Holden, Tom
(2008):
*Rational macroeconomic learning in linear expectational models.*

Preview |
PDF
MPRA_paper_10872.pdf Download (1MB) | Preview |

## Abstract

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.

Item Type: | MPRA Paper |
---|---|

Original Title: | Rational macroeconomic learning in linear expectational models |

Language: | English |

Keywords: | Rational Expectations; Partial information; Bayesian learning; Generalized Schur decomposition; Sunspots; Indeterminacy; Feasible Rational Expectations Equilibria |

Subjects: | E - Macroeconomics and Monetary Economics > E0 - General > E00 - General C - Mathematical and Quantitative Methods > C6 - Mathematical Methods ; Programming Models ; Mathematical and Simulation Modeling > C60 - General C - Mathematical and Quantitative Methods > C1 - Econometric and Statistical Methods and Methodology: General > C11 - Bayesian Analysis: General |

Item ID: | 10872 |

Depositing User: | Tom Holden |

Date Deposited: | 03 Oct 2008 01:09 |

Last Modified: | 27 Sep 2019 22:25 |

References: | Auray, Stéphane and Fève, Patrick (2007), 'On Sunspots, Habits, And Monetary Facts', Macroeconomic Dynamics, 12 (01), 72-96. Benhabib, Jess and Farmer, Roger E. A. (1994), 'Indeterminacy and Increasing Returns', Journal of Economic Theory, 63 (1), 19-41. Benhabib, Jess and Gali, Jordi (1995), 'On growth and indeterminacy: some theory and evidence', Carnegie-Rochester Conference Series on Public Policy, 43, 163-211. Benhabib, Jess and Nishimura, Kazuo (1998), 'Indeterminacy and Sunspots with Constant Returns', Journal of Economic Theory, 81 (1), 58-96. Benhabib, Jess and Farmer, Roger E. A. (2000), 'The Monetary Transmission Mechanism', Review of Economic Dynamics, 3 (3), 523-50. Benhabib, Jess, Schmitt-Grohe, Stephanie, and Uribe, Martin (1998), Monetary Policy and Multiple Equilibria (SSRN). Benhabib, Jess, Farmer, Roger E. A., and John, B. Taylor and Michael Woodford (1999), 'Chapter 6 Indeterminacy and sunspots in macroeconomics', Handbook of Macroeconomics (Volume 1, Part 1: Elsevier), 387-448. Binder, M. and Pesaran, H. (1996), 'Multivariate Linear Rational Expectations Models: Characterisation of the Nature of the Solutions and Their Fully Recursive Computation', (Faculty of Economics (formerly DAE), University of Cambridge). Blanchard, Olivier Jean and Kahn, Charles M. (1980), 'The Solution of Linear Difference Models under Rational Expectations', Econometrica, 48 (5), 1305-11. Blanchard, Olivier Jean and Summers, Lawrence H. (1987), 'Fiscal increasing returns, hysteresis, real wages and unemployment', European Economic Review, 31 (3), 543-60. Blume, Lawrence E. and Easley, David (1993), 'Rational Expectations and Rational Learning', (EconWPA). Blume, Lawrence E., Bray, Margaret M., and Easley, David (1982), 'Introduction to the Stability of Rational Expectations Equilibrium', Journal of Economic Theory, 26 (2), 313-17. Bray, Margaret (1982), 'Learning, estimation, and the stability of rational expectations', Journal of Economic Theory, 26 (2), 318-39. Cagan, Phillip (1954), 'The monetary dynamics of hyper-inflations'. Calvo, Guillermo A. (1983), 'Staggered Prices in a Utility-Maximizing Framework', Journal of Monetary Economics, 12 (3), 383-98. Cogley, Timothy and Sargent, Thomas J. (2008), 'Anticipated Utility and Rational Expectations as Approximations of Bayesian Decision Making', International Economic Review, 49, 185-221. Davidson, James (1994), Stochastic limit theory : an introduction for econometricians (Advanced texts in econometrics; Oxford; New York: Oxford University Press). Doob, Joseph L. (1953), Stochastic processes (Wiley publications in statistics; New York: Wiley). Doob, Joseph L. (1984), Classical potential theory and its probabilistic counterpart (Grundlehren der mathematischen Wissenschaften, 262; New York: Springer-Verlag). Dreze, Jacques H. (1976), 'Bayesian Limited Information Analysis of the Simultaneous Equations Model', Econometrica, 44 (5), 1045-75. Dudley, R. M. (2005), Real analysis and probability (Cambridge: Cambridge University Press). Easley, David and Kiefer, Nicholas M. (1988), 'Controlling a Stochastic Process with Unknown Parameters', Econometrica, 56 (5), 1045-64. Ellison, Martin and Pearlman, Joe (2008), 'Saddlepath Learning'. Evans, George W. and Honkapohja, Seppo (2001), Learning and expectations in macroeconomics (Frontiers of Economic Research; Princeton and Oxford: Princeton University Press). Evans, I. G. (1965), 'Bayesian Estimation of Parameters of a Multivariate Normal Distribution', Journal of the Royal Statistical Society. Series B (Methodological), 27 (2), 279-83. Hastings, W. K. (1970), 'Monte Carlo Sampling Methods Using Markov Chains and Their Applications', Biometrika, 57 (1), 97-109. Hinrichsen, Diederich and Pritchard, A. J. (2005), Mathematical systems theory (Texts in applied mathematics, 48; Berlin; New York: Springer). Horn, Roger A. and Johnson, Charles R. (1985), Matrix analysis (Cambridge [Cambridgeshire]; New York: Cambridge University Press). Howitt, Peter and McAfee, R. Preston (1988), 'Stability of Equilibria with Externalities', The Quarterly Journal of Economics, 103 (2), 261-77. Kalai, Ehud and Lehrer, Ehud (1991), 'Rational Learning Leads to Nash Equilibrium', (C.V. Starr Center for Applied Economics, New York University). Kalman, R. E. (1960), 'A New Approach to Linear Filtering and Prediction Problems', Transactions of the ASME - Journal of Basic Engineering, 82, 35-45. Kiefer, Nicholas M. and Nyarko, Yaw (1989), 'Optimal Control of an Unknown Linear Process with Learning', International Economic Review, 30 (3), 571-86. Kleibergen, Frank and Zivot, Eric (1998), 'Bayesian and Classical Approaches to Instrumental Variables Regression', (EconWPA). Kreps, David M. (1998), 'Anticipated Utility and Dynamic Choice', in Donald P. Jacobs, Ehud Kalai, and Morton Kamien (eds.), Frontiers of research in economic theory (Cambridge: Cambridge University Press), 242-74. Lubik, T. A. and Schorfheide, F. (2003), 'Computing sunspot equilibria in linear rational expectations models', Journal of Economic Dynamics and Control, 28, 273-85. Lucas, Robert E. (1972), 'Expectations and the neutrality of money', Journal of Economic Theory, 4 (2), 103-24. Marcet, Albert and Sargent, Thomas J. (1989), 'Convergence of least squares learning mechanisms in self-referential linear stochastic models', Journal of Economic Theory, 48 (2), 337-68. Mas-Colell, Andreu, Whinston, Michael Dennis, and Green, Jerry R. (1995), Microeconomic theory (New York: Oxford University Press). Mavroeidis, Sophocles and Zwols, Yori (2007), 'LiRE - An Ox package for solving Linear Rational Expecta-tions Models - Manual Version 3.0'. <http://www.econ.brown.edu/fac/Sophocles_Mavroeidis/code/lire3.pdf>, accessed 07/12/2007. McCallum, Bennett T. (1983), 'On Non-Uniqueness in Rational Expectations Models: An Attempt at Perspective', (National Bureau of Economic Research, Inc). McCallum, Bennett T. (1999), 'Role of the Minimal State Variable Criterion in Rational Expectations Models', International Tax and Public Finance, 6 (4), 621-39. Muth, John F. (1961), 'Rational Expectations and the Theory of Price Movements', Econometrica, 29 (3), 315-35. Pearlman, Joseph, Currie, David, and Levine, Paul (1986), 'Rational expectations models with partial information', Economic Modelling, 3 (2), 90-105. Port, Sidney C. (1994), Theoretical probability for applications (Wiley series in probability and mathematical statistics; New York: Wiley). Prescott, Edward C. (1972), 'The Multi-Period Control Problem Under Uncertainty', Econometrica, 40 (6), 1043-58. Quarteroni, Alfio, Sacco, Riccardo, and Saleri, Fausto (2000), Numerical mathematics (Texts in applied mathematics, 37; New York: Springer). Radner, Roy (1979), 'Rational Expectations Equilibrium: Generic Existence and the Information Revealed by Prices', Econometrica, 47 (3), 655-78. Rotemberg, Julio J. and Woodford, Michael (1992), 'Oligopolistic Pricing and the Effects of Aggregate Demand on Economic Activity', The Journal of Political Economy, 100 (6), 1153-207. Sargent, Thomas J., Fand, David, and Goldfeld, Stephen (1973), 'Rational Expectations, the Real Rate of Interest, and the Natural Rate of Unemployment', Brookings Papers on Economic Activity, 1973 (2), 429-80. Savage, Leonard J. (1954), The foundations of statistics (Wiley publications in statistics; New York: Wiley). Sims, Christopher A. (2002), 'Solving Linear Rational Expectations Models', Computational Economics, 20 (1), 1-20. Sutherland, W. A. (1975), Introduction to metric and topological spaces (Oxford [Eng.]: Clarendon Press). Taylor, John B. (1998), 'Monetary policy rules', (Chicago: University of Chicago Press). Townsend, Robert M. (1978), 'Market Anticipations, Rational Expectations, and Bayesian Analysis', International Economic Review, 19 (2), 481-94. Townsend, Robert M. (1983), 'Forecasting the Forecasts of Others', The Journal of Political Economy, 91 (4), 546-88. Walsh, Carl E. (2003), Monetary theory and policy (Second edition; Cambridge and London: MIT Press). Woodford, Michael (1987), 'Credit Policy and the Price Level in a Cash-in-Advance Economy', Proceedings of the Second International Symposium in Economic Theory and Econometrics (Barnett,-William-A.; Singleton,-Kenneth-J., eds. New approaches to monetary economics: International Symposia in Economic Theory and Econometrics series), New York and Melbourne Cambridge University Press, 1987; 52-66. Woodford, Michael (1994), 'Monetary policy and price level determinacy in a cash-in-advance economy', Economic Theory, 4 (3), 345-80. Wooldridge, Jeffrey M. (2002), Econometric analysis of cross section and panel data (Cambridge, Mass.: MIT Press). Young, H. Peyton (2004), Strategic learning and its limits (Oxford [England]; New York: Oxford University Press). |

URI: | https://mpra.ub.uni-muenchen.de/id/eprint/10872 |