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Stable near-rational sunspot equilibria

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  • Evans, George W.
  • McGough, Bruce

Abstract

We introduce a new class of solutions to nonlinear forward-looking models called near-rational sunspot equilibria (NRSE). NRSE are natural nonlinear extensions of the usual sunspot equilibria associated with the linearized version of the economy, and are near-rational in that agents use the optimal linear forecasting model when forming expectations. Generic results for existence and stability under learning are established. NRSE in indeterminate nonlinear models are found to be stable under learning provided that the corresponding linearized model's minimal state variable solution is E-stable. NRSE are readily computable, and our results make it possible to use the standard linear tools to search for stable NRSE. We illustrate our results using a canonical nonlinear New Keynesian model.

Suggested Citation

  • Evans, George W. & McGough, Bruce, 2020. "Stable near-rational sunspot equilibria," Journal of Economic Theory, Elsevier, vol. 186(C).
  • Handle: RePEc:eee:jetheo:v:186:y:2020:i:c:s0022053119301334
    DOI: 10.1016/j.jet.2019.104987
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    1. Benhabib, Jess & Schmitt-Grohe, Stephanie & Uribe, Martin, 2001. "The Perils of Taylor Rules," Journal of Economic Theory, Elsevier, vol. 96(1-2), pages 40-69, January.
    2. Benhabib Jess & Farmer Roger E. A., 1994. "Indeterminacy and Increasing Returns," Journal of Economic Theory, Elsevier, vol. 63(1), pages 19-41, June.
    3. Wei Xiong & Hongjun Yan, 2010. "Heterogeneous Expectations and Bond Markets," Review of Financial Studies, Society for Financial Studies, vol. 23(4), pages 1433-1466, April.
    4. Richard Clarida & Jordi Galí & Mark Gertler, 2000. "Monetary Policy Rules and Macroeconomic Stability: Evidence and Some Theory," The Quarterly Journal of Economics, Oxford University Press, vol. 115(1), pages 147-180.
    5. Evans, George W., 1989. "The fragility of sunspots and bubbles," Journal of Monetary Economics, Elsevier, vol. 23(2), pages 297-317, March.
    6. Klaus Adam & Albert Marcet & Juan Pablo Nicolini, 2016. "Stock Market Volatility and Learning," Journal of Finance, American Finance Association, vol. 71(1), pages 33-82, February.
    7. Marcet, Albert & Sargent, Thomas J., 1989. "Convergence of least squares learning mechanisms in self-referential linear stochastic models," Journal of Economic Theory, Elsevier, vol. 48(2), pages 337-368, August.
    8. Alberto Martin & Jaume Ventura, 2012. "Economic Growth with Bubbles," American Economic Review, American Economic Association, vol. 102(6), pages 3033-3058, October.
    9. Bullard, James & Mitra, Kaushik, 2002. "Learning about monetary policy rules," Journal of Monetary Economics, Elsevier, vol. 49(6), pages 1105-1129, September.
    10. Evans, George W. & McGough, Bruce, 2005. "Monetary policy, indeterminacy and learning," Journal of Economic Dynamics and Control, Elsevier, vol. 29(11), pages 1809-1840, November.
    11. Evans, George W & McGough, Bruce, 2018. "Equilibrium selection, observability and backward-stable solutions," Journal of Monetary Economics, Elsevier, vol. 98(C), pages 1-10.
    12. Evans, George W. & Honkapohja, Seppo, 2003. "Existence of adaptively stable sunspot equilibria near an indeterminate steady state," Journal of Economic Theory, Elsevier, vol. 111(1), pages 125-134, July.
    13. Benhabib, Jess & Evans, George W. & Honkapohja, Seppo, 2014. "Liquidity traps and expectation dynamics: Fiscal stimulus or fiscal austerity?," Journal of Economic Dynamics and Control, Elsevier, vol. 45(C), pages 220-238.
    14. Jess Benhabib & Pengfei Wang & Yi Wen, 2015. "Sentiments and Aggregate Demand Fluctuations," Econometrica, Econometric Society, vol. 83, pages 549-585, March.
    15. Hommes, Cars & Zhu, Mei, 2014. "Behavioral learning equilibria," Journal of Economic Theory, Elsevier, vol. 150(C), pages 778-814.
    16. 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.
    17. Evans, George W. & McGough, Bruce, 2005. "Stable sunspot solutions in models with predetermined variables," Journal of Economic Dynamics and Control, Elsevier, vol. 29(4), pages 601-625, April.
    18. Evans, George W. & McGough, Bruce, 2011. "Representations And Sunspot Stability," Macroeconomic Dynamics, Cambridge University Press, vol. 15(1), pages 80-92, February.
    19. Mariana García-Schmidt & Michael Woodford, 2019. "Are Low Interest Rates Deflationary? A Paradox of Perfect-Foresight Analysis," American Economic Review, American Economic Association, vol. 109(1), pages 86-120, January.
    20. Karel R. S. M. Mertens & Morten O. Ravn, 2014. "Fiscal Policy in an Expectations-Driven Liquidity Trap," Review of Economic Studies, Oxford University Press, vol. 81(4), pages 1637-1667.
    21. Duffy, John & Xiao, Wei, 2007. "Instability of sunspot equilibria in real business cycle models under adaptive learning," Journal of Monetary Economics, Elsevier, vol. 54(3), pages 879-903, April.
    22. 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.
    23. Stefano Eusepi & Bruce Preston, 2018. "The Science of Monetary Policy: An Imperfect Knowledge Perspective," Journal of Economic Literature, American Economic Association, vol. 56(1), pages 3-59, March.
    24. Woodford, Michael, 1990. "Learning to Believe in Sunspots," Econometrica, Econometric Society, vol. 58(2), pages 277-307, March.
    25. George Evans, 1985. "Expectational Stability and the Multiple Equilibria Problem in Linear Rational Expectations Models," The Quarterly Journal of Economics, Oxford University Press, vol. 100(4), pages 1217-1233.
    26. Cass, David & Shell, Karl, 1983. "Do Sunspots Matter?," Journal of Political Economy, University of Chicago Press, vol. 91(2), pages 193-227, April.
    27. James Bullard & Stefano Eusepi, 2014. "When Does Determinacy Imply Expectational Stability?," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 55, pages 1-22, February.
    28. Guesnerie, Roger, 1986. "Stationary sunspot equilibria in an N commodity world," Journal of Economic Theory, Elsevier, vol. 40(1), pages 103-127, October.
    29. 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.
    30. Costas Azariadis & Roger Guesnerie, 1986. "Sunspots and Cycles," Review of Economic Studies, Oxford University Press, vol. 53(5), pages 725-737.
    31. Jordi Gal?, 2014. "Monetary Policy and Rational Asset Price Bubbles," American Economic Review, American Economic Association, vol. 104(3), pages 721-752, March.
    32. Cochrane, John H., 2017. "The new-Keynesian liquidity trap," Journal of Monetary Economics, Elsevier, vol. 92(C), pages 47-63.
    33. Evans George W & McGough Bruce, 2005. "Indeterminacy and the Stability Puzzle in Non-Convex Economies," The B.E. Journal of Macroeconomics, De Gruyter, vol. 5(1), pages 1-46, September.
    34. Milani, Fabio, 2007. "Expectations, learning and macroeconomic persistence," Journal of Monetary Economics, Elsevier, vol. 54(7), pages 2065-2082, October.
    35. George W. Evans & Bruce Mcgough, 2018. "Interest‐Rate Pegs in New Keynesian Models," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 50(5), pages 939-965, August.
    36. Hommes, Cars & Sorger, Gerhard, 1998. "Consistent Expectations Equilibria," Macroeconomic Dynamics, Cambridge University Press, vol. 2(3), pages 287-321, September.
    37. Jianjun Miao & Zhouxiang Shen & Pengfei Wang, 2019. "Monetary Policy and Rational Asset Price Bubbles: Comment," American Economic Review, American Economic Association, vol. 109(5), pages 1969-1990, May.
    38. Branch, William A. & McGough, Bruce, 2005. "Consistent expectations and misspecification in stochastic non-linear economies," Journal of Economic Dynamics and Control, Elsevier, vol. 29(4), pages 659-676, April.
    39. Azariadis, Costas, 1981. "Self-fulfilling prophecies," Journal of Economic Theory, Elsevier, vol. 25(3), pages 380-396, December.
    40. Bray, Margaret M & Savin, Nathan E, 1986. "Rational Expectations Equilibria, Learning, and Model Specification," Econometrica, Econometric Society, vol. 54(5), pages 1129-1160, September.
    41. Evans George W. & Honkapohja Seppo, 1994. "On the Local Stability of Sunspot Equilibria under Adaptive Learning Rules," Journal of Economic Theory, Elsevier, vol. 64(1), pages 142-161, October.
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    Cited by:

    1. Evans, George W. & McGough, Bruce, 2020. "Equilibrium stability in a nonlinear cobweb model," Economics Letters, Elsevier, vol. 193(C).

    More about this item

    Keywords

    E-stability; Sunspot equilibria; Nonlinear dynamics; Indeterminacy; MSV principle;

    JEL classification:

    • C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium
    • D83 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Search; Learning; Information and Knowledge; Communication; Belief; Unawareness
    • D84 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Expectations; Speculations
    • E32 - Macroeconomics and Monetary Economics - - Prices, Business Fluctuations, and Cycles - - - Business Fluctuations; Cycles
    • E71 - Macroeconomics and Monetary Economics - - Macro-Based Behavioral Economics - - - Role and Effects of Psychological, Emotional, Social, and Cognitive Factors on the Macro Economy

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