dr inż. mirosław bełej department of real estate management and regional developmen t dr...
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dr inż. Mirosław BełejDepartment of Real Estate Management and Regional Development
dr Sławomir KuleszaDepartment of Relativistic Physics
UNIVERSITY OF WARMIA AND MAZURY IN OLSZTYNPOLAND
European Real Estate Society 19th Annual Conference 13th-16th June 2012
MODELLING THE REAL ESTATE DYNAMICS
WITH THE CATASTROPHE THEORY
POLISH REAL ESTATE MARKET1989 2004 2006 2012
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
POLISH REAL ESTATE MARKET1989 2004 2006 2012
WWW.REAS.PL
0 1 0 2 0 3 0 4 0 5 0 6 0 7 0 8 0
Da ta
2 0 0 0 zł
3 0 0 0 zł
4 0 0 0 zł
5 0 0 0 zł
6 0 0 0 zł
7 0 0 0 zł
8 0 0 0 zł
9 0 0 0 zł
1 0 0 0 0 złŚ
red
nia
ce
na
ofe
rto
wa
zł/m2
WA RS ZA W A K RA K Ó W WRO CŁ A W P O ZNA Ń G DA ŃS K
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 STABILITY2500 Euro
2250 Euro
2000 Euro
1750 Euro
1500 Euro
1250 Euro
1000 Euro
750 Euro
500 Euro
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
- 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
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
Zeeman C., 1975 economic growthCASTI J., SWAIN H., 1976
urbanization
LASZLAK M., 1976 strategic management
Zeeman C., 1977Jakimowicz A., 2010
economic cycle
Cobb L., Zacks S. 1985 biological sciencesOkiński A., 1990 chemistryEric-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)
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
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
Case study – 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 MAZURYPOLAND
HOUSING PRICES IN OLSZTYN 2003-2010
HOUSING PRICES IN OLSZTYN 2003-2010
TWO STATES OF EQUILIBRIUM
OF THE MARKET
STATE OF UNSTABLE EQUILIBRIUM
DATA ANALYSIS – 3D PLOTEvolution path on equilibrium surface
DATA ANALYSIS – 2D PLOT
logLiK - (likelihood ratio test)AIC (Akaike information criterion)BIC - Bayesian information criterion
DATA ANALYSIS – MODELS COMPARSION
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
dr inż. Mirosław BełejDepartment of Real Estate Management and Regional Development
dr Sławomir KuleszaDepartment of Relativistic Physics
UNIVERSITY OF WARMIA AND MAZURY IN OLSZTYNPOLAND
European Real Estate Society 19th Annual Conference 13th-16th June 2012
MODELLING THE REAL ESTATE DYNAMICS
WITH THE CATASTROPHE THEORY