1. dr inż. Mirosław Bełej Department of Real Estate Management and Regional Developmen t dr Sławomir Kulesza Department of Relativistic Physics UNIVERSITY OF WARMIA AND MAZURY IN OLSZTYN POLAND European Real Estate Society 19th Annual Conference 13th-16th June 2012 MODELLING THE REAL ESTATE DYNAMICS WITH THE CATASTROPHE THEORY

2. POLISH REAL ESTATE MARKET M Bełej, S.Kulesza. Modelling the real estate dynamics with the catastrophe theory. ERES 2012 1989 – SYSTEM TRANSFORMATION FROM CENTRALLY PLANNED ECONOMY (socialism) TO MARKET EKONOMY (capitalism) 2004 - POLAND JOINS THE EUROPEAN UNION 2006 - SUDDEN, UNEXPECTED LEVEL OF INCREASE IN REAL ESTATE PRICES IN POLAND 2012 - Poland & Ukraine EURO 2012 FOOTBALL CHAMPIONSHIP

3. POLISH REAL ESTATE MARKET WWW.REAS.PL

4. REAL ESTATE PRICES IN 2005-2011 SOURCE: M.Bełej. IDENTIFICATION OF SIMILARITIES IN REAL ESTATE TRENDS UNDER INSTABILITY CONDITIONS. Journal of Polish Real Estate Society vol.20 nr 2, 2012 WWW.TNN.ORG.PL INSTABILITY STABILITY 2500 Euro 2250 Euro 2000 Euro 1750 Euro 1500 Euro 1250 Euro 1000 Euro 750 Euro 500 Euro

5. Significant changes in real estate prices, observed worldwide (including Poland), are not only perturbations of long-term trends, but also appear as an internal characteristic of the real estate market. Changes in macroeconomic circumstances could destabilize a real estate market equilibrium, and then the system takes a series of quasi- discontinuous price changes towards a new state of balance. SCIENTIFIC PROBLEM

6. - Instability of system may lead to discontinuous changes -The classical methods of long-term analysis do not describe properly discontinuous changes in real estate prices - The periods of instability, reflect an crucial feature of the real estate market, and they constitute the turning points of its development, where the system is looking for a new trajectory of evolution - The evolution path of the real estate market - under the influence of the control parameters - runs mostly over the areas of long-term stability, and occasionally enters into the instability area SCIENTIFIC PROBLEM M Bełej, S.Kulesza. Modelling the real estate dynamics with the catastrophe theory. ERES 2012

7. 1972, Rene Thom: Structural stability and morphogenesis Catastrophe theory is a mathematical theory of nonlinear discontinuous phenomena. Catastrophe theory describes how small, continuous changes in control parameters generates discontinuous effects on the state of the system. Such discontinuous, jump-like changes are called phase- transitions or catastrophes. RESEARCH METHODOLOGY – CATASTROPHE THEORY

8. Zeeman C., 1975 economic growth CASTI J., SWAIN H., 1976 urbanization LASZLAK M., 1976 strategic management Zeeman C., 1977 Jakimowicz A., 2010 economic cycle Cobb L., Zacks S. 1985 biological sciences Okiński A., 1990 chemistry Eric-Jan Wagenmakers, Peter C.M. Molenaar, Raoul P.P.P. Grasman, Pascal A.I. Hartelman, Han L.J. van der Maas., 2005 psychology finance CATASTROPHE THEORY (MORPHOGENESIS)

9. CUSP CATASTROPHE MODEL Potential V depends on two control parameters: - α (asymetry coefficient), - β (bifurcation coefficient), and the state variable y in the form: The set of all equilibrium points defines the equilibrium surface described by the equation: Each dynamic system tends to the equilibrium state determined by the local minima of the potential function V M Bełej, S.Kulesza. Modelling the real estate dynamics with the catastrophe theory. ERES 2012

10. The set of equilibrium states forms a surface with a characteristic fold M Bełej, S.Kulesza. Modelling the real estate dynamics with the catastrophe theory. ERES 2012 CUSP CATASTROPHE MODEL Stability area Instability area

11. Case study – Real estate market in Poland The 4th largest province in Poland Area of 24 000 km 2 ( 7,7% of the countrys area) Population of 1 500 000 (3,7% of the countrys population ) THE UNIVERSITY OF WARMIA AND MAZURY POLAND

12. HOUSING PRICES IN OLSZTYN 2003-2010

13. TWO STATES OF EQUILIBRIUM OF THE MARKET STATE OF UNSTABLE EQUILIBRIUM

14. DATA ANALYSIS – 3D PLOT Evolution path on equilibrium surface

15. DATA ANALYSIS – 2D PLOT

16. logLiK - (likelihood ratio test) AIC (Akaike information criterion) BIC - Bayesian information criterion DATA ANALYSIS – MODELS COMPARSION

17. CONCLUSIONS Mathematical models brought by the catastrophe theory might constitute a good description of empirical data from the real estate market under sudden price changes. Sudden price changes are internal and crucial characteristic of the real estate market in the sense that they are critical points on the system evolution path towards equilibrium state. Regardless of the parameters used in the fit procedure, obtained results suggest that neither linear model nor logistic one is superior to the catastrophe model. M Bełej, S.Kulesza. Modelling the real estate dynamics with the catastrophe theory. ERES 2012

18. dr inż. Mirosław Bełej Department of Real Estate Management and Regional Developmen t dr Sławomir Kulesza Department of Relativistic Physics UNIVERSITY OF WARMIA AND MAZURY IN OLSZTYN POLAND European Real Estate Society 19th Annual Conference 13th-16th June 2012 MODELLING THE REAL ESTATE DYNAMICS WITH THE CATASTROPHE THEORY caprio@uwm.edu.pl