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The Z-Transform Method for Multidimensional Dynamic Economic Systems


  • Xiaoyong Cui

    (Guanghua School of Management, Peking University)

  • Liutang Gong

    (Guanghua School of Management, Peking University)

  • Xiaojun Zhao

    (Guanghua School of Management, Peking University)

  • Heng-fu Zou

    (Guanghua School of Management, Peking University
    Institute for Advanced Studies, Wuhan University
    CEMA in Central University of Finance and Economics)


This paper uses the Z-transform to develop a method for solving the linearized multidimensional discrete-time systems, which can be used to discuss the e¡èects of policies on economy (including the welfare gains and initial e¡èects on economy) raised by multi-sector perfect-foresight-discrete-time models. Our method is not restricted on the dimension of the dynamic system, and it cannot only analyze the effect of permanent policy change on the economy, but also it can be used to analyze the e¡èect of temporal policy change on the economy. As an application example, we analyze the effects of fiscal policy on the initial economy and social welfare in the discrete-time Uzawa-Lucas model.

Suggested Citation

  • Xiaoyong Cui & Liutang Gong & Xiaojun Zhao & Heng-fu Zou, 2012. "The Z-Transform Method for Multidimensional Dynamic Economic Systems," CEMA Working Papers 532, China Economics and Management Academy, Central University of Finance and Economics.
  • Handle: RePEc:cuf:wpaper:532

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    References listed on IDEAS

    1. Meijdam, Lex & Verhoeven, Marijn, 1998. "Comparative Dynamics in Perfect-Foresight Models," Computational Economics, Springer;Society for Computational Economics, vol. 12(2), pages 115-124, October.
    2. Casey B. Mulligan & Xavier Sala-i-Martin, 1993. "Transitional Dynamics in Two-Sector Models of Endogenous Growth," The Quarterly Journal of Economics, Oxford University Press, vol. 108(3), pages 739-773.
    3. B. Douglas Bernheim, 1981. "A Note on Dynamic Tax Incidence," The Quarterly Journal of Economics, Oxford University Press, vol. 96(4), pages 705-723.
    4. Jones, Larry E & Manuelli, Rodolfo E & Rossi, Peter E, 1993. "Optimal Taxation in Models of Endogenous Growth," Journal of Political Economy, University of Chicago Press, vol. 101(3), pages 485-517, June.
    5. Blanchard, Olivier Jean & Kahn, Charles M, 1980. "The Solution of Linear Difference Models under Rational Expectations," Econometrica, Econometric Society, vol. 48(5), pages 1305-1311, July.
    6. Chamley, Christophe, 1981. "The Welfare Cost of Capital Income Taxation in a Growing Economy," Journal of Political Economy, University of Chicago Press, vol. 89(3), pages 468-496, June.
    7. Judd, Kenneth L., 1982. "An alternative to steady-state comparisons in perfect foresight models," Economics Letters, Elsevier, vol. 10(1-2), pages 55-59.
    8. Ortigueira, Salvador, 1998. "Fiscal policy in an endogenous growth model with human capital accumulation," Journal of Monetary Economics, Elsevier, vol. 42(2), pages 323-355, July.
    9. Robert E. Lucas Jr., 2003. "Macroeconomic Priorities," American Economic Review, American Economic Association, vol. 93(1), pages 1-14, March.
    10. Xiaoyong, Cui & Gong, Liutang, 2006. "Laplace transform methods for linearizing multidimensional systems," Economics Letters, Elsevier, vol. 90(2), pages 176-182, February.
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    More about this item


    Z-transform; Steady-state comparisons; Multi-sector model;

    JEL classification:

    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques
    • E1 - Macroeconomics and Monetary Economics - - General Aggregative Models
    • H2 - Public Economics - - Taxation, Subsidies, and Revenue

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