Albu, LucianLiviu (2006): Nonlinear models: applications in economics.

PDF
MPRA_paper_3100.pdf Download (4MB)  Preview 
Abstract
The study concentrated on demonstrating how nonlinear modelling can be useful to investigate the behavioural of dynamic economic systems. Using some adequate nonlinear models could be a good way to find more refined solutions to actually unsolved problems or ambiguities in economics. Beginning with a short presentation of the simplest nonlinear models, then we are demonstrating how the dynamics of complex systems, as the economic system is, could be explained on the base of some more advanced nonlinear models and using specific techniques of simulation. We are considering the nonlinear models only as an alternative to the stochastic linear models in economics. The conventional explanations of the behaviour of economic system contradict many times the empirical evidence. We are trying to demonstrate that small modifications in the standard linear form of some economic models make more complex and consequently more realistic the behaviour of system simulated on the base of the new nonlinear models. Finally, few applications of nonlinear models to the study of inflationunemployment relationship, potentially useful for further empirical studies, are presented.
Item Type:  MPRA Paper 

Original Title:  Nonlinear models: applications in economics 
Language:  English 
Keywords:  nonlinear model; continuous time map; strange attractor; fractal dimension; natural unemployment 
Subjects:  E  Macroeconomics and Monetary Economics > E3  Prices, Business Fluctuations, and Cycles > E32  Business Fluctuations ; Cycles E  Macroeconomics and Monetary Economics > E2  Consumption, Saving, Production, Investment, Labor Markets, and Informal Economy > E27  Forecasting and Simulation: Models and Applications 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 
Item ID:  3100 
Depositing User:  Lucian Liviu Albu 
Date Deposited:  05 May 2007 
Last Modified:  26 Sep 2019 11:44 
References:  Albu, L.L. (1995): La modélisation de l’économie souterraine et des politiques fiscales, CEPREMAP  Paris, ACE  PHARE, August. Albu, L.L. (1996): “Teoria discontinuităţilor şi aplicaţii în economie” (Theory of Discontinuities and Applications in Economics), Oeconomica, 2, SOREC, IRLI, Bucharest. Albu, L.L. (1997): Strain and inflationunemployment relationship in transitional economies: a theoretical and empirical investigation, University of Leicester, Department of Economics, Centre for Economic Studies, Leicester, ACEPHARE, December. Albu, L.L. (1998): Tranziţia economiei sau tranziţia ştiinţei economice? (Transition of Economy or Transition of Economics?), Expert, Bucharest. Albu, L.L. (2002): Macroeconomie nonlineară şi prognoză – teorie şi aplicaţie (NonLinear Macroeconomics and Forecast – Theory and Aplications), Expert, Bucharest. Ameodo, A., Coullet, P., and Tresser, C. (1981): “Possible New Strange Attractors with Spiral Structure”, Communications in Mathematical Physics 79. Ameodo, A., Coullet, P., and Tresser, C. (1982): “Oscillations with Chaotical Behavior: An Ilustration of a Theorem by Shilnikov”, Journal of Statistics Physics 27. Arthur, B. (1988): ”Selfreinforcing Mechanism in Economics”, in Anderson, P.K. Arrow and D. Pines (eds.): The Economy as an Evolving Complex System, AddisonWesley, Reading, MA. Benhabib, J. (1992): Chaos and Cycles in Economic Equilibrium, Princeton University Press, Princeton. Berge, P., Pomeau, Y., and Vidal, C. (1986): Order within Chaos. New York: Wiley. Black, F. (1982): ”General Equilibrium and Business Cycles”, NBER Working Paper, 950. Blanchard, O.J. and Fischer S. (1993): Lectures on Macroeconomics, MIT Press, Cambridge, MA. Blatt, J.M. (1978): ”On the Econometric Approach to BusinessCycle Analysis”, Oxford Economic Papers, 30. Brock, W.A. (1986): ”Distinguishing Random and Deterministic Systems”, Journal of Economic Theory, 40. Brock, W.A. (1992): Pathways to Randomness in the Economy: Emergent Nonlinearity and Chaos in Economics and Finance, University of Wisconsin. Brock, W.A., Hsie, D.A., and LeBaron, B. (1991): Nonlinear Dynamics, Chaos and Instability, MIT Press, Cambridge, MA. Burns, A. (1969): ”The Business Cycle in a Changing World”, National Bureau of Economic Research, New York. Burns, A. and Mitchell, W. (1946): ”Measuring Business Cycles”, National Bureau of Economic Research, New York. Day, R.H. (1982): ”Irregular Growth Cycles”, American Economic Review, 72 (3). Daianu, D. and Albu, L.L. (1996): Strain and the InflationUnemployment Relationship: A Conceptual and Empirical Investigation. Econometric Inference into the Macroeconomic Dynamics East European Economies, University of Leicester, UK. Research Memorandum, No. 96/15. Feigenbaum, M. (1978): ”Quantitative Universality for a Class of nonlinear Transformations”, Journal of Statistical Physics, 19. Fischer, E.O. and Jammernegg, W. (1986): “Empirical Investigation of a Catastrophe Extension of the Phillipscurve”, Review of Economics and Statistics. Friedman, M. (1968): “The Role of Monetary Policy”, American Economic Review 58. Friedman, M. and Schwartz, A.J. (1963): A monetary History of the United States, 18671960, Princeton University Press. Gandolfo, G. (1983): Economic Dynamics: Methods and Models. 2nd ed., Amsterdam: NorthHolland. Gilmore, R. (1981): Catastrophe Theory for Scientists and Engineers, John Wiley, New York. Glendinning, P. and Sparrow, C. (1984): “Local and Global Behavior near Homoclinic Orbits”, Journal of Statistical Physics 35. Goodwin, R.M. (1951): ”The Nonlinear Acceleration and the Persistance of Business Cycles”, Econometrica, 19 (1). Goodwin, R.M. (1967): “A Growth Cycle”. Socialism, Capitalism and Economic Growth. C.H. Feinstein (ed.). Cambridge University Press. Graham, A. and Senge, P. (1980): ”A Long Wave Hypothesis of Innovation”, Technological Forecasting and Social Change, 17. Grandmont, J.M. (1988): Nonlinear Economic Dynamics, Academic Press, Boston. Granger, C.W.J. şi Terasvirta, T. (1993), Modelling Nonlinear Economic Relationships, Oxford University Press, Oxford. Guckenheimer, J. and Holmes, P. (1983): Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Field, Springer Verlag, BerlinHeidelberg. Henon, M. (1976): ”A Two Dimensional Mapping with a Strange Attractor”, Communications in Mathematical Physics, 50. Hermann, R. (1985): ”Stability and Chaos in a Kaldortype Model”, Department of Economics, University of Gottingen, Discussion Paper No. 22. Klein, L.R. şi Preston, R.S. (1969): ”Stochastic Nonlinear Models”, Econometrica, 37. Li, T.Y. and Yorke, J.A. (1975): ”Period Three Implies Chaos”, American Mathematical Monthly, 82. Lipsey, R.G (1960): “The Relation between Unemployment and the Rate of Change of Money Wage Rates in the United Kingdom, 18621957: A Further Analysis”, Economica 27. Lorenz, E.N. (1963): ”Deterministic Nonperiod Flows”, Journal of Atmospheric Sciences, 20. Lorenz, HW. (1989): Nonlinear Dynamical Economics and Chaotic Motion, Lecture Notes in Economic and Mathematical Systems 334, Springer Verlag, Berlin. Mandelbrot, B. (1972): “Statistical Methodology for NonPeriodic Cycles: From the Covariance to R/S Analysis”, Annals of Economic and Social Measurement 1. Marotto, F.R. (1978): ”Snapback Repellors Imply Chaos in Rn”, Journal of Mathematical Analzsis and Applications, 72. May, R.M. (1976): “Simple Mathematical Models With Very Complicated Dynamics”, Nature 261. Metzler, L.A. (1941): “The Nature and Stability of Inventory Cycles”, Review of Economic Studies 23. Mitchell, W.C. (1927): ”Business Cycles: The Problem and Its Setting”, National Bureau of Economic Research, New York. Mundell, R.A. (1990): “Debts and Deficits in Alternative Macroeconomic Models”, Revista di Politica Economica, VIIVIII, Roma. Nelson, C. and Plosser, C. (1982): ”Trends and Random Walks in Macroeconomic Time Series”, Journal of Monetary Economics 10. Okun, A.M. (1962): ”Potential GNP: Its Measurement and Significance”, Reprinted in J. Pechman (ed.), Economics for Policymaking, MIT Press, Cambridge, MA, 1983. Phillips, A.W. (1958): “The Relation between Unemployment and the Rate of Change of Money Wage Rates in the United Kingdom, 18611957”, Economica 25. Pohjola, M.T. (1981): “Stable, Cyclic and Chaotic Growth: the Dynamics of a Discrete Time Version of Goodwin’s Growth Cycle Model”, Zeitschrift fur Nationalekonomie 41. Ramsey, J.B. (1988): ”Economic and Financial Data as Nonlinear Processes”, in G.P. Dwyer şi R.W. Hafer (eds.), The Stoc Market: Bubbles, Volatility, and Chaos, Kluwer Academic Publishers, Boston. Reichlin, P. (1997): “Endogenous Cycles in Competitive Models: An Overview”, Studies in Nonlinear Dynamics and Econometrics Quarterly Journal, Volume 1, Number 4, The MIT Press, January. Rossler, O.E. (1976): ”An Equation for Continous Chaos”, Physics Letters, 57A. Ruelle, D. (1979): ”Repellers for Real Analytic Maps”, Ergodic Theory and Dynamic Systems, 2. Ruelle, D. and Takens, F. (1971): ”On the Nature of Turbulence”, Communications in Mathematical Physics, 20. Santeremo, A.M. and Seater, J.L. (1978): “The Inflation Unemployment TradeOff: A Critique of the Literature”, Journal of Economic Literature 16. Soliman, A.S. (1996): “Transition from Stable Equilibrium Points to Periodic Cycles to Chaos in a Phillips Curve System”, Journal of Macroeconomics, 18. Tong, H. (1990): Nonlinear Time Series. A Dynamical System Approach, Oxford University Press, Oxford. Vilder, R.G. (1995): Endogenous Business Cycles, Tinbergen Institute Research Series, 96. Woodcock, A.E.R. and Davis, M. (1979): Catastrophe Theory. London: Penguin. Zarnowitz, V. (1985): ”Recent Work on Business Cycles in Historical Perspective: A Review of Theories and evidence”, Journal of Economic Literature, 23. 
URI:  https://mpra.ub.unimuenchen.de/id/eprint/3100 