Prosperity or real estate bubble? Exuberance probability index of real housing prices in Chile

In this paper, we approached the concept of real estate bubble, analyzing the risk its bursting could generate for the Chilean financial market. Specifically, we analyzed the relationship between real housing prices, the economic activity index, and mortgage interest rates denominated in inflation-linked units from 1994 to 2020. The analysis was based on a second order Markov switching model with the predetermined variables mentioned later, whose parameters were obtained through the expectation-maximization algorithm. Then, we built a probability index as early warning indicator for potential imbalances in the real estate price that could put financial market stability at risk. The indicator is important to evaluate economic policy calibrations in time. A main finding was that the real housing price had a non-linear relationship with economic activity and the mortgage interest rate. Therefore, the evolution of the real estate price has been consistent with fundamental macroeconomic variables, even under a high growth regime, with increases above 12% per year. About 92% of housing price variability derived from changing macrofinancial conditions, suggesting a low margin of speculative behavior.