Wilko Bolt De Nederlandsche Bank Maria Demertzis De Nederlandsche Bank Cees Diks

1. Complex Methods in Economics An Example of Behavioural Heterogeneity in House Prices Wilko Bolt De Nederlandsche Bank Maria Demertzis De Nederlandsche Bank Cees Diks University of Amsterdam, CeNDEF Marco van der Leij University of Amsterdam, CeNDEF November 2011 Research Department

2. Why Complexity? • Our current understanding of the world • The concept of equilibrium is given and unique • All deviations are small and temporary • Everybody is the same • Little to no interaction between agents • Whole=sum of its parts • The world is more complex

3. A Way to think about Complexity • Critical Transitions • Heterogeneous Agents Models (H.A.Ms) • Networks

4. Example of Critical Transition: Birth of the Sahara • relatively moist area until about 6,000 years ago • gradual change in solar radiation, due to subtle variation in Earth’s orbit • abrupt shift in climate and vegetation cover over Saharah

5. Detecting Critical Transitions • Scheffer, Bascompte, Brock et al (Nature, Sept. 2009) • Slow recovery from perturbations • Memory of the system increases • Moving window estimation • Critical slowdown prior to regime shift characterised by • Increasing variance, and • Increasing autocorrelation

6. SP500: 1987 Crash

7. Catastrophic Bifurcations

8. The housing market • Imputed rents • Actual rents -returns on housing

9. Heterogeneous beliefs and the housing market (1) • Agent’s demand zh,t determined by maximising risk-adjusted expected future excess returns, Rt+1zh,t: • This gives the demand for agent h:

10. Heterogeneous beliefs and the housing market (2) Aggregation over 2 types of agents, market clearing Leads to the price equation: where

11. Heterogeneous beliefs and the housing market (3) Under rational expectations on the first conditional moment: Define Xt as the ratio of price to fundamental price:

12. Beliefs: Two types of agents Beliefs: Performance (realised profits): Fractions determined by logistic switching model: Estimation via nonlinear OLS

13. Stability condition: a simulated example The q=0 dynamics is locally stable if: We assume U=1.05, b=500

14. The US housing market Actual and estimated fundamental prices Their difference (in logs)

15. Parameter Estimates - US Y Y

16. Estimated time-dependent fractions -US

17. Fancharts US: House price deviations

18. Bifurcation Results – US: q Bifurcation diagram (with and without noise) • Slowly varying q can induce critical transitions • But noise overwhelms the dynamics (early transitions and/or repetitive jumps between two stochastic attractors

19. Bifurcation Results – US: Y Pitchfork bifurcation

20. The NL housing market Actual and estimated fundamental prices Their difference (in logs)

21. Parameter Estimates - NL Y Y Y

22. Estimated time-dependent fractions -NL

23. Fancharts NL: House price deviations

24. Bifurcation Results – NL: q

25. Bifurcation Results – NL: Y Value of U fixed at 1.01 Pitchfork bifurcation

26. What have we learned? Univariate model • Data justifies multiplicity of equilibria (estimated) • Visualisation of herding • Models predict very different Multivariate model • Use institutional factors to estimate fundamental prices • Multiple countries