Macroeconomics deals with the structure, behavior and performance of economies in the aggregate. It concentrates on indicators, such as aggregate output and income (GDP), unemployment rates, price indices and inflation. It studies the structure and interrelations among aggregate markets for output, labor, capital and financial instruments, and their implications for macroeconomic performance.

Macroeconomics mainly focuses on the determinants of long run economic growth in living standards and the causes and implications of short term fluctuations in economic activity.

This book is an advanced treatment of modern macroeconomics, through a sequence of dynamic general equilibrium models, based on intertemporal optimization on the part of economic agents, such as households, firms and the government. The book also analyses and discusses the role of monetary and fiscal policy in the context of such dynamic models.

The intertemporal approach, based on the use of dynamic general equilibrium models, is currently the dominant approach to macroeconomics. This is the approach adopted in this text. The book is addressed to advanced undergraduate as well as first year graduate students of economics. It is also suitable for trained economists who wish to deepen and broaden their grasp of dynamic macroeconomics. It highlights the potential but also some of the limitations of the modern intertemporal approach.

Chapter 1 serves as an introduction and overview, providing a brief survey of the evolution of macroeconomics, as well as presenting the key facts about long run economic growth and aggregate fluctuations. Accounting for these key facts is the main objective of the dynamic macroeconomic models that are analysed in the rest of the book.

Chapter 2 introduces the main elements of the intertemporal approach to macroeconomics, by means of a series of two period competitive general equilibrium models. Two period models are the simplest possible intertemporal models. As such, they help highlight both the strengths and the weaknesses of modern intertemporal macroeconomics, without the need for advanced mathematical methods.

We use these two period models to address issues such as savings and capital accumulation, intertemporal substitution in consumption and labor supply, the distinction between real and nominal variables, the classical dichotomy and the neutrality of money, monetary growth and inflation, Ricardian equivalence between debt and tax finance of public expenditure and the effects of distortionary taxation. These are themes that recur again and again in macroeconomics. The two period models of chapter 2 thus set the stage for the more advanced infinite horizon dynamic and dynamic stochastic models which are the workhorses of modern theories of economic growth and aggregate fluctuations.

The remainder of the book is divided into twenty one chapters, presenting models of economic growth, aggregate fluctuations and monetary and fiscal policy.

The process of long run economic growth is analysed in chapters 3 to 8.

Chapter 3 introduces and discusses the basic neoclassical model of savings, investment and economic growth. This is based on a neoclassical production function and an exogenous savings and investment rate. It highlights the role of physical capital accumulation, technical progress and population growth for the process of economic growth.

Chapter 4 presents and analyses the model of the representative household. In this model, savings and investment are chosen optimally by a representative household with an infinite time horizon. The household is assumed to be able to borrow and lend freely in competitive capital markets.

Overlapping generations models of growth are presented in chapter 5. These are models in which different generations of households coexist, and in which younger households enter the economy with human capital being their only asset, as there are no intergenerational transfers of capital or financial assets.

Chapter 6 discusses models which highlight the intertemporal effects of fiscal policy, focussing on the effects of government consumption and its method of financing, such as taxation and government debt.

Chapter 7 discusses models which highlight the intertemporal effects of the money supply and monetary growth. Monetary models help determine the evolution not only of real variables, but also nominal variables, expressed in money terms, such as the price level, nominal wages, inflation and nominal interest rates.

More general growth models based on externalities, human capital accumulation and endogenous technical change are discussed in chapter 8.

Chapters 9 to 12 introduce decision making under uncertainty, in the context of dynamic stochastic models, and highlight the role of expectations in macroeconomics.

Chapter 9 introduces dynamic stochastic models under rational expectations, while chapters 10 and 11 focus on models of the microeconomic foundations of consumption under uncertainty and investment and the cost of capital. Chapter 12 is an extended treatment of the role of money, alternative general equilibrium models with money and the relation between the need for seigniorage and inflation.

Chapters 13 to 18 present and analyse alternative dynamic stochastic general equilibrium models of aggregate fluctuations. Such models are the basis of the “new neoclassical synthesis”, the dominant modern approach to the study of aggregate fluctuations.

In chapter 13 we present the stochastic growth model of aggregate fluctuations, while chapter 14 analyses perfectly competitive models without capital. These are benchmark “new classical” models, based on competitive markets and perfectly flexible wages and prices.

In chapter 15 we introduce and discuss the basic Keynesian model and the Phillips curve. We then present two “new Keynesian” dynamic stochastic models of aggregate fluctuations. Keynesian models assume a number of distortions in the adjustment of wages and prices. Chapter 16 presents an imperfectly competitive model with staggered pricing, while chapter 17 introduces an alternative “new Keynesian” model with periodic wage setting by labor market insiders. Chapter 18 focuses on labor market frictions, and analyses a matching model of the determination of the “natural rate” of unemployment, while chapter 19 focuses on financial frictions and their macroeconomic implications.

Chapters 20 and 21 delve deeper into the roles of monetary and fiscal policy. The role and the effectiveness of monetary policy is analysed in chapter 20, while fiscal policy and the determination and implications of government debt are analysed in chapter 21.

Chapter 22 focuses on dynamic stochastic models with bubbles, multiple macroeconomic equilibria, self fulfilling prophecies and sunspots. Such models allow for a different view of aggregate fluctuations than the standard dynamic stochastic general equilibrium models of the “new neoclassical synthesis” examined in chapters 13 to 18, which are usually based on a unique equilibrium.

Finally, chapter 23 discusses the current state of macroeconomics, highlighting the role of theoretical models and their interactions with empirical macroeonomics. It also discusses the impact of the financial crisis and the “Great Recession” of 2008-2009. The incorporation of labor market and financial frictions into DSGE models seems to be the main direction in which macroeconomics has been heading since then.

*Dynamic Macroeconomics* is predominantly based on the intertemporal approach. It presents and analyses dynamic and dynamic stochastic general equilibrium models, in which households and firms, but also the government and the central bank, make their decisions taking full account of their intertemporal effects. The dynamic element of time, the element of uncertainty about stochastic shocks and the techniques of intertemporal optimization permeate modern macroeconomics and are central to the analysis of the models in this book.

There are two exceptions to this rule about relying on models of intertemporal optimization. chapter 3 contains an extensive discussion of the *Solow model*, which, from the perspective of the intertemporal approach, is an ad hoc general equilibrium model, in the sense that the savings rate is assumed exogenous and is not derived from intertemporal optimization on the part of households. However, this model is pivotal for the theory of economic growth, and provides the foundation for examining the implications of optimizing growth models such as the representative household and overlapping generations model. It also provides the link to models with externalities, human capital accumulation and endogenous growth. It is thus important that the Solow model and the role of savings and investment are fully analysed and understood early on.

The second exception is chapter 15, which contains a full presentation and discussion of *traditional Keynesian models*, such as the Keynesian cross, the $IS-LM$ model, the $AD-AS$ model, as well as models of the Phllips curve. These models, first sketched in the *General Theory* of Keynes (1936), were the basis upon which macroeconomics was originally developed as a separate sub-discipline of economics. They led to the original “neoclassical synthesis” and are the foundation of the “new neoclassical synthesis” and the distinction between the “new classical” and the “new Keynesian” approach to intertemporal macroeconomics. It is thus crucial that the properties, as well as the strengths and weaknesses, of these traditional Keynesian models are fully understood.

The Solow model and the traditional Keynesian models, despite the fact that they belong to previous generations of macroeconomic models, serve as the basis through which the student of modern macroeconomics can appreciate the nature and the strengths, weaknesses and policy implications of the intertemporal approach, which, unlike the traditional approach to macroeconomics, is based on dynamic and dynamic stochastic models derived from explicit microeconomic foundations.

In the dynamic general equilibrium growth models that we present, the optimal and mutually compatible decisions of households, firms and the government (or central bank) help determine key macroeconomic aggregates such as output and income, employment, consumption, investment, government expenditure and taxes, the stock of physical and human capital, the stock of government debt, the price level, real and nominal wages, real and nominal interest rates and inflation. The performance of the economy depends on which distortions are present, and how they are addressed by government policy.

In the models of aggregate fluctuations, such as the “new classical”, and the “new Keynesian” dynamic stochastic general equilibrium (DSGE) models presented here, fluctuations in aggregate real and nominal variables are the result of the individually optimal and mutually compatible reactions of households, firms and the government and central bank to stochastic real or monetary disturbances.

There are a number of elements that differentiate this book from other advanced texts on macroeconomics.

For a start, many of the concepts and the characteristics of intertemporal macroeconomics are introduced at an early stage, in chapter 2, in the context of two period intertemporal general equilibrium models, which can be analysed with the minimal mathematical superstructure. This allows the student to gain a fundamental understanding of the issues at stake early on and relatively easily.

Second, the book focuses on a full analysis of a limited number of key intertemporal models. For example in growth theory we focus on the representative household and overlapping generations models, variants of which are combined with different assumptions about technology, externalities from capital accumulation, human capital accumulation and endogenous technical progress. In the theory of aggregate fluctuations we focus on essentially four models. The stochastic growth model, and three short run models of aggregate fluctuations: a “new classical” model without capital, an imperfectly competitive “new Keynesian” model with “staggered pricing” and an alternative “new Keynesian” model with periodic wage contracts. Such models form the basis of what has been termed the *“new” neoclassical synthesis* and are analysed fully.

A third element of the approach adopted in this book is that the models are stripped down to essentials, so that they can be fully solved and analysed. Thus, most of the models used can be reduced to second order dynamic systems whose solutions can be fully characterized, either algebraically, or with the help of simple two dimensional phase diagrams. This allows the students to focus on the dynamic properties of the models and gain a deep understanding of the economics of these dynamic processes. A variety of exercises are also included, in various parts of the text, in order to encourage students to try their hand on solving versions of the main dynamic models that define modern macroeconomics.

Yet, since dynamic simulation techniques are an important element of modern dynamic macroeconomics and policy analysis, especially for higher dimensional models, the dynamic models used in the book are also simulated numerically, and their impulse response functions are plotted and discussed. This is something that should help students of this text get a better grasp of the dynamic properties of models themselves. In addition, allows for an assessment of the quantitative significance of the various effects highlighted in the theoretical models, and help determime which effects are quantitatively significant and which are not. Finally, it demonstrates to students of this text how to set up and simulate dynamic, and dynamic stochastic general equilibrium macroeconomic models, something that should help them analyse higher dimensional, more complicated and more realistic models.

It is worth keeping in mind that modern macroeconomics is not based on a single, generally accepted all encompassing model. For this reason, this book is eclectic, and treats macroeconomics as applied and policy oriented general equilibrium analysis, based on a number of alternative, relatively simple aggregate dynamic or dynamic stochastic models. We examine a plurality of models, each of which is suitable for investigating specific issues and addressing specific questions, but may be unsuitable for other issues or questions. The book highlights both the potential strengths as well as the limitations of alternative models.

However, there are some key unifying principles in the models that we adopt. The most important of these principles is the assumption that economic agents base their decisions on intertemporal optimization of some well defined objective function, under appropriate constraints. Thus, for the most part, we rely on dynamic general equilibrium models with explicit intertemporal microeconomic foundations. Where there are theoretical disagreements, alternative approaches are juxtaposed, their pros and cons are analysed, and their compatibility with the empirical evidence is also briefly discussed.

In chapter 1 we present some of the key facts about long run economic growth, and then move on to some of the key facts about aggregate fluctuations. Additional facts are also presented as we move to the particular models in the relevant chapters, and the specific issues they seek to explain. The discussion of these key facts facilitates the process of evaluating the relevance and usefulness of the theoretical models in the rest of this book.

However, it is worth stressing that the rigorous and full empirical evaluation and testing of alternative theories and models is beyond the scope of this book. The present text, although concerned with models that account for the key stylized facts about macroeconomic phenomena, is a text on macroeconomic theory, not empirical or applied macroeconomics. Texts that focus on empirical macroeconomics and macroeconometrics could complement the present text for empirically inclined students and economists, and should indeed be consulted, as macroeconomics cannot but rely on the interactions between theory and evidence.

The book assumes introductory knowledge of economic theory and mathematics for economists. The main mathematical techniques needed to analyse optimizing dynamic macroeconomic models are fully reviewed in special appendices. These appendices assume some basic prior knowledge of the material contained in mathematical textbooks for economists, but are in any case self contained. They introduce and discuss variables and functions, including some useful functional forms for the production and utility functions used in macroeconomics, derivatives and partial derivatives, optimization under constraints and the Lagrange method, linear algebra and the solution of linear models, solution methods for linear differential and difference equations, dynamic optimization techniques such as optimal control and dynamic programming, as well as random variables and stochastic processes.

The book has emerged from my lectures over more than thirty years at Birkbeck College, University of London and the Athens University of Economics and Business, both at advanced undergraduate and postgraduate levels. The last fifty years has been a period of impressive progress for dynamic macroeconomics which has transformed the discipline. The book helps trace this evolution and current trends in macroeconomics, and is thus suitable for advanced undergraduates, graduate economists and graduate students in the first year of degrees leading to an M.Sc or a Ph.D in economics and related subjects such as finance

I would like to thank a number of people who have contributed to this book, both directly and indirectly.

First and foremost my Ph.D advisors from the period 1979-1981 at the London School of Economics, George Akerlof, Steve Nickell and Chris Pissarides. They had a great positive influence in my training as a macroeconomist and my attitude as an academic economist, which has stood me well over the years. I owe them a lot.

My biggest more recent debt is to successive generations of students, and especially the students at the Master’s and PhD programs in Economics of the Athens University of Economics and Business in the last decade. They have suffered through successive versions of my lecture notes between 2009 and 2016, provided useful feedback and helped improve the original notes.

The Fletcher School at Tufts University was an ideal academic environment which allowed me to improve and complete the manuscript between 2016 and 2018.

A number of colleagues have contributed through comments and discussions that have helped bring about a number of improvements. I would particularly like to thank Marios Angeletos, Yannis Ioannides, Michael Klein, Tryphon Kollintzas, Athanasios Orphanides, Apostolis Philippopoulos and Plutarchos Sakellaris. Olivier Blanchard reviewed an early version of the full manuscript and provided helpful comments and much needed encouragement.

I would also like to thank Emily Taber, the MIT Press Economics Acquisitions Editor, for putting this manuscript through a very efficient editorial process, and also acknowledge the very helpful comments and suggestions of eight anonymous reviewers in the pre-publication process. These have been extremely useful and have led to a much improved manuscript.

Throughout the long years of writing, revising and re-writing, my wife Dika has provided much needed support and encouragement, as she has done throughout the many years of our common life. I cannot thank her enough.

Obviously, I remain solely responsible for all remaining errors.

George Alogoskoufis

*Fletcher School, Tufts University* and *Athens University of Economics and Business*

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