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Sample-Path Stability of Non-Stationary Dynamic Economic Systems

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  • Klaus Reiner Schenk-Hoppé

Abstract

The goal of this paper is to introduce and illustrate a new approach to the stability analysis of sample-paths of nonlinear stochastic economic models with non-stationary components. We place our study within the mathematical theory of random dynamical systems and apply the concept of a random fixed point which is tailor-made for the study of the long-term behavior of sample-paths in stochastic systems. The main tool for the application of this approach is a Banach-type fixed point theorem for non-stationary random dynamical systems which is proved here. The concept and the theorem are thoroughly explained and illustrated by two examples from stochastic growth theory.

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Paper provided by Institute for Empirical Research in Economics - University of Zurich in its series IEW - Working Papers with number 046.

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Handle: RePEc:zur:iewwpx:046

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Keywords: Sample-Path Stability; Random Fixed Points; Non-Stationary Random Dynamical Systems;

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  1. Binder, M. & Pesaran, M.H., 1996. "Stochastic Growth," Cambridge Working Papers in Economics 9615, Faculty of Economics, University of Cambridge.
  2. Leonard J. Mirman & Manjira Datta, 1996. "Dynamic Externalities and Policy Coordination," CRIEFF Discussion Papers 9608, Centre for Research into Industry, Enterprise, Finance and the Firm.
  3. Manjira Datta & Leonard J. Mirman, . "Externalities, Market Power, and Resource Extraction," Working Papers 97/12, Arizona State University, Department of Economics.
  4. Cogley, Timothy & Nason, James M., 1995. "Effects of the Hodrick-Prescott filter on trend and difference stationary time series Implications for business cycle research," Journal of Economic Dynamics and Control, Elsevier, vol. 19(1-2), pages 253-278.
  5. Schenk-Hoppe, Klaus Reiner & Schmalfu[ss], Bjorn, 2001. "Random fixed points in a stochastic Solow growth model," Journal of Mathematical Economics, Elsevier, vol. 36(1), pages 19-30, September.
  6. Binder, Michael & Pesaran, M Hashem, 1999. " Stochastic Growth Models and Their Econometric Implications," Journal of Economic Growth, Springer, vol. 4(2), pages 139-83, June.
  7. Fischer, Ronald D. & Mirman, Leonard J., 1992. "Strategic dynamic interaction : Fish wars," Journal of Economic Dynamics and Control, Elsevier, vol. 16(2), pages 267-287, April.
  8. Mirman, Leonard J, 1972. "On the Existence of Steady State Measures for One Sector Growth Models with Uncertain Technology," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 13(2), pages 271-86, June.
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