Recursive Macroeconomic Theory

Citation

Ljungqvist, L., & Sargent, T. J. (2018). Recursive Macroeconomic Theory (4th ed.). MIT Press.

Chapter Summary

The fourth edition is a very large graduate text, about 1,480 pages. The publisher describes it as offering both an introduction to recursive methods and more advanced material, and says that only practice in solving diverse problems conveys the advantages of the recursive approach, so the book provides many applications. Most chapters end with exercises, many of them using Matlab or Python. The edition adds two new chapters: one on Ramsey taxation and the time inconsistency of optimal policies, and one on the mechanics of matching models, together with new material on heterogeneous beliefs in complete and incomplete markets models and on aggregate labor supply elasticities in lifecycle models.

Preface to the Fourth Edition; The Imperialism of Recursive Methods; Overview

The opening material states the case for recursive methods in dynamic macroeconomics and gives an overview of what the book covers and how the parts relate.

Tools: Time Series; Dynamic Programming; Practical Dynamic Programming; Linear Quadratic Dynamic Programming; Search and Unemployment

The methods block. It starts with time series and moves to dynamic programming, with separate chapters titled Dynamic Programming, Practical Dynamic Programming and Linear Quadratic Dynamic Programming. The block ends with a first application, search and unemployment.

Competitive Equilibria and Applications: Recursive Competitive Equilibrium: I; Equilibrium with Complete Markets; Overlapping Generations; Ricardian Equivalence; Fiscal Policies in a Growth Model; Recursive Competitive Equilibrium: II; Asset Pricing Theory; Asset Pricing Empirics; Economic Growth; Optimal Taxation with Commitment

Competitive equilibrium in recursive form, with applications to complete markets, overlapping generations, Ricardian equivalence, fiscal policy in a growth model, asset pricing and its empirical performance, economic growth and optimal taxation under commitment.

Savings and Incomplete Markets: The Savings Problem and Bewley Models; Self-Insurance; Incomplete Markets Models

Households that save to insure themselves against uninsurable risk. These chapters introduce Bewley models of the savings problem, self-insurance, and models of incomplete markets.

Contracts, Commitment and Policy: Recursive Contracts; Dynamic Stackelberg Problems; Two Ramsey Problems Revisited; Incentives and Insurance; Equilibrium without Commitment; Optimal Unemployment Insurance; Credible Government Policies: I; Credible Government Policies: II

The titles cover dynamic contracting and policy design: recursive contracts, Stackelberg and Ramsey problems in which a leader commits to a plan, incentive problems and insurance, equilibrium without commitment, optimal unemployment insurance, and credible government policies.

Further Topics: Two Topics in International Trade; Classical Monetary and Labor Economics; Fiscal-Monetary Theories of Inflation; Credit and Currency; Equilibrium Search, Matching, and Lotteries; Matching Models Mechanics; Foundations of Aggregate Labor Supply

The last block applies the tools to international trade, to classical monetary and labor economics, to fiscal-monetary theories of inflation, to credit and currency, to equilibrium search with matching and lotteries, to the mechanics of matching models and to the foundations of aggregate labor supply.

Technical Appendices: Functional Analysis; Linear Projections and Hidden Markov Models

Appendix A on functional analysis and Appendix B on linear projections and hidden Markov models give the mathematical background used in the main text. The book ends with references and subject, author and Matlab indexes.

Key Concepts

Tools

• Recursive methods: writing a dynamic problem as a sequence of decisions linked by a state, so that it can be solved period by period.
• Dynamic programming: the technique that solves such problems, including its linear quadratic special case.
• Search and unemployment: the first application of the tools to the labor market.

Equilibrium and Markets

• Recursive competitive equilibrium: a competitive equilibrium defined in terms of state variables and decision rules.
• Overlapping generations and Ricardian equivalence: two classic frameworks for studying saving and the effects of government debt.
• Bewley models and self-insurance: economies in which households save to insure against idiosyncratic risk when markets are incomplete.

Contracts and Policy

• Recursive contracts: dynamic incentive contracts written with a continuation-value state.
• Ramsey and Stackelberg problems: policy problems in which a leader commits to a plan, with optimal taxation as an application.
• Credible government policies: policy plans that must be sustained without commitment.
• Matching models: models of trading frictions in labor and other markets.

Critical Analysis

Strengths

• One method, many applications. The book keeps a single toolkit, recursive methods, and applies it across consumption, asset pricing, taxation, search, contracts and monetary economics. The publisher's argument is that only practice in solving diverse problems conveys the advantages of the approach.
• Both an introduction and advanced material. The tools block at the start supports readers new to dynamic programming, and the publisher says the book offers an introduction to recursive methods as well as advanced material, while later chapters on contracts, commitment and credibility go well beyond a first course.
• Exercises with code. Most chapters end with exercises, and many exercises and examples use Matlab or Python, with a Matlab index at the end of the book.
• Revised in the fourth edition. The publisher lists two new chapters, new material on heterogeneous beliefs and a fuller account of aggregate labor supply elasticities, so the book is not a reprint of earlier editions.
• Reference value. With more than 1,400 pages, extensive references and indexes, and technical appendices, the book works as a reference for graduate students and researchers.

Limitations

• Size. At about 1,480 pages, the book cannot be read through in a first- and second-year graduate course, for which the publisher recommends it, so selection is required.
• Demanding prerequisites. It requires intermediate macroeconomics and a strong command of calculus, linear algebra and probability.
• A method-led, not a topic-led, organisation. Because chapters follow the method, a reader looking for a single topic, such as monetary policy or growth, will find it spread across several parts.

Where It Fits in the Course

This is the most advanced macroeconomics text on the list. Mankiw's Macroeconomics is a foundational introduction to national income, growth, unemployment, inflation and monetary policy, and Krugman and Wells's Macroeconomics is a principles-level text that explains the same ideas with stories and minimal algebra. Carlin and Soskice's Macroeconomics: Institutions, Instability, and Inequality is an intermediate text built on a three-equation model, and CORE's The Economy 2.0: Macroeconomics is a free introduction that starts from data and history. None of these prepares for the formal level of Ljungqvist and Sargent.

The natural step before it is Romer's Advanced Macroeconomics, a compact starting text for first-year graduate macroeconomics that presents growth, fluctuations and policy in formal models alongside empirical work. Ljungqvist and Sargent are then a next step for readers who want to learn and apply dynamic programming and recursive equilibrium methods in depth.

How to Use This Book

The book is for first- and second-year doctoral students in economics, and for researchers who need to learn or use recursive methods. Preparation should include intermediate macroeconomics, multivariable calculus, linear algebra and probability; some programming helps with the exercises.

A practical plan:

• Core: the opening chapters and the tools block, then recursive competitive equilibrium and its applications (equilibrium with complete markets, overlapping generations, asset pricing, growth).
• Second pass: the savings and incomplete markets chapters, then the search and matching chapters if labor markets are of interest.
• Advanced: recursive contracts, Stackelberg and Ramsey problems, credible government policies and the further topics, chosen according to research interest.

Work the exercises with a computer; for the programming exercises, set up the Matlab or Python code before reading the chapter, so the method can be tested while it is learned.