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One of the major controversies in macroeconomics over the last 30 years has been that on the effectiveness of stabilization policies. However, this debate, between those who believe that this kind of policies is useless if not harmful and those who argue in favor of it, has been mainly theoretical so far.
The Rational Expectation Hypothesis, Time-Varying Parameters and Adaptive Control wants to represent a step toward the construction of a common ground on which to empirically compare the two "beliefs" and to do this three strands of literature are brought together. The first strand is the research on time-varying parameters (TVP), the second strand is the work on adaptive control and the third one is the literature on linear stationary models with rational expectations (RE).
The material presented in The Rational Expectation Hypothesis, Time-Varying Parameters and Adaptive Control is divided into two parts. Part 1 combines the strand of literature on adaptive control with that on TVP. It generalizes the approach pioneered by Tse and Bar-Shalom (1973) and Kendrick (1981) and one recently used in Amman and Kendrick (2002), where the law of motion of the TVP and the hyperstructural parameters are assumed known, to the case where the hyperstructural parameters are assumed unknown. Part 2 is devoted to the linear single-equation stationary RE model estimated with the error-in-variables (EV) method. It presents a new formulation of this problem based on the use of TVP in an EV model. This new formulation opens the door to a very promising development. All the theory developed in the first part to control a model with TVP can sic et simpliciter be applied to control a model with RE.
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 The general model in state space form.- 8.7 A relevant special case: The Muth type model.- 8.8 Conclusion.- 9 The Identification Problem in Single-Equation RE Models.- 9.1 Introduction.- 9.2 The identification problem in the Muth type model: Introduction.- 9.3 The identification problem in the Muth type model: The general case.- 9.4 The identification problem in the Cagan type model: Introduction.- 9.5 The identification problem in the Cagan type model: The general case.- 9.6 The identification problem in the Taylor type model: Introduction.- 9.7 The identification problem in the Taylor type model: The general case.- 9.8 Conclusion.- Appendix 9A: The Cagan type model with n unstable roots.- Appendix 9B: The Taylor type model with n unstable roots.- 10 The Estimation Problem in Single-Equation RE Models.- 10.1 Introduction.- 10.2 A two-step estimator for the simple Muth type model.- 10.3 The maximum likelihood estimator for the simple Muth type model.- 10.4 The estimation problem in the Muth type model: The general case.- 10.5 A ‘two-step type’ estimator for the simple Cagan type model.- 10.6 The maximum likelihood estimator for the simple Cagan type model.- 10.7 The estimation problem in the Cagan type model: The general case.- 10.8 A ‘two-step type’ estimator for the simple Taylor type model.- 10.9 The maximum likelihood estimator for the simple Taylor type model.- 10.10 Conclusion.- Appendix 10A: The diffuse Kalman filter.- Appendix 10B: The information matrix of the structural and hyperstructural parameters of a state space model.- Appendix 10C: Some well known results on the estimated auto- and cross-covariances of a multivariate process.- References.- Name Index.