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I have historic monetary values given in different currencies and stemming from different points in time. I want to be able to compare them, and for that all must be given in the same currency, and inflation between the points in time must be considered as well. Eventually, all values should be given, for example, in US Dollar 2018.

What is the right way of achieving comparability in the above mentioned way? Does the base currency and the base year impact the method and/or the result, or are those independent of the choice of base currency and base year?

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If you have a single country, using the CPI to deflate values does not create a serious issue with the base year. Changing the base just changes the levels of the numbers, but they are are multiplied by the same amount. This means that rankings of prices are the same.

If you convert to a single currency, which one you pick does not matter for ordering the prices. For example, it does not matter whether you choose to convert all prices to Canadian dollars or US dollars, if the price is more expensive in one country in one currency, it will also be more expensive in the other.

This equivalence breaks down when you want to inflation adjust across countries. The choice of the currency for the inflation index affects the comparability. For example, imagine that the exchange rate between two countries in unchanged between two periods, yet the inflation rate is different. The scaling ratio between the two time periods depends on which country’s inflation index you choose. (I don’t think the choice of base year matters other than by applying a scaling factor.)

(If exchange rates followed relative inflation exactly, the country for the inflation index would not matter.)

There are different approaches you could try. I’ve never run into this kind of comparison before, so I have no idea what the accepted practice is. I would look at what you are trying to compare, and see what the best basis of comparison is. One approach is to not use a CPI index, and instead use a particular price to scale quantities, such as an average hourly wage. (This would imply that all prices are converted to the equivalent number of hours of wages that the price represents.) This converts prices to a meaningful unit, and not some arbitrary CPI indexation factor.

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