Halkos, George and Tsilika, Kyriaki (2012): Stability analysis in economic dynamics: A computational approach.

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Abstract
Modern microeconomics and macroeconomics study dynamic phenomena. Dynamics could predict future states of an economy based on its structural characteristics. Economic dynamics are modeled in discrete and continuous time context, mainly via autonomous difference and differential equations. In this study, we use Xcas and Mathematica as software tools, in order to generate results concerning the dynamic properties of the solutions of the difference and differential equation(s) models and determine whether an economic equilibrium exists. Our computational approach does not require solving the difference or differential equation(s) and makes no assumptions for initial conditions. The results provide quantitative information based on the qualitative properties of the mathematical solutions. The computer codes are fully presented and can be reproduced as they are in computationalbased research practice and education. The relevant output of CAS software is created in a way as to be interpreted without the knowledge of advanced mathematics.
Item Type:  MPRA Paper 

Original Title:  Stability analysis in economic dynamics: A computational approach 
Language:  English 
Keywords:  Stability conditions; software tools; economic equilibrium 
Subjects:  C  Mathematical and Quantitative Methods > C6  Mathematical Methods ; Programming Models ; Mathematical and Simulation Modeling > C63  Computational Techniques ; Simulation Modeling C  Mathematical and Quantitative Methods > C0  General > C02  Mathematical Methods C  Mathematical and Quantitative Methods > C8  Data Collection and Data Estimation Methodology ; Computer Programs > C88  Other Computer Software C  Mathematical and Quantitative Methods > C6  Mathematical Methods ; Programming Models ; Mathematical and Simulation Modeling > C62  Existence and Stability Conditions of Equilibrium 
Item ID:  41371 
Depositing User:  G.E. Halkos 
Date Deposited:  17 Sep 2012 13:31 
Last Modified:  28 Sep 2019 12:01 
References:  Amman H., Kendrick D. and Rust J. (Eds.). (1996). Handbook of Computational Economics (Vol. 1). Elsevier NorthHolland, Amsterdam, The Netherlands. Arrow K.J. and Hurwitz L. (1958). On the Stability of the Competitive Equilibrium I, Econometrica 26, 522552. Arrow K.J., Block H.D. and Hurwitz L. (1959). On the Stability of the Competitive Equilibrium II, Econometrica 27, 82109. Batra P. (2006). Necessary Stability Conditions for DifferentialDifference equations PAMM • Proc. Appl. Math. Mech. 6, 617–618 , doi:10.1002/pamm.200610289 Blanchard O.J. and Kahn C.M., (1980). The Solution of Linear Difference Models under Rational Expectations, Econometrica 48(5), 13051311. Chaumpsaur P., Drèze J. and Henry C., (1977). Stability Theorems with Economic Applications. Econometrica, 45(2), 273294. Chiang A., (1984). Fundamental Methods of Mathematical Economics, Third Edition. McGrawHill Book, Singapore. Folsom R.N., Boger D.C. and Mullikin H.C., (1976). Stability Conditions for Linear Constant Coefficient Difference Equations in Generalized Differenced Form. Econometrica, 44(3), 575591. Gomes O., (2010). Transitional Dynamics in StickyInformation General Equilibrium Models. Computational Economics, doi:10.1007/s106140109250y Gu K., Kharitonov, V.L. and Chen J., (2003). Stability of TimeDelay Systems. Birkhäuser, Boston. Halkos G. and Papageorgiou G., (2008). Extraction of nonrenewable resources: a differential game approach, MPRA Paper 37596, University Library of Munich, Germany. Halkos G. and Papageorgiou G., (2010). Dynamic optimization in natural resources management. Journal of Environmental Management and Tourism I 2(2), 9297. Halkos, G., Papageorgiou, G., (2011). Cyclical and constant strategies in renewable resources extraction. MPRA paper 34654, University Library of Munich, Germany. Hoy M., Livernois J., McKenna C., Rees R. and Stengos T., (2001). Mathematics for Economics, Second Edition. The MIT Press, Cambridge, Massachusetts, London, England. Huang C.J. and Crooke P.S., (1997). Mathematics and Mathematica for Economists. Oxford Blackwell Publishers, Massachusetts. Judd K. and Tesfatsion L., (Eds.). (2006). Handbook of computational economics: Agentbased computational economics (Vol. 2). Elsevier NorthHolland, Amsterdam, The Netherlands. Jury E.I., (1974). Inners and Stability of Dynamic Systems. Wiley, New York. Kendrick D.A. and Amman H.M., (1999). Programming Languages in Economics. Computational Economics, 14, 151181. Koopmans T., (1940). The Degree of Damping in Business Cycles. Econometrica, 8(1), 7989. Miranda M.J. and Fackler P.L., (2002). Applied Computational Economics and Finance. The MIT Press, Cambridge, Massachusetts, London, England. Neumann M., (1979). Weak stability for matrices. Linear and Multilinear Algebra, 7, 257–262. Parisse B., An introduction to the Xcas interface, available at http://wwwfourier.ujfgrenoble.fr/~parisse/giac/tutoriel_en.pdf Pindyck R.S. and Rubinfeld D.L., (1998). Econometric Models and Economic Forecasts, Fourth Edition. McGraw Hill, Boston. Ratto M., (2008). Analysing DSGE Models with Global Sensitivity Analysis. Computational Economics, 31, 115139. Samuelson P.A., (1947). Foundations of Economic Analysis, Harvard University Press. Strang G., (1988). Linear Algebra and its Applications 3rd edition. Harcount Brace Jovanovich College, Philadelphia, New York. Tinbergen J., (1939), Business Cycles in the U.S.,19191932, League of Nations. Varian, H.R., (Ed.). (1996). Computational economics: Economic and financial analysis with mathematica. TELOS/Springer, New York. Zhang W.B., (2005). Differential Equations, Bifurcations, and Chaos in Economics. Series on Advances in Mathematics for Applied Sciences Vol. 68, World Scientific, New Jersey. 
URI:  https://mpra.ub.unimuenchen.de/id/eprint/41371 