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.
Housing prices may collapse over the next 50 years as the population pyramid inverts and buyers demand decreases due to fewer individuals. What is the definition of long-term though?
As the housing maintenance labor force shrinks and it gets more expensive for elderly to maintain their non dense homes though, the value should decrease and become more affordable for the young who can do those labor things. Maybe?
If the elderly has any children (presumably they have), those children will inherit the house, rather than sell it at a loss. It would only decrease in price, if the children has a high need for cash, and a low/zero need for housing. This situation is still typically rare (for example, moving away permanently is one such situation). And even in those cases, you will rent out the house, rather than sell for a loss.
Therefore, the most average, and typical scenario is going to have the housing price be stable, rather than drop.
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.