  We propose a novel multi-layered nonlinear model that is able to capture and
predict the housing-demographic dynamics of the real-state market by simulating
the transitions of owners among price-based house layers. This model allows us
to determine which parameters are most effective to smoothen the severity of a
potential market crisis. The International Monetary Fund (IMF) has issued
severe warnings about the current real-state bubble in the United States, the
United Kingdom, Ireland, the Netherlands, Australia and Spain in the last
years. Madrid (Spain), in particular, is an extreme case of this bubble. It is,
therefore, an excellent test case to analyze housing dynamics in the context of
the empirical data provided by the Spanish National Institute of Statistics and
other sources of data. The model is able to predict the mean house occupancy,
and shows that i) the house market conditions in Madrid are unstable but not
critical; and ii) the regulation of the construction rate is more effective
than interest rate changes. Our results indicate that to accommodate the
construction rate to the total population of first-time buyers is the most
effective way to maintain the system near equilibrium conditions. In addition,
we show that to raise interest rates will heavily affect the poorest housing
bands of the population while the middle class layers remain nearly unaffected.
