Decision Making under Uncertainty and Bounded Rationality

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In an attempt to capture the complexity of the economic system many economists were led to the formulation of complex nonlinear rational expectations models that in many cases can not be solved analytically. In such cases, numerical methods need to be employed…

Author: Mirestean, Alin Tavi

Source: University of Maryland

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Chapter I. Review of Methods Used for Solving Non-Linear Rational Expectations Models
I.1. Introduction
I.2. Generic Model
I.3. Using Certainty Equivalence; The Extended Path Method
I.3.1. Example
I.3.2. Notes on Certainty Equivalence Methods
I.4. Local Approximation and Perturbation Methods
I.4.1. Regular and General Perturbation Methods
I.4.2. Example
I.4.3. Flavors of Perturbation Methods
I.4.4. Alternative Local Approximation Methods
I.4.5. Notes on Local Approximation Methods
I.5. Discrete State-Space Methods
I.5.1. Example. Discrete State-Space Approximation Using Value-Function Iteration
I.5.2. Fredholm Equations and Numerical Quadratures
I.5.3. Example. Using Quadrature Approximations
I.5.4. Notes on Discrete State-Space Methods
I.6. Projection Methods
I.6.1. The Concept of Projection Methods
I.6.2. Parameterized Expectations
I.6.3. Notes on Projection Methods
I.7. Comparing Numerical Methods: Accuracy and Computational Burden
I.8. Concluding Remarks
Chapter II. Using Scenario Aggregation Method to Solve a Finite Horizon Life Cycle Model of Consumption
II.1. Introduction
II.2. A Simple Life-Cycle Model with Precautionary Saving
II.3. The Concept of Scenarios
II.3.1. The Problem
II.3.2. Scenarios and the Event Tree
II.4. Scenario Aggregation
II.5. The Progressive Hedging Algorithm
II.5.1. Description of the Progressive Hedging Algorithm
II.6. Using Scenario Aggregation to Solve a Finite Horizon Life Cycle Model
II.6.1. The Algorithm
II.6.2. Simulation Results
II.6.3. The Role of the Penalty Parameter
II.6.4. More simulations
II.7. Final Remarks
Chapter III. Impact of Bounded Rationality on the Magnitude of Precautionary Saving
III.1. Introduction
III.2. Empirical Results on Precautionary Saving
III.3. The Model
III.3.1. Rule 1
III.3.2. Rule 2
III.3.3. Rule 3
III.4. Final Remarks
Appendix A. Technical notes to chapter 2
Appendix A1. Definitions for Scenarios, Equivalence Classes and Associated Probabilities
Appendix A2. Description of the Scenario Aggregation Theory
Appendix A3. Solution to a Scenario Subproblem
Appendix B. Technical notes to chapter 3
Appendix B1. Analytical Solution for a Scenario with Deterministic Interest Rate
Appendix B2. Details on the Assumptions in Rule 1
Appendix B3. Details on the Assumptions in Rule 2

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