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The forward method as a solution refinement in rational expectations models

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  • Cho, Seonghoon
  • Moreno, Antonio

Abstract

This paper generalizes the standard forward method of recursive substitution to a general class of linear rational expectations models with potentially multiple fundamental solutions. It is shown that the existence and uniqueness of the well-known forward solution are preserved in a general context. We also propose a key property embedded in the forward solution - the no-bubble condition - as an economically sensible solution refinement in the class of fundamental solutions. In the literature, the no-bubble condition has been assumed to rule out non-fundamental bubble solutions. We show that the forward solution is the only rational expectations equilibrium satisfying the no-bubble condition and consequently, it is the most relevant fundamental solution within the class of fundamental equilibria. Several economic examples are provided where the fundamental solutions obtained by other solution methods and refined by other solution selection criteria violate the no-bubble condition.

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  • Cho, Seonghoon & Moreno, Antonio, 2011. "The forward method as a solution refinement in rational expectations models," Journal of Economic Dynamics and Control, Elsevier, vol. 35(3), pages 257-272, March.
  • Handle: RePEc:eee:dyncon:v:35:y:2011:i:3:p:257-272
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    1. McCallum, Bennett T., 2004. "On the relationship between determinate and MSV solutions in linear RE models," Economics Letters, Elsevier, vol. 84(1), pages 55-60, July.
    2. King, Robert G & Watson, Mark W, 1998. "The Solution of Singular Linear Difference Systems under Rational Expectations," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 39(4), pages 1015-1026, November.
    3. Bennett McCallum, 1999. "Role of the Minimal State Variable Criterion in Rational Expectations Models," International Tax and Public Finance, Springer;International Institute of Public Finance, vol. 6(4), pages 621-639, November.
    4. Bennett T. McCallum, 2009. "Determinacy, Learnability, and Plausibility in Monetary Policy Analysis: Additional Results," Central Banking, Analysis, and Economic Policies Book Series, in: Klaus Schmidt-Hebbel & Carl E. Walsh & Norman Loayza (Series Editor) & Klaus Schmidt-Hebbel (Series (ed.),Monetary Policy under Uncertainty and Learning, edition 1, volume 13, chapter 7, pages 203-225, Central Bank of Chile.
    5. Thomas A. Lubik & Frank Schorfheide, 2004. "Testing for Indeterminacy: An Application to U.S. Monetary Policy," American Economic Review, American Economic Association, vol. 94(1), pages 190-217, March.
    6. Paul A. Samuelson, 1958. "An Exact Consumption-Loan Model of Interest with or without the Social Contrivance of Money," Journal of Political Economy, University of Chicago Press, vol. 66(6), pages 467-467.
    7. Carl E. Walsh, 2003. "Monetary Theory and Policy, 2nd Edition," MIT Press Books, The MIT Press, edition 2, volume 1, number 0262232316, December.
    8. Cho, Seonghoon & McCallum, Bennett T., 2009. "Another weakness of "determinacy" as a selection criterion for rational expectations models," Economics Letters, Elsevier, vol. 104(1), pages 17-19, July.
    9. Bennett T. Mccallum, 2011. "Causality, Structure And The Uniqueness Of Rational Expectations Equilibria," Manchester School, University of Manchester, vol. 79(s1), pages 551-566, June.
    10. 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.
    11. McCallum, Bennett T., 1983. "On non-uniqueness in rational expectations models : An attempt at perspective," Journal of Monetary Economics, Elsevier, vol. 11(2), pages 139-168.
    12. Dornbusch, Rudiger, 1976. "Expectations and Exchange Rate Dynamics," Journal of Political Economy, University of Chicago Press, vol. 84(6), pages 1161-1176, December.
    13. Binder, Michael & Pesaran, M. Hashem, 1997. "Multivariate Linear Rational Expectations Models," Econometric Theory, Cambridge University Press, vol. 13(6), pages 877-888, December.
    14. Driskill, Robert, 2006. "Multiple equilibria in dynamic rational expectations models: A critical review," European Economic Review, Elsevier, vol. 50(1), pages 171-210, January.
    15. Sims, Christopher A, 2002. "Solving Linear Rational Expectations Models," Computational Economics, Springer;Society for Computational Economics, vol. 20(1-2), pages 1-20, October.
    16. Blanchard, Olivier J, 1979. "Backward and Forward Solutions for Economies with Rational Expectations," American Economic Review, American Economic Association, vol. 69(2), pages 114-118, May.
    17. Lars Ljungqvist & Thomas J. Sargent, 2004. "Recursive Macroeconomic Theory, 2nd Edition," MIT Press Books, The MIT Press, edition 2, volume 1, number 026212274x, December.
    18. Farmer Roger E. A. & Guo Jang-Ting, 1994. "Real Business Cycles and the Animal Spirits Hypothesis," Journal of Economic Theory, Elsevier, vol. 63(1), pages 42-72, June.
    19. Klein, Paul, 2000. "Using the generalized Schur form to solve a multivariate linear rational expectations model," Journal of Economic Dynamics and Control, Elsevier, vol. 24(10), pages 1405-1423, September.
    20. Flood, Robert P & Garber, Peter M, 1980. "An Economic Theory of Monetary Reform," Journal of Political Economy, University of Chicago Press, vol. 88(1), pages 24-58, February.
    21. Devereux, Michael B & Mansoorian, Arman, 1992. "International Fiscal Policy Coordination and Economic Growth," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 33(2), pages 249-268, May.
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    Cited by:

    1. Cho, Seonghoon, 2021. "Determinacy and classification of Markov-switching rational expectations models," Journal of Economic Dynamics and Control, Elsevier, vol. 127(C).
    2. John Barrdear, 2015. "Towards a New Keynesian Theory of the Price Level," Discussion Papers 1509, Centre for Macroeconomics (CFM).
    3. Baele, Lieven & Bekaert, Geert & Cho, Seonghoon & Inghelbrecht, Koen & Moreno, Antonio, 2015. "Macroeconomic regimes," Journal of Monetary Economics, Elsevier, vol. 70(C), pages 51-71.
    4. Junior Maih, 2014. "Efficient Perturbation Methods for Solving Regime-Switching DSGE Models," Working Papers No 10/2014, Centre for Applied Macro- and Petroleum economics (CAMP), BI Norwegian Business School.
    5. Kollmann, Robert, 2021. "Liquidity traps in a world economy," Journal of Economic Dynamics and Control, Elsevier, vol. 132(C).
    6. Bennett T. McCallum, 2012. "A Continuity Refinement for Rational Expectations Solutions," NBER Working Papers 18323, National Bureau of Economic Research, Inc.
    7. Dennis Bonam & Bart Hobijn, 2021. "Generalized Stability of Monetary Unions Under Regime Switching in Monetary and Fiscal Policies," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 53(1), pages 73-94, February.
    8. Fabrizio Almeida Marodin & Marcelo Savino Portugal, 2019. "Exchange Rate Pass-Through in Brazil: À Markov Switching DSGE Estimation for the Inflation Targeting Period," Russian Journal of Money and Finance, Bank of Russia, vol. 78(1), pages 36-66, March.
    9. Thanassis Kazanas & Apostolis Philippopoulos & Elias Tzavalis, 2011. "Monetary Policy Rules And Business Cycle Conditions," Manchester School, University of Manchester, vol. 79(s2), pages 73-97, September.
    10. Seonghoon Cho, 2016. "Sufficient Conditions for Determinacy in a Class of Markov-Switching Rational Expectations Models," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 21, pages 182-200, July.
    11. Cuadra, Gabriel & Menna, Lorenzo, 2019. "Capital flows and the business cycle," Journal of Economic Dynamics and Control, Elsevier, vol. 106(C), pages 1-1.
    12. Lan, Hong & Meyer-Gohde, Alexander, 2012. "Existence and Uniqueness of Perturbation Solutions in DSGE Models," Dynare Working Papers 14, CEPREMAP.
    13. Bennett T. McCallum, 2012. "Determinacy, Learnability, Plausibility, and the Role of Money in New Keynesian Models," NBER Working Papers 18215, National Bureau of Economic Research, Inc.
    14. John Y. Campbell & Carolin Pflueger & Luis M. Viceira, 2020. "Macroeconomic Drivers of Bond and Equity Risks," Journal of Political Economy, University of Chicago Press, vol. 128(8), pages 3148-3185.
    15. Hatcher, Michael, 2022. "Solving linear rational expectations models in the presence of structural change: Some extensions," Journal of Economic Dynamics and Control, Elsevier, vol. 138(C).
    16. Christopher Gibbs & Nigel McClung, 2023. "Does my model predict a forward guidance puzzle?," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 51, pages 393-423, December.
    17. Lan, Hong & Meyer-Gohde, Alexander, 2014. "Solvability of perturbation solutions in DSGE models," Journal of Economic Dynamics and Control, Elsevier, vol. 45(C), pages 366-388.
    18. Thanassis Kazanas & Elias Tzavalis, 2011. "Unveiling the monetary policy rule in euro area," Working Papers 130, Bank of Greece.
    19. Cho, Seonghoon & McCallum, Bennett T., 2015. "Refining linear rational expectations models and equilibria," Journal of Macroeconomics, Elsevier, vol. 46(C), pages 160-169.
    20. Christopher Gibbs & Nigel McClung, 2023. "Does my model predict a forward guidance puzzle?," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 51, pages 393-423, December.
    21. repec:hum:wpaper:sfb649dp2012-015 is not listed on IDEAS

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