Economic Dynamics in Discrete Time

This book offers a unified, comprehensive, and up-to-date treatment of analytical and numerical tools for solving dynamic economic problems. The focus is on introducing recursive methods-an important part of every economists set of tools-and readers will learn to apply recursive methods to a variety of dynamic economic problems. The book is notable for its combination of theoretical foundations and numerical methods. Each topic is first described in theoretical terms, with explicit definitions and rigorous proofs; numerical methods and computer codes to implement these methods follow. Drawing on the latest research, the book covers such cutting-edge topics as asset price bubbles, recursive utility, robust control, policy analysis in dynamic New Keynesian models with the zero lower bound on interest rates, and Bayesian estimation of dynamic stochastic general equilibrium (DSGE) models. The book first introduces the theory of dynamical systems and numerical methods for solving dynamical systems, and then discusses the theory and applications of dynamic optimization. It goes on to treat equilibrium analysis, covering a variety of core macroeconomic models, and such additional topics as recursive utility (increasingly used in finance and macroeconomics), dynamic games, and recursive contracts. The book also introduces Dynare, a widely used software platform for handling a range of economic models; readers will learn to use Dynare for numerically solving DSGE models and performing Bayesian estimation of DSGE models. Mathematical appendixes present all the necessary mathematical concepts and results. Matlab codes used to solve examples are indexed and downloadable from the books website. A downloadable instructors manual is available to adopting instructors. The book is suitable for post-graduate and research students of Economics. This book describes a remarkable and valuable collection of tools for the study of economic dynamics under uncertainty. Professor Miao explores the tractable formulation of stochastic models combined with methods for solving and analyzing such models. His book will be a valuable reference for researchers and students seeking a comprehensive treatment of important advances. Lars Peter Hansen, 2013 Nobel Laureate, Economics. This book is a terrific and much-needed addition to the landscape of graduate textbooks on macroeconomics. It treats the core topic of dynamic stochastic general equilibrium models, spanning real business cycles all the way to New Keynesian models, and carefully detailing solution and estimation concepts and techniques. With its modern exposition of Dynare and the attention to numerical methods, the book is both encyclopedic as well as hands on. It will surely be in the hands of many graduate students as well as established colleagues for years to come. -Harald Uhlig, Professor of Economics, University of Chicago Jianjun Miaos book provides a clear and comprehensive introduction to the analytical and numerical methods that make up the language of modern macroeconomic theory. The mix of theory, applications, and examples renders it an excellent learning tool. It is bound to become a standard reference on the subject. -Jordi Gal, Director of CREI and Professor of Economics, Universitat Pompeu Fabra.