1. Research DepartmentComplex Methods 1/26 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 Complex Methods in Economics An Example of Behavioural Heterogeneity in House Prices Complex Methods in Economics An Example of Behavioural Heterogeneity in House Prices Research Department

2. Complex Methods 2/26 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. Research DepartmentComplex Methods 3/26 A Way to think about Complexity 1.Critical Transitions 2.Heterogeneous Agents Models (H.A.Ms) 3.Networks

4. Research DepartmentComplex Methods 4/26 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 Earths orbit abrupt shift in climate and vegetation cover over Saharah

5. Research DepartmentComplex Methods 5/26 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. Research DepartmentComplex Methods 6/26 SP500: 1987 Crash

7. Research DepartmentComplex Methods 7/26 Catastrophic Bifurcations

8. Research DepartmentComplex Methods 8/26 The housing market Imputed rents Actual rents -returns on housing

9. Research DepartmentComplex Methods 9/26 Heterogeneous beliefs and the housing market (1) Agents demand z h,t determined by maximising risk- adjusted expected future excess returns, R t+1 z h,t : This gives the demand for agent h :

10. Research DepartmentComplex Methods 10/26 Heterogeneous beliefs and the housing market (2) Aggregation over 2 types of agents, market clearing Leads to the price equation: where

11. Research DepartmentComplex Methods 11/26 Heterogeneous beliefs and the housing market (3) Under rational expectations on the first conditional moment: Define X t as the ratio of price to fundamental price:

12. Research DepartmentComplex Methods 12/26 Beliefs: Two types of agents Beliefs: Performance (realised profits): Fractions determined by logistic switching model: Estimation via nonlinear OLS

13. Research DepartmentComplex Methods 13/26 Stability condition: a simulated example The =0 dynamics is locally stable if: We assume =1.05, =500

14. Research DepartmentComplex Methods 14/26 The US housing market Actual and estimated fundamental prices Their difference (in logs)

15. Research DepartmentComplex Methods 15/26 Parameter Estimates - US Y Y

16. Research DepartmentComplex Methods 16/26 Estimated time-dependent fractions -US

17. Research DepartmentComplex Methods 17/26 Fancharts US: House price deviations

18. Research DepartmentComplex Methods 18/26 Bifurcation Results – US: Bifurcation diagram (with and without noise) Slowly varying can induce critical transitions But noise overwhelms the dynamics (early transitions and/or repetitive jumps between two stochastic attractors

19. Research DepartmentComplex Methods 19/26 Bifurcation Results – US: Y Pitchfork bifurcation

20. Research DepartmentComplex Methods 20/26 The NL housing market Actual and estimated fundamental prices Their difference (in logs)

21. Research DepartmentComplex Methods 21/26 Parameter Estimates - NL Y Y Y

22. Research DepartmentComplex Methods 22/26 Estimated time-dependent fractions -NL

23. Research DepartmentComplex Methods 23/26 Fancharts NL: House price deviations

24. Research DepartmentComplex Methods 24/26 Bifurcation Results – NL:

25. Research DepartmentComplex Methods 25/26 Bifurcation Results – NL: Y Value of fixed at 1.01 Pitchfork bifurcation

26. Research DepartmentComplex Methods 26/26 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