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Recursive methods offer a powerful approach for characterizing and solving complicated problems in dynamic macroeconomics. Recursive Macroeconomic Theory provides both an introduction to recursive methods and advanced material, mixing tools and sample applications. The second edition contains substantial revisions to about half the original material, and extensive additional coverage appears in seven chapters new to this edition. The updated and added material covers exciting new topics that further illustrate the power and pervasiveness of recursive methods.Significant improvements to original chapters include a better treatment of the existence of recursive equilibria, an enhanced account of the supermartingale convergence theorem, and an extended treatment of an optimal taxation problem in an economy in which there are incomplete markets. Completely new coverage in the second edition includes an introductory chapter, which gives an overview of the themes uniting the diverse topic

Three eminent economists provide in this book a rigorous, self-contained treatment of modern economic dynamics. Nancy L. Stokey, Robert E. Lucas, Jr., and Edward C. Prescott develop the basic methods of recursive analysis and emphasize the many areas where they can usefully be applied.After presenting an overview of the recursive approach, the authors develop economic applications for deterministic dynamic programming and the stability theory of first-order difference equations. They then treat stochastic dynamic programming and the convergence theory of discrete-time Markov processes, illustrating each with additional economic applications. They also derive a strong law of large numbers for Markov processes. Finally, they present the two fundamental theorems of welfare economics and show how to apply the methods developed earlier to general equilibrium systems.The authors go on to apply their methods to many areas of economics. Models of firm and industry investment, household consumption behavior, long-run growth, capital accumulation, job search, job matching, inventory behavior, asset pricing, and money demand are among those they use to show how predictions can be made about individual and social behavior. Researchers and graduate students in many areas of economics, both theoretical and applied, will find this book essential.

The Recursive Mind challenges the commonly held notion that language is what makes us uniquely human. In this compelling book, Michael Corballis argues that what distinguishes us in the animal kingdom is our capacity for recursion: the ability to embed our thoughts within other thoughts. "I think, therefore I am," is an example of recursive thought, because the thinker has inserted himself into his thought. Recursion enables us to conceive of our own minds and the minds of others. It also gives us the power of mental "time travel"--the ability to insert past experiences, or imagined future ones, into present consciousness.Drawing on neuroscience, psychology, animal behavior, anthropology, and archaeology, Corballis demonstrates how these recursive structures led to the emergence of language and speech, which ultimately enabled us to share our thoughts, plan with others, and reshape our environment to better reflect our creative imaginations. He shows how the recursive mind was critical to survival in the harsh conditions of the Pleistocene epoch, and how it evolved to foster social cohesion. He traces how language itself adapted to recursive thinking, first through manual gestures, then later, with the emergence of Homo sapiens, vocally. Toolmaking and manufacture arose, and the application of recursive principles to these activities in turn led to the complexities of human civilization, the extinction of fellow large-brained hominins like the Neandertals, and our species' supremacy over the physical world.

Gregory Bateson was one of the most original social scientists of this century. He is widely known as author of key ideas used in family therapy - including the well-known condition called 'double bind' . He was also one of the most influential figures in cultural anthropology. In the decade before his death in 1980 Bateson turned toward a consideration of ecology. Standard ecology concentrates on an ecosystem's biomass and on energy budgets supporting life. Bateson came to the conclusion that understanding ecological organization requires a complete switch in scientific perspective. He reasoned that ecological phenomena must be explained primarily through patterns of information and that only through perceiving these informational patterns will we uncover the elusive unity, or integration, of ecosystems.Bateson believed that relying upon the materialist framework of knowledge dominant in ecological science will deepen errors of interpretation and, in the end, promote eco-crisis. He saw recursive patterns of communication as the basis of order in both natural and human domains. He conducted his investigation first in small-scale social settings; then among octopus, otters, and dolphins. Later he took these investigations to the broader setting of evolutionary analysis and developed a framework of thinking he called 'an ecology of mind.' Finally, his inquiry included an ecology of mind in ecological settings - a recursive epistemology.This is the first study of the whole range of Bateson's ecological thought - a comprehensive presentaionof Bateson's matrix of ideas. Drawing on unpublished letters and papers, Harries-Jones clarifies themes scattered throughout Bateson's own writings, revealing the conceptual consistency inherent in Bateson's position, and elaborating ways in which he pioneered aspects of late twentieth-century thought.

The Recursive Mind challenges the commonly held notion that language is what makes us uniquely human. In this compelling book, Michael Corballis argues that what distinguishes us in the animal kingdom is our capacity for recursion: the ability to embed our thoughts within other thoughts. "I think, therefore I am," is an example of recursive thought, because the thinker has inserted himself into his thought. Recursion enables us to conceive of our own minds and the minds of others. It also gives us the power of mental "time travel"--the ability to insert past experiences, or imagined future ones, into present consciousness. Drawing on neuroscience, psychology, animal behavior, anthropology, and archaeology, Corballis demonstrates how these recursive structures led to the emergence of language and speech, which ultimately enabled us to share our thoughts, plan with others, and reshape our environment to better reflect our creative imaginations. He shows how the recursive mind was critical to survival in the harsh conditions of the Pleistocene epoch, and how it evolved to foster social cohesion. He traces how language itself adapted to recursive thinking, first through manual gestures, then later, with the emergence of Homo sapiens, vocally. Toolmaking and manufacture arose, and the application of recursive principles to these activities in turn led to the complexities of human civilization, the extinction of fellow large-brained hominins like the Neandertals, and our species' supremacy over the physical world.

Text: English, German (translation)

This book has grown out of a set of lecture notes prepared originally for a NATO Summer School on "The Theory and Practice of Systems ModelLing and Identification" held between the 17th and 28th July, 1972 at the Ecole Nationale Superieure de L'Aeronautique et de L'Espace. Since this time I have given similar lecture courses in the Control Division of the Engineering Department, University of Cambridge; Department of Mechanical Engineering, University of Western Australia; the University of Ghent, Belgium (during the time I held the IBM Visiting Chair in Simulation for the month of January, 1980), the Australian National University, and the Agricultural University, Wageningen, the Netherlands. As a result, I am grateful to all the reci­ pients of these lecture courses for their help in refining the book to its present form; it is still far from perfect but I hope that it will help the student to become acquainted with the interesting and practically useful concept of recursive estimation. Furthermore, I hope it will stimulate the reader to further study the theoretical aspects of the subject, which are not dealt with in detail in the present text. The book is primarily intended to provide an introductory set of lecture notes on the subject of recursive estimation to undergraduate/Masters students. However, the book can also be considered as a "theoretical background" handbook for use with the CAPTAIN Computer Package.

This self-contained reference for statisticians and engineers in system and control theory, analyzes the effect of convergent recursive estimation algorithms and stochastic approximation on the dependent noise case and the classic independent case. It discusses control and adaptive control problems related to recursive estimation, and introduces the combined probabilistic and differential equation method of data analysis.

This self-contained reference for statisticians and engineers in system and control theory, analyzes the effect of convergent recursive estimation algorithms and stochastic approximation on the dependent noise case and the classic independent case. It discusses control and adaptive control problems related to recursive estimation, and introduces the combined probabilistic and differential equation method of data analysis.

Recursive methods offer a powerful approach in dynamic macroeconomics. This book contains both an introduction to recursive tools, including standard applications such as asset pricing, and advanced material, including analyses of reputational mechanisms and contract design. The tools are presented with enough technical sophistication to get the reader started working on practical problems. When numerical simulations are called for, the book provides suggestions for how to proceed, as well as references for further reading. The applications cover many substantive issues in macroeconomics, such as equilibrium asset prices, market incompleteness, wealth distribution, fiscal-monetary theories of inflation, government debt, optimal labor and capital taxation, time consistency and credible government policies, optimal social insurance, economic growth, and labor market dynamics.

The substantially revised fourth edition of a widely used text, offering both an introduction to recursive methods and advanced material, mixing tools and sample applications.Recursive methods provide powerful ways to pose and solve problems in dynamic macroeconomics. Recursive Macroeconomic Theory offers both an introduction to recursive methods and more advanced material. Only practice in solving diverse problems fully conveys the advantages of the recursive approach, so the book provides many applications. This fourth edition features two new chapters and substantial revisions to other chapters that demonstrate the power of recursive methods. One new chapter applies the recursive approach to Ramsey taxation and sharply characterizes the time inconsistency of optimal policies. These insights are used in other chapters to simplify recursive formulations of Ramsey plans and credible government policies. The second new chapter explores the mechanics of matching models and identifies a common channel through which productivity shocks are magnified across a variety of matching models. Other chapters have been extended and refined. For example, there is new material on heterogeneous beliefs in both complete and incomplete markets models; and there is a deeper account of forces that shape aggregate labor supply elasticities in lifecycle models. The book is suitable for first- and second-year graduate courses in macroeconomics. Most chapters conclude with exercises; many exercises and examples use Matlab or Python computer programming languages.

A substantially revised new edition of a widely used text, offering both an introduction to recursive methods and advanced material.Recursive methods offer a powerful approach for characterizing and solving complicated problems in dynamic macroeconomics. Recursive Macroeconomic Theory provides both an introduction to recursive methods and advanced material, mixing tools and sample applications. Only experience in solving practical problems fully conveys the power of the recursive approach, and the book provides many applications. This third edition offers substantial new material, with three entirely new chapters and significant revisions to others. The new content reflects recent developments in the field, further illustrating the power and pervasiveness of recursive methods.New chapters cover asset pricing empirics with possible resolutions to puzzles; analysis of credible government policy that entails state variables other than reputation; and foundations of aggregate labor supply with time averaging replacing employment lotteries. Other new material includes a multi-country analysis of taxation in a growth model, elaborations of the fiscal theory of the price level, and age externalities in a matching model.The book is suitable for both first- and second-year graduate courses in macroeconomics and monetary economics. Most chapters conclude with exercises. Many exercises and examples use Matlab programs, which are cited in a special index at the end of the book.

A substantially revised new edition of a widely used text, offering both an introduction to recursive methods and advanced material.Recursive methods offer a powerful approach for characterizing and solving complicated problems in dynamic macroeconomics. Recursive Macroeconomic Theory provides both an introduction to recursive methods and advanced material, mixing tools and sample applications. Only experience in solving practical problems fully conveys the power of the recursive approach, and the book provides many applications. This third edition offers substantial new material, with three entirely new chapters and significant revisions to others. The new content reflects recent developments in the field, further illustrating the power and pervasiveness of recursive methods.New chapters cover asset pricing empirics with possible resolutions to puzzles; analysis of credible government policy that entails state variables other than reputation; and foundations of aggregate labor supply with time averaging replacing employment lotteries. Other new material includes a multi-country analysis of taxation in a growth model, elaborations of the fiscal theory of the price level, and age externalities in a matching model.The book is suitable for both first- and second-year graduate courses in macroeconomics and monetary economics. Most chapters conclude with exercises. Many exercises and examples use Matlab programs, which are cited in a special index at the end of the book.

Offers three simple rules which, when applied consistently, provide insight into the mysteries which govern the universe

Three eminent economists provide in this book a rigorous, self-contained treatment of modern economic dynamics. Nancy L. Stokey, Robert E. Lucas, Jr., and Edward C. Prescott develop the basic methods of recursive analysis and emphasize the many areas where they can usefully be applied.After presenting an overview of the recursive approach, the authors develop economic applications for deterministic dynamic programming and the stability theory of first-order difference equations. They then treat stochastic dynamic programming and the convergence theory of discrete-time Markov processes, illustrating each with additional economic applications. They also derive a strong law of large numbers for Markov processes. Finally, they present the two fundamental theorems of welfare economics and show how to apply the methods developed earlier to general equilibrium systems.The authors go on to apply their methods to many areas of economics. Models of firm and industry investment, household consumption behavior, long-run growth, capital accumulation, job search, job matching, inventory behavior, asset pricing, and money demand are among those they use to show how predictions can be made about individual and social behavior. Researchers and graduate students in many areas of economics, both theoretical and applied, will find this book essential.

The substantially revised fourth edition of a widely used text, offering both an introduction to recursive methods and advanced material, mixing tools and sample applications.Recursive methods provide powerful ways to pose and solve problems in dynamic macroeconomics. Recursive Macroeconomic Theory offers both an introduction to recursive methods and more advanced material. Only practice in solving diverse problems fully conveys the advantages of the recursive approach, so the book provides many applications. This fourth edition features two new chapters and substantial revisions to other chapters that demonstrate the power of recursive methods. One new chapter applies the recursive approach to Ramsey taxation and sharply characterizes the time inconsistency of optimal policies. These insights are used in other chapters to simplify recursive formulations of Ramsey plans and credible government policies. The second new chapter explores the mechanics of matching models and identifies a common channel through which productivity shocks are magnified across a variety of matching models. Other chapters have been extended and refined. For example, there is new material on heterogeneous beliefs in both complete and incomplete markets models; and there is a deeper account of forces that shape aggregate labor supply elasticities in lifecycle models. The book is suitable for first- and second-year graduate courses in macroeconomics. Most chapters conclude with exercises; many exercises and examples use Matlab or Python computer programming languages.

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Text: English, German (translation)

Gregory Bateson was one of the most original social scientists of this century. He is widely known as author of key ideas used in family therapy - including the well-known condition called 'double bind' . He was also one of the most influential figures in cultural anthropology. In the decade before his death in 1980 Bateson turned toward a consideration of ecology. Standard ecology concentrates on an ecosystem's biomass and on energy budgets supporting life. Bateson came to the conclusion that understanding ecological organization requires a complete switch in scientific perspective. He reasoned that ecological phenomena must be explained primarily through patterns of information and that only through perceiving these informational patterns will we uncover the elusive unity, or integration, of ecosystems.Bateson believed that relying upon the materialist framework of knowledge dominant in ecological science will deepen errors of interpretation and, in the end, promote eco-crisis. He saw recursive patterns of communication as the basis of order in both natural and human domains. He conducted his investigation first in small-scale social settings; then among octopus, otters, and dolphins. Later he took these investigations to the broader setting of evolutionary analysis and developed a framework of thinking he called 'an ecology of mind.' Finally, his inquiry included an ecology of mind in ecological settings - a recursive epistemology.This is the first study of the whole range of Bateson's ecological thought - a comprehensive presentaionof Bateson's matrix of ideas. Drawing on unpublished letters and papers, Harries-Jones clarifies themes scattered throughout Bateson's own writings, revealing the conceptual consistency inherent in Bateson's position, and elaborating ways in which he pioneered aspects of late twentieth-century thought.

The aim of this textbook is to present an account of the theory of computation. After introducing the concept of a model of computation and presenting various examples, the author explores the limitations of effective computation via basic recursion theory. Self-reference and other methods are introduced as fundamental and basic tools for constructing and manipulating algorithms. From there the book considers the complexity of computations and the notion of a complexity measure is introduced. Finally, the book culminates in considering time and space measures and in classifying computable functions as being either feasible or not. The author assumes only a basic familiarity with discrete mathematics and computing, making this textbook ideal for a graduate-level introductory course. It is based on many such courses presented by the author and so numerous exercises are included. In addition, the solutions to most of these exercises are provided.