Reconstructing Macroeconomics: A Perspective from Statistical Physics and Combinatorial Stochastic Processes

Half-title......Page 3
Series-title......Page 5
Title......Page 7
Copyright......Page 8
Dedication......Page 9
Contents......Page 11
Preface byMasanao Aoki......Page 17
Acknowledgments......Page 18
Preface by Hiroshi Yoshikawa......Page 19
1 Introduction: A New Approach to Macroeconomics......Page 21
Equilibrium as Distribution – The Role of Demand in Macroeconomics......Page 33
Uncertainty Trap, Policy Ineffectiveness, and Long Stagnation of the Macroeconomy......Page 34
Slow Dynamics of Macro System: Inflexible Prices......Page 36
Business Cycles......Page 37
Labor Market Dynamics – A New Look at the Natural Unemployment and Okun’s Law......Page 40
Demand Saturation–Creation and Economic Growth......Page 41
Stock Prices and the Real Economy......Page 44
Summing Up......Page 46
2 The Methods: Jump Markov Process and Random Partitions......Page 48
2.1. First Class of Methods: Stochastic Dynamics......Page 49
Jump Markov Process......Page 50
Setting Up the Master Equation......Page 52
Solving the Master Equation......Page 54
The Fokker–Planck Equation......Page 60
Potential Representation and Multiple Equilibria......Page 62
2.2. Second Class of Methods: Random Cluster Formation......Page 63
Dynamics of Clustering Processes......Page 64
Partition Vector......Page 68
Poisson–Dirichlet Distribution: The Distribution of Order Statistics of Market Shares......Page 72
Appendix 2.1: Alternate Derivation of Ewens Sampling Formula......Page 73
Appendix 2.2: Cluster Size Distribution and Stirling Numbers......Page 74
Appendix 2.3: Application of Generating Function to Random Process of the Number of Types......Page 76
3 Equilibrium as Distribution: The Role of Demand in Macroeconomics......Page 78
Binary Choice Model......Page 80
Microeconomic Foundations for Transition Rates......Page 82
Value Function and Dynamic Optimization......Page 86
Diamond Search Model......Page 88
3.2. Equilibrium in the Macroeconomy......Page 93
Distribution of Productivity in Equilibrium – The Boltzmann–Gibbs Distribution......Page 98
The Old Keynesian Cross......Page 103
Differences in Productivity – A Glance at Data......Page 104
3.3. Concluding Remarks......Page 107
4 Uncertainty Trap: Policy Ineffectiveness and Long Stagnation of the Macroeconomy......Page 109
4.1. The Model......Page 110
The Master Equation......Page 113
4.2. Uncertainty and Policy Ineffectiveness......Page 117
Multiple Equilibria......Page 119
The Effectiveness of Policy......Page 122
4.3. The Japanese Economy during the 1990s – A Case Study......Page 124
The Economy......Page 125
Monetary Policy and Investment......Page 129
Liquidity Trap and Inflation Targeting......Page 132
Some Suggestive Evidence......Page 137
4.4. Concluding Remarks......Page 139
5 Slow Dynamics of Macro System: No Mystery of Inflexible Prices......Page 141
5.1. Tree Models for Spillover of Exogenous Shocks......Page 142
Trees......Page 143
Ultrametric Dynamics of Spillover Probabilities......Page 145
Power Laws......Page 150
Economic Temperature......Page 152
5.2. Inflexible Prices......Page 153
The Metropolis Algorithm......Page 159
Model......Page 160
5.4. Concluding Remarks......Page 163
Appendix 5.1. Incomplete Gamma Function......Page 164
Two-State Example......Page 165
Three-State Example......Page 166
6.1. Introduction......Page 168
6.2. The Model......Page 172
Holding Time......Page 176
Output and Excess Demand......Page 177
6.3. Stationary Equilibrium......Page 178
6.4. Two-Sector Model......Page 179
The Expected Value of GDP......Page 183
6.5. Simulation......Page 187
Aggregate Fluctuations......Page 188
Demand, GDP, and Employment......Page 189
Allocative Disturbances......Page 194
Emergence of New Sectors......Page 200
6.6. Discussion......Page 202
Appendix 6.1: Dynamics of the Two-Sector Model......Page 206
Two-Sector Dynamics......Page 207
Most Likely Path and Stationary Probability Distributions in Region…......Page 209
7.1. Background......Page 210
Total Output and Excess Demand......Page 216
State of Each Sector......Page 218
Unemployment Pools......Page 220
7.3. Simulation......Page 222
7.4. Discussion......Page 230
Natural Unemployment......Page 232
Okun\'s Law......Page 233
Procyclical Productivity......Page 236
8.1. Introduction......Page 238
8.2. The Model......Page 242
Final Goods......Page 243
Emergence of New Final Goods or Industries......Page 245
The Basic Result......Page 247
An Extension: The Non-Poisson Polya Urn Model......Page 252
The Firm\'s Investment Decisions......Page 254
The Consumer\'s Consumption/Saving Decisions......Page 257
8.5. Discussion......Page 263
The Postwar Japanese Experience: A Case Study......Page 267
Appendix 8.1......Page 273
9.1. Introduction......Page 275
Distribution of Agent Types......Page 276
Size Distribution of Strategy Clusters......Page 278
Number of Clusters and Value of Theta......Page 279
Fractions......Page 280
The Expected Share of the Largest Fraction......Page 281
Two Largest Fractions......Page 283
Market Excess Demand......Page 284
Market Equilibrium......Page 285
Power Laws for the Distribution of Prices......Page 287
9.4. Concluding Remark......Page 289
Appendix 9.1: Joint Probability Density for r Largest Fractions......Page 290
Appendix 9.2: The Calculation of the Expected Share of the Largest Fraction......Page 292
10.1. Introduction......Page 295
10.2. The Power-Law Behavior of Stock Prices and Returns......Page 298
Normal Distribution......Page 299
Power Laws and Levy Flight......Page 301
Asset Prices......Page 303
10.3. The Problem with the Standard Asset Pricing Model......Page 306
Model of \"Rational Bubbles\"......Page 307
Difficulty Faced by the Standard Model......Page 308
The Real Economy......Page 311
Exponential Distribution......Page 315
Financial Returns......Page 318
10.5. Concluding Remarks on Real and Financial Markets......Page 321
Appendix 10.1: Power Laws Derived from the Langevin Equation......Page 322
2. Yule Process......Page 324
4. Yule–Simon Model......Page 325
5. The Chinese Restaurant Process and Its Variants......Page 326
References......Page 329
Author Index......Page 341
Subject Index......Page 345