Incorporating mortgage rates and spread in the tests for multiple bubbles in housing: four US cities 1987 to 2024

We test the occurrence of exuberance in the price of houses in four major cities of the USA, from January 1987 to March 2024 with two models: one adopts the usual approach and does not consider other structural factors besides the rent, and the other includes variable interest and mortgage rates as structural determinants of the house prices. For the latter we adopt the logarithmic approximation of the asset-pricing model of Campbell and Shiller (1997) to take them into account the determination of the price to rent ratio. This includes mortgage and the market interest rates, in addition to rents, as fundamental variables in the determination of house prices. We then inspect the residual of that regression for the presence of explosive roots with the GSADF test, and date-stamp them with the BSASDF test. The comparison of the bubbles identified with the two models leads us to conclude that interest and mortgage rate changes are responsible for a large part of the bubbles usually identified in the models that exclude them. This lends support to the view that the exuberance episodes identified by other studies that do not consider those rates are not speculative phenomena.