Modeling aggregate behavior and fluctuations in economics: stochastic views of interacting agents
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Cambridge [u.a.]
Cambridge Univ. Press
2002
|
| Edition: | 1. publ. |
| Subjects: | |
| Links: | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009882952&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| Item Description: | Hier auch später erschienene, unveränderte Nachdrucke |
| Physical Description: | XV, 263 S. |
| ISBN: | 0521781264 0521606195 |
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| 100 | 1 | |a Aoki, Masanao |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Modeling aggregate behavior and fluctuations in economics |b stochastic views of interacting agents |c Masanao Aoki |
| 250 | |a 1. publ. | ||
| 264 | 1 | |a Cambridge [u.a.] |b Cambridge Univ. Press |c 2002 | |
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| 650 | 4 | |a Mathematisches Modell | |
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| 650 | 4 | |a Supply and demand -- Mathematical models | |
| 650 | 4 | |a Consumption (Economics) -- Mathematical models | |
| 650 | 4 | |a Business cycles -- Mathematical models | |
| 650 | 4 | |a Statics and dynamics (Social sciences) -- Mathematical models | |
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Record in the Search Index
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|---|---|
| adam_text | CONTENTS
Preface
xiii
1
Overviews
1
1.1
Our Objectives and Approaches
1
1.2
Partial List of Applications
2
1.3
States: Vectors of Fractions of Types and Partition Vectors
3
1.3.1
Vectors of Fractions
4
1.3.2
Partition Vectors
5
1.4
Jump Markov Processes
6
1.5
The Master Equation
7
1.6
Decomposable Random Combinatorial Structures
8
1.7
Sizes and Limit Behavior of Large Fractions
8
2
Setting Up Dynamic Models
9
2.1
Two Kinds of State Vectors
10
2.2
Empirical Distributions
11
2.3
Exchangeable Random Sequences
12
2.4
Partition Exchangeability
13
2.5
Transition Rates
16
2.6
Detailed-Balance Conditions and Stationary Distributions
17
3
The Master Equation
19
3.1
Continuous-Time Dynamics
19
3.2
Power-Series Expansion
23
3.3
Aggregate Dynamics and Fokker-Planck Equation
25
3.4
Discrete-Time Dynamics
25
4
Introductory Simple and Simplified Models
27
4.1
A Two-Sector Model of Fluctuations
27
VII
iii
Contents
4.2
Closed Binary Choice Models
30
4.2.1
A Pólya
Distribution Model
31
4.3
Open Binary Models
32
4.3.1
Examples
35
4.4
Two Logistic Process Models
35
4.4.1
Model
1:
The Aggregate Dynamics and Associated
Fluctuations
35
4.4.2
Model
2:
Nonlinear Exit Rate
37
4.4.3
A Nonstationary
Pólya
Model
38
4.5
An Example: A Deterministic Analysis of Nonlinear Effects
May Mislead!
40
5
Aggregate Dynamics and Fluctuations of Simple Models
41
5.1
Dynamics of Binary Choice Models
41
5.2
Dynamics for the Aggregate Variable
43
5.3
Potentials
45
5.4
Critical Points and Hazard Function
47
5.5
Multiplicity
-
An Aspect of Random Combinatorial
Features
49
6
Evaluating Alternatives
52
6.1
Representation of Relative Merits of Alternatives
53
6.2
Value Functions
54
6.3
Extreme Distributions and Gibbs Distributions
57
6.3.1
Type I: Extreme Distribution
58
6.4
Approximate Evaluations of Value Functions with a Large
Number of Alternatives
60
6.5
Case of Small Entry and Exit Probabilities: An Example
60
6.6
Approximate Evaluation of Sums of a Large Number
of Terms
61
6.7
Approximations of Error Functions
62
6.7.1
Generalization
64
6.7.2
Example
65
7
Solving Nonstationary Master Equations
66
7.1
Example: Open Models with Two Types of Agents
66
7.1.1
Equilibrium Distribution
67
7.1.2
Probability-Generating-Function Method
67
7.1.3
Cumulant
Generating Functions
68
7.2
Example: A Birth-Death-with-Immigration Process
69
7.2.1
Stationary Probability Distribution
70
7.2.2
Generating Function
70
Contents ix
7.2.3 Time-Inhomogeneous Transition Rates 73
7.2.4 The Cumulant-Generating-Function 74
7.3 Models
for
Market
Shares by
Imitation
or
Innovation 75
7.3.1
Deterministic
Innovation
Process
76
7.3.2
Deterministic
Imitation
Process
77
7.3.3
A Joint Deterministic Process
78
7.3.4
A Stochastic Dynamic Model
79
7.4
A Stochastic Model with Innovators and Imitators
80
7.4.1
Case of a Finite Total Number of Firms
83
7.5
Symmetric Interactions
84
7.5.1
Stationary State Distribution
84
7.5.2
Nonstationary Distributions
84
8
Growth and Fluctuations
85
8.1
Two Simple Models for the Emergence of New Goods
87
8.1.1
Poisson
Growth Model
87
8.1.2
An Urn Model for Growth
88
8.2
Disappearance of Goods from Markets
90
8.2.1
Model
91
8.2.2
Stability Analysis
92
8.3
Shares of Dated Final Goods Among Households
93
8.3.1
Model
94
8.4
Deterministic Share Dynamics
95
8.5
Stochastic Business-Cycle Model
96
8.6
A New Model of Fluctuations and Growth: Case with
Underutilized Factor of Production
99
8.6.1
The Model
100
8.6.2
Transition-Rate Specifications
101
8.6.3
Holding Times
102
8.6.4
Aggregate Outputs and Demands
103
8.6.5
Equilibrium Sizes of the Sectors (Excess
Demand Conditions)
104
8.6.6
Behavior Out of Equilibrium: Two-Sector Model
105
8.6.7
Stationary Probability Distribution:
The Two-Sector Model
107
8.6.8
Emergence of New Sectors
110
8.6.9
Simulation Runs for Multi-Sector Model
111
8.6.10
Discussion
112
8.7
Langevin-Equation Approach
117
8.7.1
Stationary Density Function
119
8.7.2
The Exponential Distribution of the Growth
Rates of Firms
119
χ
Contents
8.8
Time-Dependent Density and Heat
Equation
121
8.9
Size Distribution for Old and New Goods
122
8.9.1
Diffusion-Equation Approximation
122
8.9.2
Lines of Product Developments and Inventions
123
9
A New Look at the Diamond Search Model
127
9.1
Model
129
9.2
Transition Rates
129
9.3
Aggregate Dynamics: Dynamics for the Mean of
the Fraction
130
9.4
Dynamics for the Fluctuations
131
9.5
Value Functions
132
9.5.1
Expected-Value Functions
133
9.6
Multiple Equilibria and Cycles: An Example
134
9.6.1
Asymmetrical Cycles
136
9.6.1.1
Approximate Analysis
136
9.6.1.2
Example
137
9.7
Equilibrium Selection
138
9.8
Possible Extensions of the Model
139
10
Interaction Patterns and Cluster Size Distributions
141
10.1
Clustering Processes
141
10.2
Three Classes of Transition Rates
144
10.2.1
Selections
144
10.2.2
Multisets
146
10.2.2.1
Capacity-Limited Processes
150
10.2.3
Assemblies
150
10.2.3.1
Internal Configurations of Assemblies 1
51
10.3
Transition-Rate Specifications in a Partition Vector
153
10.4
Logarithmic Series Distribution
153
10.4.1
Frequency Spectrum of the Logarithmic
Series Distribution
156
10.5
Dynamics of Clustering Processes
157
10.5.1
Examples of Clustering-Process Distributions
157
10.5.2
Example: Ewens Sampling Formula
162
10.5.3
Dynamics of Partition Patterns: Example
164
10.6
Large Clusters
165
10.6.1
Expected Value of the Largest Cluster Size
166
10.6.2
Joint Probability Density for the Largest
r
Fractions
169
10.7
Moment Calculations
171
10.8
Frequency Spectrum
172
10.8.1
Definition
173
Contents xi
10.8.2 Herfindahl
índex
of Concentration
173
10.8.3
A Heuristic Derivation
174
10.8.4
Recursion Relations
176
10.8.5
Examples of Applications
177
10.8.6
Discrete Frequency Spectrum
177
10.9
Parameter Estimation
178
11
Share Market with Two Dominant Groups of Traders
180
11.1
Transition Rates
181
11.2
E
wens Distribution
183
11.2.1
The Number of Clusters and Value of
θ
184
11.2.2
Expected Values of the Fractions
185
11.2.3
The Largest Two Shares
186
11.3
Market Volatility
187
11.4
Behavior of Market Excess Demand
188
11.4.1
Conditions for Zero Excess Demand
188
11.4.2
Volatility of the Market Excess Demand
189
11.4.3
Approximate Dynamics for Price Differences
and Power Law
190
11.4.3.1
Simulation Experiments
192
Appendix
195
A.I Deriving Generating Functions via Characteristic Curves
195
A.2 Urn Models and Associated Markov Chains
197
A.2.1
Pólya sUrn
197
A.2.2
Hoppe s Urn
197
A.2.3 Markov Chain Associated with the Urn
199
A.3 Conditional Probabilities for Entries, Exits, and Changes
of Type
200
A.3.1 Transition Probabilities
200
A.3.
2
Transition Rates
202
A.4 Holding Times and Skeletal Markov Chains
202
A.4.
1
Sojourn-Time Models
205
A.5 Stirling Numbers
206
A.5.
1
Introduction
206
A.5.
2
Recursions
207
A.5.3 Relations with Combinatorics
209
A.5.4 Explicit Expressions and Asymptotic Relations
210
A.5.
5
Asymptotics
212
A.6 Order Statistics
213
A.7
Poisson
Random Variables and the Ewens Sampling
Formula
214
xii Contents
АЛ.
1
Approximations
by
Poisson
Random
Variables
214
АЛ.
2
Conditional
Poisson
Random
Variables
216
Α.
8
Exchangeable Random
Partitions
219
A.8.1 Exchangeable Random Sequences
219
A.8.2 Partition Exchangeability
221
A.9 Random Partitions and Permutations
224
A.9.1 Permutations
224
A.9.
2
Random Partitions
225
A.9.3 Noninterference of Partitions
228
A.9.
4
Consistency
229
A.
10
Dirichlet Distributions
229
A.
10.1
Beta Distribution
229
A.
10.2
Dirichlet Distribution
230
A.
10.3
Marginal Dirichlet Distributions
232
A.
10.4
Poisson-Dirichlet Distribution
232
A.
10.5
Size-Biased Sampling
233
A.
11
Residual Allocation Models
234
A.
12
GEM and Size-Biased Distributions
235
A.
13
Stochastic Difference Equations
240
A.
14
Random Growth Processes
242
A.
15
Diffusion Approximation to Growth Processes
243
References
245
Index
253
|
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| dewey-search | 338.5212 338.5/212 21 |
| dewey-sort | 3338.5212 |
| dewey-tens | 330 - Economics |
| discipline | Mathematik Wirtschaftswissenschaften |
| edition | 1. publ. |
| format | Book |
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| indexdate | 2024-12-20T11:04:35Z |
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| isbn | 0521781264 0521606195 |
| language | English |
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| spellingShingle | Aoki, Masanao Modeling aggregate behavior and fluctuations in economics stochastic views of interacting agents Dynamisches Modell / Stochastischer Prozess / Konsumentenverhalten / Konjunktur / Wirtschaftswachstum / Theorie Interaktion - Stochastisches Modell - Dynamische Makroökonomie Mathematisches Modell Demand (Economic theory) -- Mathematical models Supply and demand -- Mathematical models Consumption (Economics) -- Mathematical models Business cycles -- Mathematical models Statics and dynamics (Social sciences) -- Mathematical models Stochastic processes -- Mathematical models Stochastisches Modell (DE-588)4057633-4 gnd Interaktion (DE-588)4027266-7 gnd Dynamische Makroökonomie (DE-588)4200428-7 gnd |
| subject_GND | (DE-588)4057633-4 (DE-588)4027266-7 (DE-588)4200428-7 |
| title | Modeling aggregate behavior and fluctuations in economics stochastic views of interacting agents |
| title_auth | Modeling aggregate behavior and fluctuations in economics stochastic views of interacting agents |
| title_exact_search | Modeling aggregate behavior and fluctuations in economics stochastic views of interacting agents |
| title_full | Modeling aggregate behavior and fluctuations in economics stochastic views of interacting agents Masanao Aoki |
| title_fullStr | Modeling aggregate behavior and fluctuations in economics stochastic views of interacting agents Masanao Aoki |
| title_full_unstemmed | Modeling aggregate behavior and fluctuations in economics stochastic views of interacting agents Masanao Aoki |
| title_short | Modeling aggregate behavior and fluctuations in economics |
| title_sort | modeling aggregate behavior and fluctuations in economics stochastic views of interacting agents |
| title_sub | stochastic views of interacting agents |
| topic | Dynamisches Modell / Stochastischer Prozess / Konsumentenverhalten / Konjunktur / Wirtschaftswachstum / Theorie Interaktion - Stochastisches Modell - Dynamische Makroökonomie Mathematisches Modell Demand (Economic theory) -- Mathematical models Supply and demand -- Mathematical models Consumption (Economics) -- Mathematical models Business cycles -- Mathematical models Statics and dynamics (Social sciences) -- Mathematical models Stochastic processes -- Mathematical models Stochastisches Modell (DE-588)4057633-4 gnd Interaktion (DE-588)4027266-7 gnd Dynamische Makroökonomie (DE-588)4200428-7 gnd |
| topic_facet | Dynamisches Modell / Stochastischer Prozess / Konsumentenverhalten / Konjunktur / Wirtschaftswachstum / Theorie Interaktion - Stochastisches Modell - Dynamische Makroökonomie Mathematisches Modell Demand (Economic theory) -- Mathematical models Supply and demand -- Mathematical models Consumption (Economics) -- Mathematical models Business cycles -- Mathematical models Statics and dynamics (Social sciences) -- Mathematical models Stochastic processes -- Mathematical models Stochastisches Modell Interaktion Dynamische Makroökonomie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009882952&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT aokimasanao modelingaggregatebehaviorandfluctuationsineconomicsstochasticviewsofinteractingagents |