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Likely, the issue here is that inflation calculations use a basket of goods that are substituted over time. Comparisons over time are not the best because a basket of goods from 2021 might include an iPhone, while a basket of goods from 1850 might include a pound of hay... 


That all being said, possibly using a harmonious pricing index might be more fruitful for this discussion. I believe that the UK and Canada use the HPI over CPI, mainly due to the issue of substitutes and compliments over time.