A Finite States Contraction Algorithm for Dynamic Models

  • Jenny X. Li
Part of the Applied Optimization book series (APOP, volume 74)


The purpose of this work is to develop and apply numerical methods for a class of dynamic models. With a proper change of variables the dynamics system which governs the equilibrium path is shown to be equivalent to a functional or an operator equation. An algorithm which combines the finite element method with a contraction mapping iteration, providing existence and uniqueness for the equilibrium path, then follows. Numerical evidences show that the proposed algorithm is a powerful tool for solving dynamic models.


dynamic models contraction algorithm monetary economics. 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. W. Baumol, The transactions demand for cash: An inventory theoretic approach, Quarterly Journal of Economics, 90 (1952), 545–56.CrossRefGoogle Scholar
  2. J. Bona and S. Grossman, Price and interest rate dynamics in a transaction-based model for money, Preprint, University of Chicago, Department of Economics 1983.Google Scholar
  3. S. Grossman and L. Weiss, A transactions-based model of the monetary transmission mechanism, The American Economy Review, v. 73, 5 (1983), 971–880.Google Scholar
  4. T. Bewley, The optimum quantity of money, in John H. Kareken and Neil Wallace, eds., Models of Monetary Economies, Federal Reserve Bank of Minneapolis, (1980), 169–210.Google Scholar
  5. J. Bryant and N. Wallace, The efficiency of interest-bearing national debt, Journal of Political Economy, 87 (1979), 365–82.CrossRefGoogle Scholar
  6. C. W. Robert, A reconsideration of the microfoundations of monetary policy, Western Economic Journal, 6 (1967), 1–8.Google Scholar
  7. L. J. Christiano, Modeling the liquidity effect of a money shock, Federal Reserve Bank of Minneapolis Quarterly Review. 15 (1991), 3–34.Google Scholar
  8. J. J. Cochrane, The return of the liquidity effect: A study of the short-run relation between money growth and interest rates, Journal of Business and Economics Statistics. 7 (1989), 75–111.Google Scholar
  9. J. Grandmont and Y. Younes, On the role of money and the existence of a monetary equilibrium, Review of Economic Studies, 39 (1972), 355–72.CrossRefGoogle Scholar
  10. S. Grossman, A transactions based model of the monetary transmission mechanism: part II, Working paper No. 974, National Bureau of Economic Research, Cambridge, 1982.Google Scholar
  11. S. Grossman, Monetary dynamics with proportional transaction costs and fixed payment periods, Working paper No. 1663, National Bureau of Economic Research, Cambridge, 1985.Google Scholar
  12. F. H. Hahn, On some problems of proving existence of an equilibrium in a monetary economy, in F.H. Hahn and F.R.P. Brechung, eds., The Theory of Interest Rates, London: Macmillan, (1965), 126–35.Google Scholar
  13. P. Hartley, Distributional effects and the neutrality of money, unpublished doctoral dissertation, University of Chicago, 1980.Google Scholar
  14. B. Jovanovic, Inflation and welfare in the steady state, Journal of Political Economy, 90 (1982), 561–77.CrossRefGoogle Scholar
  15. J. X. Li, Essays in Mathematical Economics and Economic Theory, Ph. D. Dissertation, Department of Mathematics, Cornell, 1993. Google Scholar
  16. R. Lucas, Equilibrium in a pure currency economy, Economic Inquiry, 28 (1980), 203–20.CrossRefGoogle Scholar
  17. R. Lucas, N. L. Stokey, Money and interest in a cash-in-advance economy, Working paperNo.1618, National Bureau of Economic Research, Cambridge, 1985.Google Scholar
  18. B. T. Mccallum, The role of overlapping-generations models in monetary economics, Working paper No.989, National Bureau of Economic Research, Cambridge, 1982.Google Scholar
  19. J. Rotemberg, A monetary equilibrium model with transactions costs, mimeo, 1982.Google Scholar
  20. T. Sargent and N. Wallace, The real bills doctrine vs. The quantity theory: A reconsideration, Journal of Political Economy, 90 (1982), 121–237.CrossRefGoogle Scholar
  21. J. Tobin, The interest-elasticity of the transactions demand for cash, Review of Economics and Statistics, 38 (1956), 241–47.CrossRefGoogle Scholar
  22. R. M. Townsend, Models of money with spatially separated agents, in John H. Kareken and Neil Wallace, eds., Models of Monetary Economies, Federal Reserve Bank of Minneapolis, (1980), 265–303.Google Scholar
  23. R. M. Townsend, Asset return anomalies. A choice-theoretic, monetary explanation, unpublished manuscript, 1982.Google Scholar
  24. M. W. Hirsch and C. C. Pugh, Stable manifold and hyperbolic sets, Global Analysis (Proc. Sympos. Pure Math., Vol. XIV, Berkeley 1968 ), pp 133–163.Google Scholar
  25. Jose-Victor and Rigs-Rull, Life-cycle economics and aggregate fluctuations, The Review of Economic Studies. vol. 63, No.3.(July. 1996 ), 465–489Google Scholar
  26. A.C. Stockman, A Theory of Exchange Rate Determination. The Journal of Political Economy. vol. 88, No. 4. (1980) pp 673–698CrossRefGoogle Scholar
  27. H.M. Polemarchakis, The Economic Inplication of an Incomplite Asset Market. The Americal Economic Review. vol. 80, No. 4. (1990), 280–293Google Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2002

Authors and Affiliations

  • Jenny X. Li
    • 1
  1. 1.Department of Mathematics and Department of EconomicsPenn State UniversityUniversity ParkUSA

Personalised recommendations