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Publisher: Cambridge University Press | ISBN: 0521831067 | edition 2006 | PDF | 352 pages | 2,76 mb
The authors treat macroeconomic models as composed of large numbers of micro-units or agents of several types, and explicitly discuss stochastic dynamic and combinatorial aspects of interactions among them. In mainstream macroeconomics sound microfoundations for macroeconomics has meant incorporating sophisticated intertemporal optimization by representative agents into models. Optimal growth theory, once meant to be normative, is now taught as a descriptive theory in mainstream macroeconomic courses.
Contents
Preface by Masanao Aoki page xv
Preface by Hiroshi Yoshikawa xvii
1 Introduction: A New Approach toMacroeconomics 1
Equilibrium as Distribution – The Role of Demand in
Macroeconomics 13
Uncertainty Trap, Policy Ineffectiveness, and Long Stagnation
of the Macroeconomy 14
Slow Dynamics of Macro System: Inflexible Prices 16
Business Cycles 17
Labor Market Dynamics – A New Look at the Natural
Unemployment and Okun’s Law 20
Demand Saturation–Creation and Economic Growth 21
The Types of Investors and Stock Market 24
Stock Prices and the Real Economy 24
Summing Up 26
2 TheMethods: JumpMarkov Process and Random Partitions 28
Two Classes of Methods 29
2.1 First Class of Methods: Stochastic Dynamics 29
Jump Markov Process 30
Setting Up the Master Equation 32
Solving the Master Equation 34
The Fokker–Planck Equation 40
Potential Representation and Multiple Equilibria 42
Dynamics about an Equilibrium Point 43
2.2 Second Class of Methods: Random Cluster Formation 43
Dynamics of Clustering Processes 44
Partition Vector 48
Poisson–Dirichlet Distribution: The Distribution of Order
Statistics of Market Shares 52
Appendix 2.1: Alternate Derivation of Ewens Sampling
Formula 53
Appendix 2.2: Cluster Size Distribution and Stirling Numbers 54
Appendix 2.3: Application of Generating Function to
Random Process of the Number of Types 56
3 Equilibrium as Distribution: The Role of Demand
inMacroeconomics 58
3.1 Microeconomic Foundations 60
Binary Choice Model 60
Microeconomic Foundations for Transition Rates 62
Value Function and Dynamic Optimization 66
Diamond Search Model 68
3.2 Equilibrium in the Macroeconomy 73
Distribution of Productivity in Equilibrium – The
Boltzmann–Gibbs Distribution 78
The Old Keynesian Cross 83
Differences in Productivity – A Glance at Data 84
3.3 Concluding Remarks 87
4 Uncertainty Trap: Policy Ineffectiveness and Long Stagnation
of theMacroeconomy 89
4.1 The Model 90
The Master Equation 93
4.2 Uncertainty and Policy Ineffectiveness 97
Multiple Equilibria 99
The Effectiveness of Policy 102
4.3 The Japanese Economy during the 1990s – A Case Study 104
The Economy 105
Monetary Policy and Investment 109
Liquidity Trap and Inflation Targeting 112
Some Suggestive Evidence 117
4.4 Concluding Remarks 119
5 Slow Dynamics ofMacro System: NoMystery
of Inflexible Prices 121
5.1 Tree Models for Spillover of Exogenous Shocks 122
Trees 123
Ultrametric Dynamics of Spillover Probabilities 125
Power Law 130
Economic Temperature 132
5.2 Inflexible Prices 133
5.3 “Flat Landscape” Problems and Slow Dynamics 139
The Metropolis Algorithm 139
Model 140
5.4 Concluding Remarks 143
Appendix 5.1: Incomplete Gamma Function 144
Appendix 5.2: Examples of Ultrametric Dynamics 145
Two-State Example 145
Three-State Example 146
6 Business Cycles: An Endogenous Stochastic Approach 148
6.1 Introduction 148
6.2 The Model 152
Transition Rates 156
Holding Time 156
Output and Excess Demand 157
6.3 Stationary Equilibrium 158
6.4 Two-Sector Model 159
The Expected Value of GDP 162
6.5 Simulation 167
Aggregate Fluctuations 168
Demand, GDP, and Employment 170
Allocative Disturbances 175
Emergence of New Sectors 181
6.6 Discussion 183
Appendix 6.1: Dynamics of the Two-Sector Model 187
Master Equation 187
Two-Sector Dynamics 188
Most Likely Path and Stationary Probability Distributions
in Region R3 ∪ R4 189
7 LaborMarket: A New Look at the Natural Unemployment
and Okun’s Law 190
7.1 Background 190
7.2 The Model 196
Total Output and Excess Demand 196
State of Each Sector 198
Unemployment Pools 200
7.3 Simulation 202
7.4 Discussion 210
Natural Unemployment 212
Okun’s Law 213
Procyclical Productivity 216
8 Demand Saturation–Creation and Economic Growth 218
8.1 Introduction 218
8.2 The Model 222
Final Goods 223
Intermediate Good 225
Emergence of New Final Goods or Industries 225
8.3 Growth of the Macroeconomy 227
The Basic Result 227
An Extension: The Non-Poisson Polya Urn Model 232
8.4 Foundations for the Logistic Growth of Demand 234
The Firm’s Investment Decisions 234
The Consumer’s Consumption/Saving Decisions 237
8.5 Discussion 243
The Postwar Japanese Experience: A Case Study 247
9 The Types of Investors and Volatility in FinancialMarkets:
Analyzing Clusters of Heterogeneous Agents 255
9.1 Introduction 255
9.2 Cluster Formation in Financial Markets 256
Distribution of Agent Types 256
Size Distribution of Strategy Clusters 258
Number of Clusters and Value of θ 259
Fractions 260
The Expected Share of the Largest Fraction 261
Two Largest Fractions 263
9.3 Market Volatility 264
Market Excess Demand 264
Market Equilibrium 265
Power Laws for the Distribution of Prices 267
9.4 Concluding Remark 269
Appendix 9.1: Joint Probability Density for r Largest Fractions 270
Appendix 9.2: The Calculation of the Expected Share
of the Largest Fraction 272
10 Stock Prices and the Real Economy: Power-Law versus Exponential
Distributions 275
10.1 Introduction 275
10.2 The Power-Law Behavior of Stock Prices and Returns 278
Normal Distribution 279
Power Laws and L´evy Flight 281
Asset Prices 283
Growth of Real Variables 286
10.3 The Problem with the Standard Asset Pricing Model 286
Model of “Rational Bubbles” 287
Difficulty Faced by the Standard Model 288
10.4Underlying Mechanism: A Truncated L´evy Flight Model 291
The Real Economy 291
Exponential Distribution 295
Financial Returns 298
10.5 Concluding Remarks on Real and Financial Markets 301
Appendix 10.1: Power Laws Derived from the Langevin Equation 302
Appendix 10.2: Examples of Power Laws in Clusters 304
Large Deviations and Power Laws 304
Yule Process 304
Birth–Death Process with Second-Order Balanced Rates 305
Yule–Simon Model 305
The Chinese Restaurant Process and Its Variants 306
References 309
Author Index 321
Subject Index 325
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