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Solving linear difference systems with lagged expectations by a method of undetermined coefficients

Author

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  • Pengfei Wang
  • Yi Wen
Abstract
This paper proposes a solution method to solve linear difference models with lagged expectations. Variables with lagged expectations expand the model's state space greatly when N is large; and getting the system into a canonical form solvable by the traditional methods involves substantial manual work (e.g., arranging the state vector and the associated coefficient matrices to accommodate variables with lagged expectations), which is prone to human errors. Our method avoids the need of expanding the state space of the system and shifts the burden of analysis from the individual economist/model solver toward the computer. Hence it can be a very useful tool in practice, especially in testing and estimating economics models with a high order of lagged expectations. Examples are provided to demonstrate the usefulness of the method. We also discuss the implications of lagged expectations on the equilibrium properties of indeterminate DSGE models, such as the serial correlation properties of sunspots shocks in these models.

Suggested Citation

  • Pengfei Wang & Yi Wen, 2006. "Solving linear difference systems with lagged expectations by a method of undetermined coefficients," Working Papers 2006-003, Federal Reserve Bank of St. Louis.
    • Handle: RePEc:fip:fedlwp:2006-003
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    References listed on IDEAS

    as
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    11. Sims, Christopher A, 2002. "Solving Linear Rational Expectations Models," Computational Economics, Springer;Society for Computational Economics, vol. 20(1-2), pages 1-20, October.
    12. Christiano, Lawrence J, 2002. "Solving Dynamic Equilibrium Models by a Method of Undetermined Coefficients," Computational Economics, Springer;Society for Computational Economics, vol. 20(1-2), pages 21-55, October.
    13. Benjamin D. Keen, 2007. "Sticky Price And Sticky Information Price‐Setting Models: What Is The Difference?," Economic Inquiry, Western Economic Association International, vol. 45(4), pages 770-786, October.
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    Cited by:

    1. Wang, Pengfei & Wen, Yi, 2007. "Inflation dynamics: A cross-country investigation," Journal of Monetary Economics, Elsevier, vol. 54(7), pages 2004-2031, October.
    2. repec:hum:wpaper:sfb649dp2007-069 is not listed on IDEAS
    3. N. Gregory Mankiw & Ricardo Reis, 2007. "Sticky Information in General Equilibrium," Journal of the European Economic Association, MIT Press, vol. 5(2-3), pages 603-613, 04-05.
    4. Meyer-Gohde, Alexander, 2010. "Linear rational-expectations models with lagged expectations: A synthetic method," Journal of Economic Dynamics and Control, Elsevier, vol. 34(5), pages 984-1002, May.
    5. Trabandt, Mathias, 2003. "Sticky Information vs. Sticky Prices : A Horse Race in a DSGE Framework," SFB 373 Discussion Papers 2003,41, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
    6. Benedetto Molinari, 2014. "Sticky information and inflation persistence: evidence from the U.S. data," Empirical Economics, Springer, vol. 46(3), pages 903-935, May.
    7. Meyer-Gohde, Alexander, 2007. "Solving linear rational expectations models with lagged expectations quickly and easily," SFB 649 Discussion Papers 2007-069, Humboldt University Berlin, Collaborative Research Center 649: Economic Risk.
    8. Loisel, Olivier, 2024. "Stabilization policy and lags," Journal of Mathematical Economics, Elsevier, vol. 111(C).

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    Keywords

    Monetary policy; Macroeconomics;

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