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Sample-Path Stability of Non-Stationary Dynamic Economic Systems

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Klaus Reiner Schenk-Hoppé

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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 - IEW in its series IEW - Working Papers with number iewwp046.

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Handle: RePEc:zur:iewwpx:046

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

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Find related papers by JEL classification:
C62 - Mathematical and Quantitative Methods - - Mathematical Methods and Programming - - - Existence and Stability Conditions of Equilibrium

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  1. Datta, Manjira & Mirman, Leonard J, 2000. "Dynamic Externalities and Policy Coordination," Review of International Economics, Blackwell Publishing, vol. 8(1), pages 44-59, February. [Downloadable!] (restricted)
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  2. 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. [Downloadable!] (restricted)
  3. Timothy Cogley & James M. Nason, 1993. "Effects of the Hodrick-Prescott filter on trend and difference stationary time series: implications for business cycle research," Working Papers in Applied Economic Theory 93-01, Federal Reserve Bank of San Francisco.
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  4. Binder, M. & Pesaran, M.H., 1996. "Stochastic Growth," Cambridge Working Papers in Economics 9615, Faculty of Economics, University of Cambridge.
  5. Klaus Reiner Schenk-Hoppé & Björn Schmalfuss, . "Random Fixed Points in a Stochastic Solow Growth Model," IEW - Working Papers iewwp065, Institute for Empirical Research in Economics - IEW. [Downloadable!]
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  6. Datta, Manjira & Mirman, Leonard J., 1999. "Externalities, Market Power, and Resource Extraction," Journal of Environmental Economics and Management, Elsevier, vol. 37(3), pages 233-255, May. [Downloadable!] (restricted)
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  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. [Downloadable!] (restricted)
  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. [Downloadable!] (restricted)
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