A Stylized Model of Boom and Bust Housing Cycles'
speaker: Roberto Dieci (Università di Bologna)abstract: We develop a dynamic model in discrete time, that may be regarded as a stylized mathematical representation of what is going on in speculative housing markets. We assume that housing prices adjust with respect to excess demand in the usual way. The supply of houses is determined by the depreciation of houses and new constructions, which, in turn, depend positively on housing prices. We discriminate between real and speculative demand for houses. While real demand depends negatively on housing prices, speculative demand is influenced by expectations about future prices. With regard to this, our approach is inspired by recent work on agent-based financial market models (see Hommes 2006 and LeBaron 2006 for comprehensive surveys). Guided by empirical evidence, speculators rely on two possible heuristics when they make their predictions, namely, extrapolative and regressive forecasting rules. Extrapolative rules add a positive feedback to the dynamics of financial markets and thus tend to be destabilizing. By predicting some kind of mean reversion, the effect of regressive rules, is likely to be stabilizing. The relative importance of these competing views evolves over time, subject to market circumstances. To be precise, we assume that the more housing prices deviate from their long-run ‘fundamental’ level, the more agents are convinced that some kind of mean reversion is about to set in. The underlying argument is that agents are aware that any bubble will ultimately burst, a situation where mean reversion rules predict the direction of the market movement correctly. A related rule selection scenario is used, for instance, in He and Westerhoff (2005) to understand the cyclical behavior of commodity prices. As it turns out, the dynamics of our model is driven by a two-dimensional nonlinear map which may display irregular boom and bust housing price cycles, as repeatedly observed in many actual markets, and documented e.g., by Shiller (2007a, 2007b). Such a map may have up to three fixed points. Besides a so-called long-run fundamental steady state, two further steady states may also exist: one located below and one above this value. The fundamental steady state may lose its stability via a so-called pitchfork bifurcation, after which two new ‘nonfundamental’ steady states emerge, or via a socalled Neimark-Sacker bifurcation, after which (quasi-)periodic housing price dynamics set in. Both scenarios may evolve into more complex dynamics. Price paths appear to be quite irregular since both real and speculative forces jointly impact on the formation of housing prices and, in turn, realized prices affect agents’ demand and supply decisions.
timetable:
Fri 2 Oct, 15:00 - 15:45, Aula 3
documents:
dieci
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