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dr inż. Mirosław Bełej Department of Real Estate Management and Regional Developmen t

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

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dr inż. Mirosław Bełej Department of Real Estate Management and Regional Developmen t

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

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

  3. POLISH REAL ESTATE MARKET 2006 1989 2004 2012 WWW.REAS.PL

  4. 2500 Euro 2250 Euro 2000 Euro 1750 Euro 1500 Euro 1250 Euro 1000 Euro 750 Euro 500 Euro INSTABILITY STABILITY 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

  5. SCIENTIFIC PROBLEM • 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 changestowards a new state of balance.

  6. SCIENTIFIC PROBLEM • - Instability of system maylead to discontinuouschanges • Theclassicalmethods of long-term analysis do not describeproperlydiscontinuouschangesinreal estate prices • The periods ofinstability, reflect an crucial feature of the real estate market, and they constitute the turning points of its development, wherethe 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 M Bełej, S.Kulesza. Modelling the real estate dynamics with the catastrophe theory . ERES 2012

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

  8. CATASTROPHE THEORY (MORPHOGENESIS)

  9. CUSP CATASTROPHE MODEL Each dynamic system tends to the equilibrium state determined by the local minima of the potential function V 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: M Bełej, S.Kulesza. Modelling the real estate dynamics with the catastrophe theory . ERES 2012

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

  11. Casestudy – Real estate market in Poland The 4th largest province in Poland Area of 24 000 km2(7,7% of the country’s area) Population of 1 500 000 (3,7% of the country’s population) THE UNIVERSITY OF WARMIA AND MAZURY POLAND

  12. HOUSING PRICES IN OLSZTYN 2003-2010

  13. HOUSING PRICES IN OLSZTYN 2003-2010 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. DATA ANALYSIS – MODELS COMPARSION logLiK - (likelihood ratio test) AIC (Akaike information criterion) BIC - Bayesian information criterion

  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 characteristicof 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 Development 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

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