Endogenous Price Bubbles in a Multi-Agent System of the Housing Market

Abstract

Economic history shows a large number of boom-bust cycles, with the U.S. real estate market as one of the latest examples. Classical economic models have not been able to provide a full explanation for this type of market dynamics. Therefore, we analyze home prices in the U.S. using an alternative approach, a multi-agent complex system. Instead of the classical assumptions of agent rationality and market efficiency, agents in the model are heterogeneous, adaptive, and boundedly rational. We estimate the multi-agent system with historical house prices for the U.S. market. The model fits the data well and a deterministic version of the model can endogenously produce boom-and-bust cycles on the basis of the estimated coefficients. This implies that trading between agents themselves can create major price swings in absence of fundamental news.

Fig 1. U.S. House Price Index and Fundamental Value Estimate.

Panel A of Fig 1 displays the log-real U.S. house price index P _t and the log-real fundamental value estimate F _t. The upper part of Panel B displays the weight W _t, the fraction of investors using the fundamentalist forecasting rule (right axis). The lower part of Panel B (left axis), displays P _t- F _t, the difference between the house price and its fundamental value.

Fig 2. Simulated House Price Index Values.

Panel A of Fig 2 displays the simulated behaviour of the log real house price index P _t and the proportion of investors applying the fundamentalist forecasting rule (W _t), using the estimated model parameters. The fundamental value F _t is fixed at 10. In Panel B, we display both the simulated and the actual difference between P _t and F _t. In Panel C we add exogenous random noise to the house price process, and in Panel D we add exogenous noise to both the price process and the fundamental value process.

Fig 3. Sensitivity Analysis: Bifurcation Plots.

Fig 3 displays bifurcation plots that show how the equilibrium price process changes in response to changes in the three behavioural model coefficients (α, β, and γ). In this sensitivity analysis we change one coefficient at a time, while keeping all other coefficients constant at their estimated values. Panel A displays the bifurcation plot for the fundamentalist coefficient α, Panel B the plot for the chartist coefficient β, and Panel C the plot for the switching parameter γ. The vertical lines represent the coefficient values estimated in the data.