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.
A classic graduate textbook which, together with Ljungqvist's and Sargent's always-being-updated Recursive Macroeconomic Theory, is a great introduction to modern macro. (For the record, I'm finishing the first year of a PhD program and consider myself more of an applied micro guy.) Like all textbooks 30+ years old, it is becoming dated, but the core methods and mathematical proofs are there. If it's a representative sampling of today's macroeconomic methods you're looking for, Ljungqvist and Sargent is the best place to go. However, even I would find myself going back to Stokey, Lucas, and Prescott at times for clarification.
Bell's work on dynamic programming forms the core of recursive methods; in a way this is quite interesting. A lot of formal frameworks have been used to understand economics, and a lot more work needs to be done. Stochastic dynamic programming, which appears to combine SDE's with dynamic programming, for me is new. I probably should finish this at some point.