Chapter 1 Introduction Dynamic Macroeconomics Prof. George Alogoskoufis Fletcher School, Tufts University and Athens University of Economics and Business 1.1 The Nature and Evolution of Macroeconomics 1.1.1 Pre-Keynesian Macroeconomics 1.1.2 Classical and Keynesian Macroeconomics 1.1.3 Microeconomic Foundations of Macroeconomics 1.1.4 Dynamic and Dynamic Stochastic General Equilibrium Models 1.2 Key Facts about Long Run Economic Growth 1.2.1 Cross Country Differences in Per Capita Output and Income 1.2.2 The Evolution of Per Capita Output and Income over Time 1.2.3 Growth and Convergence in the Main Industrial Economies 1.3 Key Facts about Aggregate Fluctuations 1.3.1 The Frequency, Severity and Duration of Recessions 1.3.2 Unemployment and Recessions 1.3.3 Trends and Fluctuations in the Price Level and the Rate of Inflation 1.3.4 The Price Level, Inflation and Monetary and Fiscal Policy 1.4 Conclusions Part A: Models of Economic Growth Chapter 2 Savings, Investment and Economic Growth 2.1 The Solow Growth Model 2.1.1 The Neoclassical Production Function 2.1.2 The Cobb Douglas Production Function 2.1.3 Population Growth and Technical Progress 2.1.4 Savings, Capital Accumulation and Economic Growth 2.1.5 The Balanced Growth Path and the Convergence Process 2.1.6 The Rate of Growth of Capital and Output 2.1.7 The Significance of the Inada Conditions 2.2 The Savings Rate and the Golden Rule 2.2.1 The Savings Rate and the Balanced Growth Path 2.2.2 The Savings Rate, Consumption and the Golden Rule 2.2.3 The Elasticity of Steady State Output with Respect to the Savings Rate 2.3 The Speed of Convergence towards the Balanced Growth Path 2.4 Competitive Markets, the Real Interest Rate and Real Wages 2.5 The Process of Economic Growth and the Solow Model 2.5.1 The Kaldor Stylized Facts of Economic Growth 2.5.2 Differences in Economic Growth between Economies 2.5.3 Conditional Convergence 2.5.4 Convergence with a Cobb Douglas Production Function 2.6 Dynamic Simulations of the Solow Model 2.7 Conclusions Annex 1 to Chapter 2: The CES Production Function Annex 2 to Chapter 2: The Solow Model in Discrete Time Chapter 3 The Representative Household Model 3.1 The Ramsey Model!1
3.1.1 The Production Function 3.1.2 The Utility Function of the Representative Household 3.1.3 The Accumulation of Capital by the Representative Household 3.1.4 The Efficiency of the Competitive Equilibrium 3.1.5 Conditions for Utility Maximization of the Representative Household 3.1.6 The Euler Equation for Consumption 3.1.7 The Inter-temporal Budget Constraint of the Representative Household 3.1.8 The Transversality Condition with an Infinite Time Horizon 3.1.9 The Consumption Function of the Representative Household 3.2 Dynamic Adjustment and the Balanced Growth Path in the Ramsey Model 3.2.1 Dynamic Adjustment towards the Balanced Growth Path 3.2.2 The Balanced Growth Path and the Modified Golden Rule 3.2.3 Effects of a Permanent Increase in the Pure Rate of Time Preference 3.3 Properties of the Adjustment Path and the Speed of Convergence 3.4 Dynamic Simulations of the Ramsey Model 3.5 Conclusions Annex to Chapter 3: The Ramsey Model in Discrete Time Chapter 4 Models of Overlapping Generations 4.1 The Diamond Model 4.1.1 Definitions 4.1.2 The Production Function 4.1.3 The Inter-temporal Utility Function of Households 4.1.4 Markets and the Behavior of Households 4.1.5 Capital Accumulation and the Dynamic Adjustment of the Economy 4.1.6 The Diamond Model with Logarithmic Preferences and Cobb Douglas Technology 4.1.7 The Speed of Adjustment in the Simplified Diamond Model 4.1.8 The Possibility of Dynamic Inefficiency 4.1.9 Dynamic Simulations of the Diamond Model 4.2 The Blanchard-Weil Model of Perpetual Youth 4.2.1 Definitions 4.2.2 The Production Function 4.2.3 The Inter-temporal Utility Function of Households and Aggregate Consumption 4.2.4 Dynamic Adjustment towards the Balanced Growth Path 4.2.5 Dynamic Simulations of the Blanchard-Weil Model 4.3 Conclusions Annex to Chapter 4: The Blanchard-Weil Model in Discrete Time Chapter 5 Fiscal Policy and Economic Growth 5.1 The Government Budget Constraint 5.1.1 Primary Government Expenditure, Taxes and Government Debt 5.1.2 Overall and Primary Government Deficits 5.1.3 The Sustainability of Budgetary Policy 5.2 Ricardian Equivalence and the Ramsey Model 5.2.1 Ricardian Equivalence between Government Debt and Taxes 5.2.2 Government Expenditure, Taxes and Government Debt in the Ramsey Model 5.3 Dynamic Effects of Fiscal Policy in the Blanchard-Weil Model 5.3.1 The Blanchard-Weil Model with Government Expenditure and Government Debt 5.3.2 Government Debt, Taxes and Redistribution across Generations 5.3.2 A Dynamic Simulation of Fiscal Policies in the Blanchard Weil Model 5.4 The Dynamic Effects of Distortionary Taxation 5.4.1 Distortionary and Non-Distortionary Taxes 5.4.2 Dynamic Effects of Capital Income Taxation 5.4.3 A Dynamic Simulation of an Increase in Capital Income Taxation 5.5 Conclusions!2
Chapter 6 Money, Inflation and Economic Growth 6.1 Private Consumption and Money Demand in the Ramsey Model 6.1.1 Money in the Utility Function of Households 6.1.2 Nominal and Real Interest Rates and the Opportunity Cost of Real Money Balances 6.1.3 The First Order Conditions for an Optimum 6.1.4 The Money Demand Function 6.1.5 The Rate of Growth of the Money Supply and Inflation 6.1.6 The Euler Equation for Consumption 6.2 Capital Accumulation in a Ramsey Model With Money 6.2.1 The Real Interest Rate and the Real Wage 6.2.2 The Inflation Tax and the Accumulation of Capital 6.3 The Growth Path and the Rate of Growth of the Money Supply 6.3.1 The Balanced Growth Path in the Ramsey Model with Money 6.3.2 The Super Neutrality of Money and Inflation 6.4 Effects of Money Supply Growth in an Overlapping Generations Model 6.4.1 The Blanchard-Weil Model with Money 6.4.2 The Real Effects of the Rate of Growth of the Money Supply 6.4.3 A Dynamic Simulation of the Effects of the Rate of Growth of the Money Supply 6.5 Conclusions Chapter 7 Externalities, Human Capital and Endogenous Growth 7.1 Externalities from Capital Accumulation and Endogenous Growth 7.1.1 Definitions 7.1.2 The Production Function 7.1.3 Externalities from the Accumulation of Capital 7.1.4 Determination of the Real Interest Rate and the Real Wage 7.1.5 The Savings Rate and the Endogenous Growth Rate 7.1.6 Externalities and Endogenous Growth in the Ramsey Model 7.1.7 The Inefficiency of Competitive Equilibrium with Externalities 7.1.8 Endogenous Growth in the Blanchard-Weil Model 7.1.9 Fiscal Policy and Endogenous Growth 7.1.10 Exogenous and Endogenous Growth Models and Convergence 7.2 Investment in Human Capital and Economic Growth 7.2.1 The Generalized Solow Model and Spending on Education and Training 7.2.2 The Balanced Growth Path in the Generalized Solow Model 7.2.3 Endogenous Growth in the Generalized Solow Model 7.2.4 The Jones Model of Human Capital Accumulation 7.2.5 The Lucas Model of Endogenous Growth 7.3 Growth Models Based on the Generation of Ideas and Innovations 7.3.1 Key Features of Ideas and Innovations 7.3.2 The Key Elements of an Ideas and Innovations Growth Model 7.3.3 Endogenous Determination of the Rate of Technical Progress 7.3.4 The Balanced Growth Path with Endogenous Technical Progress 7.4 The New Stylized Facts of Economic Growth 7.5 Conclusions Annex to Chapter 7: The Lucas Model of Human Capital and Endogenous Growth Part B: Consumption, Investment and Money Chapter 8 Consumption and Portfolio Choice under Uncertainty 8.1 Consumption and Portfolio Choice Under Uncertainty!3
8.1.1 The Random Walk Model of Consumption 8.1.2 The Consumption Capital Asset Pricing Model 8.2 From the First Order Conditions to the Full Analysis of Consumption 8.2.1 The Case of Logarithmic Preferences 8.2.2 Quadratic Preferences and Certainty Equivalence 8.2.3 The Permanent Income Hypothesis with Quadratic Preferences 8.2.4 The Consumption Capital Asset Pricing Model with Quadratic Preferences 8.3 Precautionary Savings and Borrowing Constraints 8.4 Conclusions Chapter 9 Dynamic Models of Investment 9.1 Optimal Investment with Convex Adjustment Costs 9.1.1 The Choice of Optimal Investment 9.1.2 The Case of Zero Adjustment Costs 9.1.3 The Investment Function with Convex Adjustment Costs 9.1.4 The Determinants of q 9.1.5 The Dynamic Adjustment of q and the Capital Stock K 9.2 Investment under Uncertainty 9.2.1 The Value of a Firm under Uncertainty 9.2.2 The Lucas and Prescott Model of Investment under Uncertainty 9.2.3 Investment under Uncertainty in an Imperfectly Competitive Market 9.3 Conclusions Chapter 10 Money, Interest and Prices 10.1 The Functions of Money 10.2 The Supply of Money and Central Banks 10.3 The Demand for Money 10.4 Nominal Interest Rates and Short Run Equilibrium in the Money Market 10.5 The Long Run Neutrality of Money 10.6 Money and the Price Level in Dynamic General Equilibrium Models 10.6.1 The Samuelson Overlapping Generations Model 10.6.2 Money in the Utility Function of a Representative Household 10.6.3 Cash in Advance in a Representative Household Model 10.6.4 Cash in Advance in an Overlapping Generations Model 10.7 Nominal and Real Interest Rates and the Money Supply 10.7.1 Money in the Utility Function of a Representative Household 10.7.2 Cash in Advance in a Representative Household Model 10.7.3 Cash in Advance in an Overlapping Generations Model 10.7.4 The Liquidity Effect in Representative Household Models 10.8 Interest Rate Pegging and Price Level Indeterminacy 10.8.1 Price Level Indeterminacy under Interest Rate Pegging 10.8.2 Solutions to the Price Level Indeterminacy Problem under Interest Rate Pegging 10.9 Seigniorage and Inflation 10.9.1 Monetary Growth, Inflation and Seigniorage 10.9.2 The Seigniorage Laffer Curve 10.9.3 A High Inflation Equilibrium and the Transition to Hyperinflation 10.10 Conclusions Part C: Models of Aggregate Fluctuations Chapter 11 The Stochastic Growth Model and Aggregate Fluctuations 11.1 The Stochastic Growth Model!4
11.1.1 Extending the Ramsey Model to Account for Aggregate Fluctuations 11.1.2 The Behavior of Firms 11.1.3 The Representative Household 11.1.4 Population, Efficiency of Labor and Government Expenditure 11.1.5 Labor Supply of the Representative Household 11.1.6 Inter-temporal Substitution in Labor Supply 11.1.7 Uncertainty and the Behavior of the Representative Household 11.2 A Simplified Version of the Stochastic Growth Model 11.3 Conclusions Annex to Chapter 11: A Log-Linear Approximation to the Stochastic Growth Model Chapter 12 Keynesian Models and the Phillips Curve 12.1 The Structure of the Original Keynesian Model 12.1.1 The Keynesian Cross 12.1.2 The IS-LM Model 12.1.3 The Aggregate Demand (AD), Aggregate Supply (AS) Model 12.1.4 Aggregate Fluctuations and Aggregate Demand Policies 12.2 The Theory of Discretionary Monetary and Fiscal Policy 12.2.1 The Tinbergen Theil Theory of Discretionary Aggregate Demand Policies 12.2.2 Monetary and Fiscal Policy with a Full Employment Target 12.2.3 Monetary and Fiscal Policy with a Full Employment Target and a Price Level Target 12.3 The Phillips Curve and Inflationary Expectations 12.3.1 The Phillips Curve and the Tradeoff between Inflation and Unemployment 12.3.2 The Instability of the Phillips Curve and Inflationary Expectations 12.4 The Natural Rate of Unemployment and Aggregate Demand Policies 12.4.1 The Path of Inflation and Unemployment under Adaptive Expectations 12.4.2 Rules versus Discretion in Aggregate Demand Policy 12.4.3 Inflation and Unemployment under Rational Expectations 12.5 Conclusions Annex to Chapter 12: The Samuelson Multiplier Accelerator Model Chapter 13 A Perfectly Competitive New Classical Model 13.1 A Perfectly Competitive New Classical Model without Capital 13.1.1 The Representative Household 13.1.2 The Representative Firm 13.1.3 General Equilibrium 13.2 Monetary Factors in the New Classical Model 13.2.1 An Exogenous Path for the Money Supply 13.2.2 An Exogenous Path for the Nominal Interest Rate 13.2.3 An Inflation Based Interest Rate Rule 13.2.4 Non-Neutrality of Money in New Classical Models 13.3 Conclusions Chapter 14 A Model of Imperfect Competition and Staggered Pricing 14.1 An Imperfectly Competitive Model of Aggregate Fluctuations 14.1.1 The Representative Household 14.1.2 The Representative Firm and Optimal Pricing 14.1.3 Equilibrium with Full Price Flexibility 14.1.4 The Inefficiency of the Natural Rate 14.2 Staggered Price Adjustment and Aggregate Fluctuations 14.2.1 Optimal Pricing with Staggered Price Adjustment!5
14.2.2 Equilibrium in the Market for Goods and Services and the New Keynesian IS Curve 14.2.3 Labor Market Equilibrium and the New Keynesian Phillips Curve 14.2.4 The Structure of the Imperfectly Competitive Model with Staggered Pricing 14.2.5 Real and Monetary Shocks and Aggregate Fluctuations 14.2.6 A Dynamic Simulation of the Model 14.3 Conclusions Annex to Chapter 14: The Rotemberg Model of Convex Costs of Price Adjustment Chapter 15 A Model with Periodic Wage Contracts 15.1 Insiders, Wage Setting and the Phillips Curve 15.1.1 Output, Employment and Labor Demand 15.1.2 Wage Setting and Employment in an Insider Outsider Model 15.1.3 An Expectations Augmented Phillips Curve 15.1.4 The Natural Rate of Unemployment and the Natural Level of Output 15.2 The Determination of Aggregate Consumption and Money Demand 15.3 Equilibrium in the Product and Money Markets 15.3.1 The New Keynesian IS and LM Curves 15.3.2 The Natural and the Current Real Interest Rate 15.3.3 Equilibrium Fluctuations with Exogenous Real Shocks 15.4 Aggregate Fluctuations under an Exogenous Money Supply Rule 15.4.1 The Real Effects of Monetary Shocks 15.4.2 The Effects of Real and Monetary Shocks on Prices and Output 15.5 Aggregate Fluctuations under a Feedback Nominal Interest Rate Rule 15.6 Unemployment Persistence, Inflation and Monetary Policy 15.6.1 Nominal Wage Contracts in a Dynamic Insider Outsider Model 15.6.2 Wage Determination, Unemployment Persistence and the Phillips Curve 15.6.3 The Relation between Output and Unemployment Persistence 15.6.4 Fluctuations of Unemployment and Inflation under a Taylor Rule 15.6.5 A Dynamic Simulation of the Effects of Monetary and Real Shocks 15.7 Conclusions Chapter 16 Unemployment and Matching in the Labour Market 16.1 Alternative Views of the Labor Market and Equilibrium Unemployment 16.2 The Matching Function 16.3 Flows Into and Out of Employment and Equilibrium Unemployment 16.4 Firms and the Creation of Vacancies and Jobs 16.4.1 The Present Value of Net Expected Profits from an Existing Job 16.4.2 The Present Value of Net Expected Profits from a Vacancy and the Creation of Vacancies 16.4.3 Free Entry and the Job Creation Condition 16.5 The Behavior of Unemployed Job Seekers 16.6 Wage Bargaining and the Wage Equation 16.7 Wage Determination and Equilibrium Unemployment 16.8 Implications of Shifts in the Parameters of the Model 16.8.1 Implications of an Increase in Labor Productivity 16.8.2 Implications of a Rise in Unemployment Benefits 16.8.3 Implications of a Rise in the Real Interest Rate 16.8.4 Implications of an Increase in the Probability of Termination of a Job 16.9 Dynamic Adjustment to the Steady State 16.9.1 The Dynamic Adjustment of Unemployment and Vacancies 16.9.2 Numerical Simulations of the Model 16.10 Conclusions Part D: Monetary and Fiscal Policy!6
Chapter 17 The Role of Monetary Policy 17.1 Rules versus Discretion in Monetary Policy 17.2 Rules, Discretion and Credibility in a New Keynesian Model 17.2.1 The Social Welfare Loss from Inflation and Unemployment 17.2.2 Monetary Policy under Discretion: The Problem of Credibility 17.2.3 Monetary Policy under an Inflation Rule 17.2.4 Reputation and Credibility in the Implementation of Monetary Policy 17.3 The Choice of Monetary Policy Instrument 17.4 Optimal Monetary Policy in the Presence of Stochastic Real Shocks 17.5 Optimal Monetary Policy and the Taylor Rule 17.6 Monetary Shocks and the Optimal Feedback Policy Rule 17.7 Conclusions Chapter 18 Fiscal Policy and the Determination of Public Debt Chapter 19 Models of Bubbles, Multiple Equilibria and Financial Crises Chapter 20 Recent Developments in Macroeconomics Mathematical Annexes Annex 1 Ordinary Differential Equations 1.1 Definitions 1.2 First Order Linear Differential Equations 1.2.1 Constant Coefficients 1.2.2 Variable Right Hand Side 1.2.3 Variable Coefficients 1.2.4 Homogeneous and Non-homogeneous Differential Equations 1.3 Second Order Linear Differential Equations 1.3.1 Homogeneous Equations with Constant Coefficients 1.3.2 Non-homogeneous Equations with Constant Coefficients 1.4 A Pair of First Order Linear Differential Equations 1.5 A System of n First Order Linear Differential Equations 1.5.1 Eigenvalues and Eigenvectors 1.5.2 Solving the n-th Order System of Linear Differential Equations Annex 2 Difference Equations 2.1 Lag Operators 2.2 First Order Linear Difference Equations 2.3 Second Order Linear Difference Equations 2.4 A Pair of First Order Linear Difference Equations 2.5 A System of n First Order Linear Difference Equations Annex 3 Methods of Inter-temporal Optimization!7
3.1 The Form of Dynamic Optimization Problems 3.2 The Method of Optimal Control 3.3 The Optimal Control Method in Continuous Time 3.4 Dynamic Programming and the Bellman Equation 3.5 An Example Based on Optimal Savings in Continuous Time Annex 4 Stochastic Processes 4.1 Stochastic Processes 4.2 Autoregressive Stochastic Processes 4.3 Moving Average Stochastic Processes 4.4 Autoregressive Moving Average Stochastic Processes Annex 5 Models with Rational Expectations 5.1 The Definition of Rational Expectations 5.2 Rational Expectations for Linear Autoregressive Processes 5.3 First Order Linear Models with Rational Expectations 5.3.1 The Method of Repeated Substitutions 5.3.2 The Factorization Method 5.3.3 The Method of Undetermined Coefficients 5.3.4 Two Economic Examples 5.3.5 Alternative Assumptions about the Evolution of Exogenous Variables 5.4 Second Order Linear Models with Rational Expectations 5.4.1 The Factorization Method 5.4.2 The Method of Undetermined Coefficients 5.4.3 An Economic Example 5.5 Multivariate Linear Models with Rational Expectations 5.5.1 The Blanchard Kahn Method 5.5.2 Other Solution Methods 5.5.3 An Economic Example of the Blanchard Kahn Method!8