Non-homogeneous Random Walks for Housing Prices

Abstract

The random walk formalism has applications in many areas, with economy being one of the most notable examples. In this work, we apply this formalism to a relevant problem in modern society, such as the access to housing and its prices. A 1-D non-homogeneous random walk model serves to interpret the collected data from a citizen science public experiment on which the participants had to rent a house. Half of these games had rules which simulated regulations limiting the maximum and minimum rent prices, in order to gauge the possible effects of these policies. Although regulations do not significantly affect the prices paid by the participants, they foment demand at higher prices and reduced price variability as shown by the root mean square displacement. Finally, a bubble phase and a declining phase are distinguished, thanks to which the model of the random walk is extrapolated to larger periods of time beyond the scope of the game.