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That calculation does not factor into the rent you will not pay when you buy a house and live in it. Imputed rent is a thing and you need to consider it. If you don't live in the house you wouldn't let the house sit vacant: you would rent it. In your formula the rent can be thought of as if it's a dividend of the investment.

Alternatively just read the linked article; the linked article makes the correct fair comparison. You will arrive at that conclusion by reading just the second paragraph, which says

> data on total housing returns (price appreciation plus rents) has been lacking (Shiller 2000 provides some historical data on house prices but not on rents). In this article we build on more comprehensive work on house prices (Knoll, Schularick, and Steger 2017) and newly constructed data on rents (Knoll 2017) to enable us to track the total returns of the largest component of the national capital stock.

Shiller is explicitly mentioned. And the article authors disregarded it because it failed to include rent.




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