Wold The Fix-Point Approach to Interdependent Systems

1. Auflage 2014
ISBN: 978-1-4832-9630-2
Verlag: Elsevier Science & Techn.
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, Band Volume 132, 348 Seiten, Web PDF

Reihe: Contributions to Economic Analysis

The Fix-Point Approach to Interdependent Systems

Autoren/Hrsg.

Wold, H.

Inhaltsverzeichnis

1;Front Cover;1
2;The Fix-Point Approach to Interdependent Systems;4
3;Copyright Page;5
4;Table of Contents;14
5;INTRODUCTION TO THE SERIES;6
6;FOREWORD BY HARALD CRAMÉR;8
7;PREFACE BY THE EDITOR;12
8;Chapter 1. THE FIX-POINT APPROACH TO INTERDEPENDENT SYSTEMS;16
8.1;1. Challenges of Simultaneous Equations Systems: Operative Interpretation and Statistical Estimation;16
8.2;2. The FP Method: Groundwork;31
8.3;3. Comparison of FP versus Classical Estimation Methods for ID Systems;36
8.4;4. Incentives for the Present Volume: Joint Statement of the Authors;47
9;Chapter 2. ITERATIVE ALGORITHMS FOR FIX-POINT ESTIMATION, THEIR DESIGN AND CONVERGENCE PROPERTIES;52
9.1;1. Introduction;52
9.2;2. The Model and the GEID Estimator;52
9.3;3. Framework for the Analysis;53
9.4;4. The Design o! the Iterative Algorithms;55
9.5;5. Exact Convergence Theorems for Local Convergence;59
9.6;6. Apparent Convergence and Decompositions of the Exact Convergence Theorems;62
9.7;7. Approximate Convergence Conditions;66
9.8;8. On the Significance of the B Matrix for the Convergence Analysis;68
9.9;9. Convergence to Multiple Parameter Sets;69
9.10;10. Applications;70
10;Chapter 3. THE GEID SPECIFICATION;80
10.1;1. Introduction and Summary;80
10.2;2. Specification of the Model;81
10.3;3. The GEID Estimator;84
10.4;4. On the Choice of GEID Structure;87
11;Chapter 4. THE PARAMETRIC FIX-POINT (PFP) AND THE ALGEBRAIC FIX-POINT (AFP) METHODS;92
11.1;1. The Parametric Fix-Point (PFP) Method as Applied to Systems without Identities;92
11.2;2. The Parametric Fix-Point (PFP) Method in the Presence of Identities;98
11.3;3. Convergence Properties of the Parametric Fix-Point (PFP) Method;102
11.4;4. The Parametric Fractional Fix-Point (PFFP) Method;103
11.5;5. The Parametric Recursive Fix-Point (PRFP) Method;104
11.6;6. The Fix-Point Method with Pseudovariables;106
11.7;7. The Algebraic Fix-Point (AFP) Method;108
11.8;8. Application to a Model with Two Overidentified Behaviour Relations and One Identity;111
11.9;9. Alternative Procedures when Subsystems Occur;122
12;Chapter 5. ESTIMATION OF REAL-WORLD MODELS BY FIX-POINT AND OTHER METHODS;124
12.1;1. Introduction;124
12.2;2. The IIV Method;124
12.3;3. Estimation of the Klein–Goldberger Model;127
12.4;4. Estimation of a Model of the Czechoslovak Economy;139
12.5;5. The Performance of FP Compared with other Methods for Some Other Real-World Models;154
12.6;Appendix A: The Klein-Goldberger Model;158
12.7;Appendix B: The Model of the Czechoslovak Economy;165
13;Chapter 6. A SEARCH FOR ASYMPTOTICALLY EFFICIENT ESTIMATORS;174
13.1;1. Introduction;174
13.2;2. Serially Uncorrelated Errors;175
13.3;3. Autoregressive Errors;186
13.4;4. Computational Methods and Applications;199
13.5;5. Summary and Discussion;210
14;Chapter 7. EXTENSIONS OF THE GEID AND IIV ESTIMATORS;212
14.1;1. Introduction;212
14.2;2. Estimation Methods;212
14.3;3. Monte Carlo Studies;217
14.4;4. Estimation of Fair's Model of the U.S. Economy;221
14.5;5. Estimation of Other Real-World Models;232
15;Chapter 8. ALGORITHMS FOR REORDERING INTERDEPENDENT SYSTEMS;240
15.1;1. Introduction;240
15.2;2. Principles Used for Selecting Orderings and Constructing Algorithms;241
15.3;3. An Algorithm that Produces the Block-Triangular Structure of the B
Matrix of a Block-Recursive System;244
15.4;4. Algorithms for Ordering the Relations of a Simultaneous Block;245
15.5;5. Case Studies;247
16;Chapter 9. AN ANALYSIS OF THE NONLINEAR KLEIN–GOLDBERGER MODEL USING FIX-POINT ESTIMATION AND OTHER METHODS;258
16.1;1. Introduction;258
16.2;2. Nonlinear Interdependent Systems;259
16.3;3. The Nonlinear Klein–Goldberger Model;268
16.4;4. Results from the Empirical Investigation;274
16.5;5. Conclusion;294
16.6;Appendix;296
17;Chapter 10. ON FIX-POINT ESTIMATION IN INTERDEPENDENT SYSTEMS WITH SPECIFICATION ERRORS;298
17.1;1. Introduction;298
17.2;2. The Design of a Monte Carlo Study;301
17.3;3. Some Results of the Study;307
17.4;4. Conclusions;317
18;Chapter 11. FIX-POINT ESTIMATES OF THE STRUCTURE OF A MODEL USING DIFFERENT Y PROXY STARTS;318
18.1;1. Introduction;318
18.2;2. A Typical Experiment;320
18.3;3. The Generation of Synthetic Data for GEID Experiments;327
19;LIST OF ABBREVIATIONS AND NOTATIONS;334
20;LIST OF REFERENCES;338
21;AUTHOR INDEX;346
22;SUBJECT INDEX;348