# Geary–Khamis dollar

The Geary–Khamis dollar (also known as the international dollar) is a hypothetical currency.

## As a function

Currency conversions involving PPP can be conceptualized as a 6-place function taking as parameters:

Parameter Unit Set of possible values Example Notes
Target currency Whatever unit the currency is in (e.g. yuan if the currency is renminbi) {x : x is a currency} = {US dollar, renminbi, ...} US dollar
Year associated with the currency Time Z \ {0} 2005
Location with respect to the PPP calculation Unitless 𝒫({x : x is a point on Earth}), i.e. some subset of points on Earth United States This is almost always the location where the target currency is used. If not, it is usually some well-known and coherent region of Earth, like Africa. This can also be some artificial combination of multiple regions, e.g. OECD dollars are US dollars valued at average OECD price levels.[1]
Year associated with the location Time Z \ {0} 2005 This is almost always the same as the year associated with the currency.
Some basket of goods Unitless 𝒫(Goods), where Goods is the set of goods and 𝒫 denotes the power set {McDonalds Big Mac} Is a market basket really just a set? Do we need to specify weights (e.g. via sales volume) on the goods (in which case the basket is more like a set of tuples (g, w))?
Price index/aggregation method/PPP formula Unitless {x : x is a PPP formula} Gini–Eltetö–Köves–Szulc (GEKS) method Could this be taken outside the unit? the different formulas can be seen to be "competing" to find the "best" PPP, so that the concept of PPP itself is independent, and this could be more of an algorithmic/empirical question. i.e. the unit might conceptually make sense without specifying a formula. A PPP value should tell a story like "[Value] is how much [target currency] from [currency year] buys in [location] during [location year]", and this story might make sense without the basket of goods and price index being specified [i.e. fixing those is still a practical question, but is not required to tell the story]. Maybe the story doesn't make sense unless you add "... where by 'buy' we mean 'buy things in this basket of goods' and by 'how much' we mean 'how much according to this conversion formula'." For instance, the Big Mac Index is not a "serious" attempt at determining the "best" PPP, but as long as the market basket is specified this is not a "problem".

Only after fixing all the parameters can the unit make sense next to a number.

Of these, the Geary–Khamis dollar partially fixes the parameters: it sets the target currency to the US dollar and the location to the United States. The other parameters are decided by the author of the publication. Therefore formally the Geary–Khamis dollar can be seen as a "unit schema" or "unit-producing function" that takes a year as input and outputs an actual unit.

On the source side:

• Source currency
• Year associated with the currency

## Difference with the US dollar for a particular year

e.g. 2000 GK dollar vs 2000 US dollar

Is there a difference?

## Devec database

Multiple metrics in the devec database use the Geary–Khamis dollar (at various years) for units. At the MySQL prompt:

```select metric,units from data
where region = 'Japan' and units REGEXP 'international dollar'
group by metric,units;
```

The `where region = 'Japan'` is just to restrict the search space, since `region` is an indexed column in the table.