Synopses & Reviews
The purpose of this book is to present the available methodologies for the solution of large-scale macroeconometric models. This work reviews classical solution methods and introduces more recent techniques, such as parallel computing and nonstationary iterative algorithms. The development of new and more efficient computational techniques has significantly influenced research and practice in macroeconometric modeling. This volume supplies practitioners and researchers with both a general presentation of numerical solution methods and specific discussions about particular problems encountered in the field. The work is organized into five chapters. Solution techniques for linear and nonlinear systems are reviewed and a graph-theoretical approach to perform this analysis is introduced. A model simulation on parallel computers of large-scale macroeconometric models is also described. Finally, a theoretical framework of rational expectation models is presented.
Synopsis
This book is the result of my doctoral dissertation research at the Department of Econometrics of the University of Geneva, Switzerland. This research was also partially financed by the Swiss National Science Foundation (grants 12- 31072.91 and 12-40300.94). First and foremost, I wish to express my deepest gratitude to Professor Manfred Gilli, my thesis supervisor, for his constant support and help. I would also like to thank the president of my jury, Professor Fabrizio Carlevaro, as well as the other members of the jury, Professor Andrew Hughes Hallett, Professor Jean-Philippe Vial and Professor Gerhard Wanner. I am grateful to my colleagues and friends of the Departement of Econometrics, especially David Miceli who provided constant help and kind understanding during all the stages of my research. I would also like to thank Pascale Mignon for proofreading my text and im- proving my English. Finally, I am greatly indebted to my parents for their kindness and encourage- ments without which I could never have achieved my goals. Giorgio Pauletto Department of Econometrics, University of Geneva, Geneva, Switzerland Chapter 1 Introduction The purpose of this book is to present the available methodologies for the solution of large-scale macroeconometric models. This work reviews classical solution methods and introduces more recent techniques, such as parallel com- puting and nonstationary iterative algorithms.
Table of Contents
Preface.
1: Introduction. 2: A Review of Solution Techniques. 2.1. LU Factorization.
2.2. QR Factorization.
2.3. Direct Methods for Sparse Matrices.
2.4. Stationary Iterative Methods.
2.5. Nonstationary Iterative Methods.
2.6. Newton Methods.
2.7. Finite Difference Newton Method.
2.8. Simplified Newton Method.
2.9. Quasi-Newton Methods.
2.10. Nonlinear First-Order Methods.
2.11. Solution by Minimization.
2.12. Globally Convergent Methods.
2.13. Stopping Criteria and Scaling.
3: Solution of Large-Scale Macroeconometric Models. 3.1. Block Triangular Decomposition of the Jacobian Matrix.
3.2. Orderings of the Jacobian Matrix.
3.3. Point Methods versus Block Methods.
3.4. Essential Feedback Vertex Sets and the Newton Method.
4: Model Simulation on Parallel Computers. 4.1. Introduction to Parallel Computing.
4.2. Model Simulation Experiences.
5: Rational Expectations Models. 5.1. Introduction.
5.2. The Model MULTIMOD.
5.3. Solution Techniques for Forward-Looking Models.
A: Appendix. A.1. Finite Precision Arithmetic.
A.2. Condition of a Problem.
A.3. Complexity of Algorithms. Index.