Bubbles and crashes in house prices under heterogeneous expectations

We introduce heterogeneous expectations in a standard housing market model linking housing rental levels to buying prices via imputed rents. The resulting model displays nonlinear aggregate price fluctuations around the fundamental value. For many parameter values the fundamental price is unstable, while there are two non-fundamental equilibrium prices on either side of the fundamental price. Using quarterly data on rents and house prices, we estimate the model parameters for five different countries, US, UK, NL, JP and CH. We find that the data support heterogeneity in expectations, with temporary switching between trend extrapolation and mean-reversion beliefs, and that the estimated parameter values lie within the region with multiple equilibria. For all five countries we identify temporary hosue price bubbles, driven or amplified by trend extrapolation. The qualitative predictions of such non-linear models are very different from standard linear benchmarks, with import implications for policy.