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Rational macroeconomic learning in linear expectational models

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  • Holden, Tom

Abstract

The partial information rational expectations solution to a general linear multivariate expectational macro-model is found when agents are uncertain about the true values of the model’s parameters. Necessary and sufficient conditions for convergence to the full information rational expectations solution are given, and the core of an algorithm for the Bayesian updating of beliefs is provided. In the course of this a new class of full information rational expectations equilibria is described and some of its desirable properties proven.

Suggested Citation

  • Holden, Tom, 2008. "Rational macroeconomic learning in linear expectational models," MPRA Paper 10872, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:10872
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    File URL: https://mpra.ub.uni-muenchen.de/10872/1/MPRA_paper_10872.pdf
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    1. Benhabib Jess & Farmer Roger E. A., 1994. "Indeterminacy and Increasing Returns," Journal of Economic Theory, Elsevier, vol. 63(1), pages 19-41, June.
    2. 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.
    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. Jess Benhabib & Roger E.A. Farmer, 2000. "The Monetary Transmission Mechanism," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 3(3), pages 523-550, July.
    5. Woodford, Michael, 1994. "Monetary Policy and Price Level Determinacy in a Cash-in-Advance Economy," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 4(3), pages 345-380.
    6. Auray, Stéphane & Fève, Patrick, 2008. "On Sunspots, Habits, And Monetary Facts," Macroeconomic Dynamics, Cambridge University Press, vol. 12(1), pages 72-96, February.
    7. Young, H. Peyton, 2004. "Strategic Learning and its Limits," OUP Catalogue, Oxford University Press, number 9780199269181.
    8. Lubik, Thomas A. & Schorfheide, Frank, 2003. "Computing sunspot equilibria in linear rational expectations models," Journal of Economic Dynamics and Control, Elsevier, vol. 28(2), pages 273-285, November.
    9. Radner, Roy, 1979. "Rational Expectations Equilibrium: Generic Existence and the Information Revealed by Prices," Econometrica, Econometric Society, vol. 47(3), pages 655-678, May.
    10. Kalai, Ehud & Lehrer, Ehud, 1993. "Rational Learning Leads to Nash Equilibrium," Econometrica, Econometric Society, vol. 61(5), pages 1019-1045, September.
    11. 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.
    12. Townsend, Robert M, 1978. "Market Anticipations, Rational Expectations, and Bayesian Analysis," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 19(2), pages 481-494, June.
    13. Calvo, Guillermo A., 1983. "Staggered prices in a utility-maximizing framework," Journal of Monetary Economics, Elsevier, vol. 12(3), pages 383-398, September.
    14. Jess Benhabib & Kazuo Nishimura, 2012. "Indeterminacy and Sunspots with Constant Returns," Springer Books, in: John Stachurski & Alain Venditti & Makoto Yano (ed.), Nonlinear Dynamics in Equilibrium Models, edition 127, chapter 0, pages 311-346, Springer.
    15. 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.
    16. Bennett T. McCallum, 2000. "Role of the Minimal State Variable Criterion," NBER Working Papers 7087, National Bureau of Economic Research, Inc.
    17. Blanchard, Olivier J. & Summers, Lawrence H., 1987. "Hysteresis in unemployment," European Economic Review, Elsevier, vol. 31(1-2), pages 288-295.
    18. Ellison, Martin & Pearlman, Joseph, 2011. "Saddlepath learning," Journal of Economic Theory, Elsevier, vol. 146(4), pages 1500-1519, July.
    19. Stephanie Schmitt-Grohe & Jess Benhabib & Martin Uribe, 2001. "Monetary Policy and Multiple Equilibria," American Economic Review, American Economic Association, vol. 91(1), pages 167-186, March.
    20. Blanchard, Olivier J. & Summers, Lawrence H., 1987. "Fiscal increasing returns, hysteresis, real wages and unemployment," European Economic Review, Elsevier, vol. 31(3), pages 543-560, April.
    21. Peter Howitt & R. Preston McAfee, 1988. "Stability of Equilibria with Externalities," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 103(2), pages 261-277.
    22. Kleibergen, Frank & Zivot, Eric, 2003. "Bayesian and classical approaches to instrumental variable regression," Journal of Econometrics, Elsevier, vol. 114(1), pages 29-72, May.
    23. Rotemberg, Julio J & Woodford, Michael, 1992. "Oligopolistic Pricing and the Effects of Aggregate Demand on Economic Activity," Journal of Political Economy, University of Chicago Press, vol. 100(6), pages 1153-1207, December.
    24. Sims, Christopher A, 2002. "Solving Linear Rational Expectations Models," Computational Economics, Springer;Society for Computational Economics, vol. 20(1-2), pages 1-20, October.
    25. Thomas J. Sargent, 1973. "Rational Expectations, the Real Rate of Interest, and the Natural Rate of Unemployment," Brookings Papers on Economic Activity, Economic Studies Program, The Brookings Institution, vol. 4(2), pages 429-480.
    26. Dreze, Jacques H, 1976. "Bayesian Limited Information Analysis of the Simultaneous Equations Model," Econometrica, Econometric Society, vol. 44(5), pages 1045-1075, September.
    27. Blume, L. E. & Bray, M. M. & Easley, D., 1982. "Introduction to the stability of rational expectations equilibrium," Journal of Economic Theory, Elsevier, vol. 26(2), pages 313-317, April.
    28. Benhabib, Jess & Gali, Jordi, 1995. "On growth and indeterminacy: some theory and evidence," Carnegie-Rochester Conference Series on Public Policy, Elsevier, vol. 43(1), pages 163-211, December.
    29. Pearlman, Joseph & Currie, David & Levine, Paul, 1986. "Rational expectations models with partial information," Economic Modelling, Elsevier, vol. 3(2), pages 90-105, April.
    30. Jacobs,Donald P. & Kalai,Ehud & Kamien,Morton I. & Schwartz,Nancy L. (ed.), 1998. "Frontiers of Research in Economic Theory," Cambridge Books, Cambridge University Press, number 9780521635387, January.
    31. Lucas, Robert Jr., 1972. "Expectations and the neutrality of money," Journal of Economic Theory, Elsevier, vol. 4(2), pages 103-124, April.
    32. Binder, M. & Pesaran, H., 1996. "Multivariate Linear Rational Expectations Models: Characterisation of the Nature of the Solutions and Their Fully Recursive Computation," Cambridge Working Papers in Economics 9619, Faculty of Economics, University of Cambridge.
    33. repec:fth:starer:9613 is not listed on IDEAS
    34. Prescott, Edward C, 1972. "The Multi-Period Control Problem Under Uncertainty," Econometrica, Econometric Society, vol. 40(6), pages 1043-1058, November.
    35. Kiefer, Nicholas M & Nyarko, Yaw, 1989. "Optimal Control of an Unknown Linear Process with Learning," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 30(3), pages 571-586, August.
    36. Timothy Cogley & Thomas J. Sargent, 2008. "Anticipated Utility And Rational Expectations As Approximations Of Bayesian Decision Making," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 49(1), pages 185-221, February.
    37. Townsend, Robert M, 1983. "Forecasting the Forecasts of Others," Journal of Political Economy, University of Chicago Press, vol. 91(4), pages 546-588, August.
    38. Lawrence Blume & David Easley, 1993. "Rational Expectations and Rational Learning," Game Theory and Information 9307003, University Library of Munich, Germany.
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    Cited by:

    1. Tom Holden, 2012. "Learning from learners," School of Economics Discussion Papers 1512, School of Economics, University of Surrey.

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    More about this item

    Keywords

    Rational Expectations; Partial information; Bayesian learning; Generalized Schur decomposition; Sunspots; Indeterminacy; Feasible Rational Expectations Equilibria;
    All these keywords.

    JEL classification:

    • E00 - Macroeconomics and Monetary Economics - - General - - - General
    • C60 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - General
    • C11 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Bayesian Analysis: General

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