The Rational Expectation Hypothesis, Time-Varying Parameters and Adaptive Control

1 Introduction.- 1.1 Introduction.- 1.2 Adaptive control and time-varying parameters.- 1.3 Time-varying parameters and the rational expectations hypothesis.- 1.4 The organization of the book.- 1.5 Suggestion for future research.- 1: Adaptive Control and Time-Varying Parameters.- 2 Kendrick's (1981) Case.- 2.1 Introduction.- 2.2 Statement of the problem.- 2.3 One-period ahead projection of the mean and variance of the augmented state vector z.- 2.4 The nominal path for the states and controls.- 2.5 Riccati equations for the K matrix of the augmented system.- 2.6 Riccati equations for the p vector of the augmented system.- 2.7 Updating and projecting the covariances of the augmented system.- 2.8 The approximate cost-to-go.- 2.9 Updating the state vector of the augmented system.- 2.10 Conclusion.- 3 The Uncertain Parameter Mean Case.- 3.1 Introduction.- 3.2 Statement of the problem.- 3.3 One-period ahead projection of the mean and variance of the augmented state vector z.- 3.4 The nominal path for the states and controls.- 3.5 Riccati equations for the K matrix of the augmented system.- 3.6 Riccati equations for the p vector of the augmented system.- 3.7 Updating and projecting the covariances of the augmented system.- 3.8 The approximate cost-to-go.- 3.9 Updating the state vector of the augmented system.- 3.10 A numerical example.- 3.11 Conclusion.- 4 The Complete Uncertainty Case.- 4.1 Introduction.- 4.2 Statement of the problem.- 4.3 One-period ahead projection of the mean and variance of the augmented state vector z.- 4.4 The nominal path for the states and controls.- 4.5 Riccati equations for the K matrix of the augmented system.- 4.6 Riccati equatons for the p vector of the augmented system.- 4.7 Updating and projecting the covariances of the augmented system.- 4.8 The approximate cost-to-go.- 4.9 Updating the state vector of the augmented system.- 4.10 Conclusion.- 5 Adaptive Control in the Presence of Time-Varying Parameters.- 5.1 Introduction.- 5.2 Parameters generated by a stationary stochastic process.- 5.3 Time-varying parameters in a control theory framework.- 5.4 The comparison of results.- 5.5 The effect of time-varying parameters on the approximate cost-to-go.- 5.6 The plan of the Monte Carlo experiment.- 5.7 The numerical results.- 5.8 Conclusion.- 6 The Nonconvexities Problem in Adaptive Control Models.- 6.1 Introduction.- 6.2 The problem.- 6.3 Introducing EZGRAD.- 6.4 A description of EZGRAD.- 6.5 The plan of the Monte Carlo experiment.- 6.6 The numerical results.- 6.7 Conclusion.- 2: Time-Varying Parameters and the Rational Expectations Hypotesis.- 7 The Rational Expectations Hypotesis in Linear Stationary Models: A New Formulation of Single-Equation Models.- 7.1 Introduction.- 7.2 The Cagan's (1956) hyper-inflation model.- 7.3 The Cagan type model with an intercept and a disturbance term.- 7.4 A generalization of the Cagan type model: An M-period ahead future expectation.- 7.5 A generalization of the Cagan type model: Several future expectations.- 7.6 A generalization of the Cagan type model: Several future expectations and k?1 exogenous variables.- 7.7 A generalization of the Cagan Type model: Future expectations, exogenous variables and lagged values.- 7.8 The Taylor's (1977) macroeconomic model.- 7.9 The Taylor type model with an intercept and an exogenous variable.- 7.10 A generalization of the Taylor type model: Several future expectations.- 7.11 A generalization of the Taylor type model: Future expectations, exogenous variables and lagged values.- 7.12 A single equation model: The general case.- 7.13 Current and future expectations: The Muth's (1961) model and the final generalization.- 7.14 Conclusion.- 8 The State Space Representation of Single-Equation RE Models.- 8.1 Introduction.- 8.2 The Cagan type model in state space form.- 8.3 The Cagan type model in state space form: An example.- 8.4 The Taylor type model in state space form.- 8.5 The Taylor type model in state space form: An example.- 8.6

Marco P. Tucci graduated in Economics at the University of Sienna, then he went to the University of Texas at Austin (USA) where he got his Ph. D. specializing in Control Theory, Econometrics and Empirical Macroeconomics. He is currently Associate Professor at the University of Sienna and a member of the Society of Computational Economics. He has published in the Journal of Computational Economics, Journal of Economic Dynamics and Control, Journal of Structural Changes and Economic Dynamics, Economic Notes and has contributed to books. He is referee for the above mentioned journals and for Macroeconomic Dynamics.