This book contributes substantively to state-of-the-art macroeconomic modeling by providing a method for modeling large collections of heterogeneous agents subject to non-pairwise externality called field effects, i.e. feedback of aggregate effects on individual agents or agents using state-dependent strategies. Adopting a level of microeconomic description which keeps track of compositions of fractions of agents by 'types' or 'strategies', time evolution of the microeconomic states is described by (backward) Chapman-Kolmogorov equations. Macroeconomic dynamics naturally arise by expansion of the solution in some power series of the number of participants. Specification of the microeconomic transition rates thus leads to macroeconomic dynamic models. This approach provides a consistent way for dealing with multiple equilibria of macroeconomic dynamics by ergodic decomposition and associated calculations of mean first passage times, and stationary probabilities of equilibria further provide useful information on macroeconomic behavior.
• State-of-the-art contribution to macroeconomic modeling by one of the leading theorists in the field • Author of previous books known for their rigor and innovativeness • Wide appeal, will be of interest to applied mathematicians, operations researchers, and statisticians as well as economists
Part I. Introduction: 1. Introduction; 2. Simple illustrative and motivating examples; 3. Empirical distributions: statistical laws in macroeconomics; Part II. Modeling Interactions: 4. Modeling interactions I: Jump Markov processes; 5. Modeling interactions II: master equations and field effects; 6. Modeling interactions III: pairwise and multiple-pair interactions; Part III. Hierarchical Dynamics and Critical phenomena: 7. Sluggish dynamics and hierarchical state spaces; 8. Self-organizing and other critical phenomena in economic models; 9. Appendices; Symbol Index; Subject Index.