Reduced Forms of Rational Expectations Models

Table of contents

1. Cover
2. Halftitle
3. Title
4. Copyright
5. Contents
6. Introduction to the Series
7. Introduction
   1. Plan of the monograph
   2. References
8. 1. Expectation Schemes
   1. 1. Expectations
      1. 1.1. Basic notions
      2. 1.2. Successive predictions
   2. 2. Adaptive scheme
      1. 2.1. The adaptive form
      2. 2.2. The extrapolative form
   3. 3. Rational scheme
      1. 3.1. Optimal predictions
      2. 3.2. Some properties of optimal predictions
      3. 3.3. Prediction errors and updating
   4. References
9. 2. A Model with Current Expectations
   1. 1. An equilibrium model in an uncertain environment
      1. 1.1. A Walrasian equilibrium model
      2. 1.2. Extension of the model
      3. 1.3. The linear case
   2. 2. Dynamic properties of the current expectation model
      1. 2.1. The rational expectations model
      2. 2.2. Comparison of the constrained and unconstrained reduced forms
      3. 2.3. Comparison of various expectation schemes
   3. 3. Learning processes
   4. References
10. 3. A Model with Future Expectations
    1. 1. Examples
       1. 1.1. Hyperinflation models
       2. 1.2. The Taylor model
       3. 1.3. Some remarks on the price equation
       4. 1.4. The evolution of an asset price
    2. 2. A description of the solution methods
       1. 2.1. The “forward” — “backward” approach
       2. 2.2. Linear solutions
       3. 2.3. The general solution
    3. 3. Properties of the solution set
       1. 3.1. Impact of a terminal condition
       2. 3.2. Impact of an initial condition
       3. 3.3. Sunspots
       4. 3.4. Stationary solutions
       5. 3.5. Variability of the linear stationary solutions
    4. 4. Learning processes
    5. References
11. 4. Dynamic Extensions
    1. 1. Some examples
       1. 1.1. A model with various expectations of the current endogenous variable
       2. 1.2. A model with a two-periods-ahead future expectation
       3. 1.3. A model with one current expectation and one future expectation
       4. 1.4. Some remarks
    2. 2. Solutions to the general univariate model
       1. 2.1. The model
       2. 2.2. Expression of the expectations in terms of realizations
       3. 2.3. Constraints on the updating terms
       4. 2.4. Some consequences
       5. 2.5. Some applications
    3. 3. Linear solutions
       1. 3.1. The general form of the linear solutions
       2. 3.2. (Asymptotic) stationarity of the linear solutions
       3. 3.3. An example
    4. References
12. 5. Multivariate Models
    1. 1. Dynamic macroeconometric models
    2. 2. A simple case
       1. 2.1. The case without recursivities
       2. 2.2. The special case of a nilpotent structural matrix
       3. 2.3. The general case
    3. 3. The general model
       1. 3.1. Canonical forms
       2. 3.2. Reduction of the canonical form
       3. 3.3. Reduction of the general model
       4. 3.4. Linear stationary solutions
    4. 4. Rational expectations and non-stationary models
       1. 4.1. Decomposition of an ARIMA series and cointegration
       2. 4.2. Application to rational expectations models
    5. 5. Concluding remarks
    6. References
13. 6. A Mean-Variance Model
    1. 1. The model
       1. 1.1. Demand function of the speculators
       2. 1.2. Excess supply function of storable good
       3. 1.3. Equilibrium condition
    2. 2. Evolution of the equilibrium price
    3. 3. Risk premia
       1. 3.1. Asymptotic behavior of the solutions
       2. 3.2. Comparative statics
    4. References
14. Index