Modeling Aggregate Behavior and Fluctuations in Economics: Stochastic Views of Interacting Agents

Modeling Aggregate Behavior and Fluctuations in Economics: Stochastic Views of Interacting Agents

by Masanao Aoki
     
 

ISBN-10: 0521606195

ISBN-13: 9780521606196

Pub. Date: 09/28/2004

Publisher: Cambridge University Press

This book analyzes how a large but finite number of agents interact, and what sorts of macroeconomic statistical regularities or patterns may evolve from these interactions. By keeping the number of agents finite, the book examines situations such as fluctuations about equilibria, multiple equilibria and asymmetrical cycles of models which are caused by model states…  See more details below

Overview

This book analyzes how a large but finite number of agents interact, and what sorts of macroeconomic statistical regularities or patterns may evolve from these interactions. By keeping the number of agents finite, the book examines situations such as fluctuations about equilibria, multiple equilibria and asymmetrical cycles of models which are caused by model states stochastically moving from one basin of attraction to another. All of these are not tractable using traditional deterministic modeling approaches. The book also discusses how agents may form clusters with stationary distributions of cluster sizes. These have important applications in analyzing volatilities of asset returns.

Product Details

ISBN-13:
9780521606196
Publisher:
Cambridge University Press
Publication date:
09/28/2004
Edition description:
New Edition
Pages:
263
Product dimensions:
5.98(w) x 8.98(h) x 0.71(d)

Table of Contents

Preface
1Overviews1
1.1Our Objectives and Approaches1
1.2Partial List of Applications2
1.3States: Vectors of Fractions of Types and Partition Vectors3
1.4Jump Markov Processes6
1.5The Master Equation7
1.6Decomposable Random Combinatorial Structures8
1.7Sizes and Limit Behavior of Large Fractions8
2Setting Up Dynamic Models9
2.1Two Kinds of State Vectors10
2.2Empirical Distributions11
2.3Exchangeable Random Sequences12
2.4Partition Exchangeability13
2.5Transition Rates16
2.6Detailed-Balance Conditions and Stationary Distributions17
3The Master Equation19
3.1Continuous-Time Dynamics19
3.2Power-Series Expansion23
3.3Aggregate Dynamics and Fokker-Planck Equation25
3.4Discrete-Time Dynamics25
4Introductory Simple and Simplified Models27
4.1A Two-Sector Model of Fluctuations27
4.2Closed Binary Choice Models30
4.3Open Binary Models32
4.4Two Logistic Process Models35
4.5An Example: A Deterministic Analysis of Nonlinear Effects May Mislead!40
5Aggregate Dynamics and Fluctuations of Simple Models41
5.1Dynamics of Binary Choice Models41
5.2Dynamics for the Aggregate Variable43
5.3Potentials45
5.4Critical Points and Hazard Function47
5.5Multiplicity - An Aspect of Random Combinatorial Features49
6Evaluating Alternatives52
6.1Representation of Relative Merits of Alternatives53
6.2Value Functions54
6.3Extreme Distributions and Gibbs Distributions57
6.4Approximate Evaluations of Value Functions with a Large Number of Alternatives60
6.5Case of Small Entry and Exit Probabilities: An Example60
6.6Approximate Evaluation of Sums of a Large Number of Terms61
6.7Approximations of Error Functions62
7Solving Nonstationary Master Equations66
7.1Example: Open Models with Two Types of Agents66
7.2Example: A Birth-Death-with-Immigration Process69
7.3Models for Market Shares by Imitation or Innovation75
7.4A Stochastic Model with Innovators and Imitators80
7.5Symmetric Interactions84
8Growth and Fluctuations85
8.1Two Simple Models for the Emergence of New Goods87
8.2Disappearance of Goods from Markets90
8.3Shares of Dated Final Goods Among Households93
8.4Deterministic Share Dynamics95
8.5Stochastic Business-Cycle Model96
8.6A New Model of Fluctuations and Growth: Case with Underutilized Factor of Production99
8.7Langevin-Equation Approach117
8.8Time-Dependent Density and Heat Equation121
8.9Size Distribution for Old and New Goods122
9A New Look at the Diamond Search Model127
9.1Model129
9.2Transition Rates129
9.3Aggregate Dynamics: Dynamics for the Mean of the Fraction130
9.4Dynamics for the Fluctuations131
9.5Value Functions132
9.6Multiple Equilibria and Cycles: An Example134
9.7Equilibrium Selection138
9.8Possible Extensions of the Model139
10Interaction Patterns and Cluster Size Distributions141
10.1Clustering Processes141
10.2Three Classes of Transition Rates144
10.3Transition-Rate Specifications in a Partition Vector153
10.4Logarithmic Series Distribution153
10.5Dynamics of Clustering Processes157
10.6Large Clusters165
10.7Moment Calculations171
10.8Frequency Spectrum172
10.9Parameter Estimation178
11Share Market with Two Dominant Groups of Traders180
11.1Transition Rates181
11.2Ewens Distribution183
11.3Market Volatility187
11.4Behavior of Market Excess Demand188
A.1Deriving Generating Functions via Characteristic Curves195
A.2Urn Models and Associated Markov Chains197
A.3Conditional Probabilities for Entries, Exits, and Changes of Type200
A.4Holding Times and Skeletal Markov Chains202
A.5Stirling Numbers206
A.6Order Statistics213
A.7Poisson Random Variables and the Ewens Sampling Formula214
A.8Exchangeable Random Partitions219
A.9Random Partitions and Permutations224
A.10Dirichlet Distributions229
A.11Residual Allocation Models234
A.12GEM and Size-Biased Distributions235
A.13Stochastic Difference Equations240
A.14Random Growth Processes242
A.15Diffusion Approximation to Growth Processes243
References245
Index253

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