# With a Regulatory Regime That Freely Accomodates Housing Construction, Lower Interest Rates Drive Down Rents Instead of Driving Up the Price of Homes

In my travels to the central banks of many countries, when I dig into concerns about financial stability, I often find that the biggest financial stability worry associated with low or temporarily negative interest rates is about the effect of low interest rates on the price of houses in the capital city or other major cities. Let me analyze this issue.

The simplest case is when the anticipated real interest rate r is constant from now on and there are no tax complications. Suppose also that the home will last forever if appropriately maintained, with anticipated Rent and Maintenance constant from now on. Then the price P based on these anticipated values should be

P = (Rent - Maintenance) / r

If no additional construction is allowed, and the economy is fairly static even after the interest rate changes (say because of a changed desire for saving), Rent and Maintenance should stay close to the same, so Price should go up when r goes down.

But if construction is freely allowed within certain parameters–say along the lines I propose in “Density is Destiny,” which makes land costs small relative to the physical cost of building, than in the long run, the price of a home must equal the cost of constructing, say, the floor of the building corresponding to that home. With P a constant, it is useful to rearrange the equation above to

Rent = Maintenance +r P

Thus, for example,

• If, in the long run, the real interest rate is a small positive number in relation to the standard construction price of a home, than rent should be a little above maintenance.
• In the limit, as the real interest rates goes down toward zero, rent should just equal maintenance.
• If, in the long run, the real interest rate is negative, then the equation seems to say that rent should be below maintenance. But the equation doesn’t really work when the long-run real interest rate is negative, since if rent were below maintenance, the home would be a burden rather than a benefit, and no one would pay anything for it. In other words, the price is equal to the cost of building a home as long as it is worth someone’s while to build one. But if rent were below maintenance in the long run, no one would build one. On the other side, note that the interest rate on an infinite-term bond–a consol–can never be negative in equilibrium. If I give you money and can never demand anything back other than interest, having a negative coupon payment where I pay you would mean I have only give you money and you never give me anything back. I won’t do it. So at a minimum, negative interest rates must either be temporary or include either some return of the principal within finite time, or an option to demand the principal back at some finite time.

If the interest rate is expected to move around, the same essential principles apply. For fixed rent and maintenance–corresponding in my simple example to a prohibition against new construction–any path of lower interest rates raises the present value of a home, so the price of a home goes up. For a fixed price of a home–corresponding in my simple example to a policy very favorable to new construction–almost any path of lower interest rates will lead to more construction and lower rents.