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> asset classes such as stocks and real estate.

Which is not inflation, but asset appreciation (i.e. the goal of investment). Inflation measures the price level of consumables. Stock and real estate is not consumed.

[tom_mellior]

One person's "asset appreciation" on real estate is another person's inflation of housing costs.

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Housing is part of the CPI https://www.bls.gov/cpi/factsheets/

[tom_mellior]

Yes. That was my point: House owners' assets "appreciate" by inflating non-owners' prices.