International dollar

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:

${\displaystyle P_i=\frac{\left(p_{i1}{q}_{i1}/{\mathrm{P}\mathrm{P}\mathrm{P}}_1\right)+\left(p_{i2}{q}_{i2}/{\mathrm{P}\mathrm{P}\mathrm{P}}_2\right)+\cdots +\left(p_{iM}{q}_{iM}/{\mathrm{P}\mathrm{P}\mathrm{P}}_M\right)}{q_{i1}+q_{i2}+\cdots +q_{iM}}}$

This equation implies that the international price of the i-th commodity is calculated by dividing the total output of the i-th commodity in all selected countries, converted into international dollars, using purchasing power parities, by the total quantity produced of the i-th commodity. The previous equation can be rewritten as follows:

${\displaystyle P_i=\sum _{j=1}^M\left(p_{ij}/{\mathrm{P}\mathrm{P}\mathrm{P}}_j\right)\frac{q_{ij}}{\sum _{j=1}^M{q}_{ij}}}$

This equation suggests that Pi is a weighted average of international prices pij after conversion into international dollars using PPPj. PPPj is by the Geary–Khamis system defined through this equation:

${\displaystyle {\mathrm{P}\mathrm{P}\mathrm{P}}_j=\frac{\sum _{i=1}^N{p}_{ij}{q}_{ij}}{\sum _{i=1}^N{P}_i{q}_{ij}}}$

The numerator of the equation represents the total value of output in the j-th country expressed in national currency, and the denominator is the value of the j-th country's output evaluated by repricing at international prices Pi in international dollars. Then PPPj gives the number of national currency units per international dollar.

Advantages

Geary–Khamis international dollar is widely used by foreign investors and institutions such as the IMF, FAO and World Bank. It has become so widely used because it has made it possible to compare living standards between countries. Thanks to the international dollar, they can see a more trustworthy economic situation in the country and decide whether to provide additional loans (or any other investments) to said country, or not. It also offers some comparison of purchasing power parities all around the world (developing countries tend to have higher PPPs). Some traders even use the Geary–Khamis method to determine if a country's currency is undervalued or overvalued. Exchange rates are frequently used for comparing currencies; however, this approach does not reflect the real value of currency in said country. It is better to include PPP or the prices of goods in said country. International dollar solves this by taking into account exchange rates, PPP and average commodity prices. The Geary–Khamis method is the best method for comparisons of agricultural outputs.