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
What more can be said. It is the gold standard of graduate macro for a reason. Extensive in the range of topics, from the standard dynastic neoclassical model with compete markets and no frictions, to various alternatives that deviate from this idealization. Topics range from mathematical preliminaries (Markov processes, filters, dynamic programming, etc.) and the basics of recursive competition equilibrium to Bewley models, Ramsey taxation problem, growth, labor search models, and so on.
I'm not a macro person for sure (I'm finishing the first year of a PhD program, with a primary field mostly likely in public economics), but I will say this is a worthwhile investment for any aspiring economist.