of interrelated linear equations that need to be solved simultaneously. The GK method produces PPPs that are transitive and actual final expenditures that are additive.
Inflation adjusting When comparing between countries and between years, the international dollar figures may be adjusted to compensate for inflation. In that case, the base year is chosen, and all figures will be expressed in constant international dollars for that specified base year. Researchers must understand which adjustments are reflected in the data (Marty Schmidt):
Population adjustments (In which case, figures represent per capita monies); Currency exchange rate adjustments (In which case, figures will be expressed in one currency unit (typically US$, International $, € £ or ¥); Purchasing power parity adjustments and/or average commodity prices (in which case, figures are typically expressed as International $); Inflation adjustments (in which case, figures have been adjusted, based on changes in an inflation index such as the consumer price index, to represent currency for a "base" year, such as 2000).
Description of Geary–Khamis system It is an iterative method based on the solution of (m + n) linear equations; a country's currency is chosen as the reference monetary unit and set equal to 1, and all the values of the Purchasing Power Parities are initially set equal to 1, for example, and the system is solved, iterating until the PPP values converge. Suppose PPPj is the parity of the j-th currency with a currency called international dollars, which may reflect any currency; however, the US dollar is the most commonly used. Then the international price Pi is defined as an international average of the prices of the i-th commodity in various countries. Prices in these countries are expressed in their national currencies. The Geary–Khamis method solves this by using national prices after conversion into a common currency using the purchasing power parities (PPP). Hence, the international price, Pi of the i-th commodity, is defined as:
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