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Stability analysis of an implicitly defined labor market model

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  • Mendes, Diana A.
  • Mendes, Vivaldo M.

Abstract

Until very recently, the pervasive existence of models exhibiting well-defined backward dynamics but ill-defined forward dynamics in economics and finance has apparently posed no serious obstacles to the analysis of their dynamics and stability, despite the problems that may arise from possible erroneous conclusions regarding theoretical considerations and policy prescriptions from such models. A large number of papers have dealt with this problem in the past by assuming the existence of symmetry between forward and backward dynamics, even in the case when the map cannot be invertible either forward or backwards. However, this procedure has been seriously questioned over the last few years in a series of papers dealing with implicit difference equations and inverse limit spaces. This paper explores the search and matching labor market model developed by Bhattacharya and Bunzel [J. Bhattacharya, H. Bunzel, Chaotic Planning Solution in the Textbook Model of Equilibrium Labor Market Search and Matching, Mimeo, Iowa State University, 2002; J. Bhattacharya, H. Bunzel, Economics Bulletin 5 (19) (2003) 1–10], with the following objectives in mind: (i) to show that chaotic dynamics may still be present in the model for acceptable parameter values, (ii) to clarify some open questions related with the admissible dynamics in the forward looking setting, by providing a rigorous proof of the existence of cyclic and chaotic dynamics through the application of tools from symbolic dynamics and inverse limit theory.

Suggested Citation

  • Mendes, Diana A. & Mendes, Vivaldo M., 2008. "Stability analysis of an implicitly defined labor market model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(15), pages 3921-3930.
    • Handle: RePEc:eee:phsmap:v:387:y:2008:i:15:p:3921-3930
    DOI: 10.1016/j.physa.2008.02.079
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    References listed on IDEAS

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    1. John J. McCall, 1982. "The Economics of Information and Uncertainty," NBER Books, National Bureau of Economic Research, Inc, number mcca82-1, December.
    2. Kennedy, Judy & Stockman, David R. & Yorke, James A., 2008. "The inverse limits approach to chaos," Journal of Mathematical Economics, Elsevier, vol. 44(5-6), pages 423-444, April.
    3. Barnett,William A. & Geweke,John & Shell,Karl (ed.), 1989. "Economic Complexity: Chaos, Sunspots, Bubbles, and Nonlinearity," Cambridge Books, Cambridge University Press, number 9780521355636.
    4. David Stockman & Judy Kennedy, 2006. "Chaotic Equilibria in Models with Ill-Defined Forward Dynamics," Working Papers 06-03, University of Delaware, Department of Economics.
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    Cited by:

    1. Nika Lazaryan & Thomas A. Lubik, 2019. "Global dynamics in a search and matching model of the labor market," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 68(2), pages 461-497, September.
    2. Nika Lazaryan & Thomas A. Lubik, 2017. "Global Dynamics in a Search and Matching Model of the Labor Market," Working Paper 17-12, Federal Reserve Bank of Richmond.

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