I have various trade values from 1900 that I would like to express in current money. The figures are in British Pounds Sterling, but I need current values in US Dollars.
What I have done is to take the historical values from the EH.NET web site at http://eh.net/hmit/ and update it to year 2000. So one Pound from 1900 has the purchasing power of 61.03 Pounds now. Then I converted these current Pound values to US Dollars at the today's exchange rate of $1.40 per Pound and get $85.44.
This all seemed fine until I tried it the other way. That is, the exchange rate in 1900 was a Pound was worth $4.87, and present purchasing power of a 1900 dollar is $20.39. This would mean a 1900 British pound has the same purchasing power as $99.30 today.
Have I used the right methodology?
The Answer
What you are observing is that what economists call purchase power parity (PPP) does not always work. In principle at all times any good should cost the same in two different countries after converting from one currency to the other. This is the principle of PPP.
In practice it does not work that way. Let us look at an example. Let us ask what a British Pound from 1900 (and 1930) is worth today in Dollars.
There are two ways to do it.
The first way is to convert a 1900 Pound to a 1900 Dollar and then ask how much the purchase power of a Dollar has change in the last 100 years. It took $4.87 to purchase one Pound in 1900, and one Dollar in 1900 has the same purchasing power as $20.39 today. So one Pound in 1900 had the same purchasing power as $99.30 today.
The second way is to ask how much the purchase power of a Pound has changed in the last 100 years and then convert it to Dollars in today's prices. One Pound from 1900 has the same purchasing power as 61.03 Pounds today and it takes $1.41 to buy a Pound today. So using this technique, one Pound in 1900 had the same purchasing power as $86.05.
Using the same two techniques for 1930 comes up with a Pound in that year having the same purchasing power as either $50.06 or $66.54 today.
There is no "right" answer. Sometimes exchange rates are such that one currency is "overvalued" relative to PPP. For example, sometimes after buying Pounds with Dollars, everything in the UK is less expensive than in the US. Then in other years it maybe the reverse.
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