Acknowledgements We wrote this book during the 1990’s and early 2000’s while teaching graduate courses in macro and monetary economics. We owe a substantial debt to the students in these classes for learning with us. We would especially like to thank Marco Bassetto, Victor Chernozhukov, Riccardo Colacito | Acknowledgements We wrote this book during the 1990 s and early 2000 s while teaching graduate courses in macro and monetary economics. We owe a substantial debt to the students in these classes for learning with us. We would especially like to thank Marco Bassetto Victor Chernozhukov Riccardo Colacito Mariacristina DeNardi William Dupor William Fuchs George Hall Cristobal Huneeus Sa-giri Kitao Hanno Lustig Sergei Morozov Eva Nagypal Monika Piazzesi Navin Kartik Martin Schneider Juha Seppala Yongseok Shin Christopher Sleet Stijn Van Nieuwerburgh Laura Veldkamp Neng Wang Chao Wei Mark Wright Sevin Yeltekin Bei Zhang and Lei Zhang. Each of these people made substantial suggestions for improving this book. We expect much from members of this group as we did from an earlier group of students that Sargent 1987b thanked. We received useful comments and criticisms from Jesus Fernandez-Villaverde Gary Hansen Jonathan Heathcote Berthold Herrendorf Mark Huggett Charles Jones Narayana Kocherlakota Dirk Krueger Per Krusell Francesco Lippi Rodolfo Manuelli Beatrix Paal Adina Popescu Jonathan Thomas and Nicola Tosini. Rodolfo Manuelli kindly allowed us to reproduce some of his exercises. We indicate the exercises that he donated. Some of the exercises in chapters 6 9 and 25 are versions of ones in Sargent 1987b . Francois Velde provided substantial help with the TgX and Unix macros that produced this book. Angelita Dehe and Maria Bharwada helped typeset it. We thank . Gordon Associates for copy editing. For providing good environments to work on this book Ljungqvist thanks the Stockholm School of Economics and Sargent thanks the Hoover Institution and the departments of economics at the University of Chicago Stanford University and New York University. - xvii - Preface to the second edition Recursive Methods Much of this book is about how to use recursive methods to study macroeconomics. Recursive methods are very important in the analysis of dynamic systems in economics and