Contents
List of Figures and Table
Preface
1 Introduction
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 Deterministic and Stochastic Dynamic 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 Evolution of Per Capita Output and Income over Time
1.2.3 Economic Growth and Convergence since 1820
1.3 Key Facts about Aggregate Fluctuations
1.3.1 Frequency, Severity, and Duration of Recessions
1.3.2 Unemployment in Booms and Recessions
1.3.3 Trends and Fluctuations in the Price Level and Inflation
1.3.4 Monetary Policy and Government Debt
1.3.5 Monetary Policy and Inflation in the Postwar Period
1.4 Conclusion
2 The Intertemporal Approach
2.1 Models, Variables, and Functions
2.2 General Equilibrium in a One-Period Competitive Model
2.2.1 Endowments, Preferences, and the Optimal Behavior of Households
2.2.2 The Production Function and the Profit-Maximizing Behavior of Firms
2.2.3 The Cobb-Douglas Production Function
2.2.4 General Equilibrium in the One-Period Model
2.3 Savings and Investment in a Two-Period Competitive Model
2.3.1 The Representative Household in a Two-Period Model
2.3.2 Implications of the Euler Equation for Consumption
2.3.3 The Case of a Constant Elasticity of Intertemporal Substitution
2.3.4 Firms, Technology, and the Optimal Output Path
2.3.5 General Equilibrium in the Two-Period Model
2.3.6 Diagrammatic Exposition of the Intertemporal Equilibrium
2.3.7 Implications for Growth and Business Cycle Theory
2.4 Consumption and Labor Supply in a One-Period Competitive Model
2.4.1 The Optimal Choice of Consumption and Labor Supply
2.4.2 Income and Substitution Effects on Labor Supply
2.4.3 The Frisch Elasticity of Labor Supply
2.4.4 The Production Function and the Optimal Decisions of Firms
2.4.5 General Equilibrium and the Determination of Output and Employment
2.5 Consumption and Labor Supply in a Two-Period Competitive Model
2.5.1 Optimal Consumption and Labor Supply in a Two-Period Model
2.5.2 Intertemporal Substitution in Consumption and Labor Supply
2.5.3 Optimal Production Decisions of Firms
2.5.4 General Equilibrium and the Determination of Output and Employment
2.5.5 Implications for Business Cycle Theory
2.6 Money, Prices, and Inflation in a Two-Period Competitive Model
2.6.1 The Representative Household and the Demand for Money
2.6.2 The Classical Dichotomy and the Neutrality of Money
2.6.3 The Two-Period Competitive Model and Classical Monetary Theory
2.7 Fiscal Policy in a Two-Period Competitive Model
2.7.1 Government Expenditure and Taxes in a One-Period Economy
2.7.2 Income Taxes and Labor Supply
2.7.3 Government Expenditure, Taxes, and Debt in a Two-Period Economy
2.7.4 Ricardian Equivalence between Tax and Debt Finance
2.7.5 Income Taxation and Aggregate Savings and Investment
2.7.6 Implications for Fiscal Policy and Government Debt
2.8 The Treatment of Time and the Intertemporal Approach
2.9 Conclusion
3 Savings, Investment, and Economic Growth
3.1 The Solow Growth Model
3.1.1 The Neoclassical Production Function
3.1.2 The Cobb-Douglas Production Function
3.1.3 Population Growth and Technical Progress
3.1.4 Savings, Capital Accumulation, and Economic Growth
3.1.5 The Balanced Growth Path and the Convergence Process
3.1.6 The Rate of Growth of Capital and Output
3.1.7 Significance of the Inada Conditions
3.2 Competitive Markets, the Real Interest Rate, and Real Wages
3.3 The Savings Rate and the Golden Rule
3.3.1 The Savings Rate and the Balanced Growth Path
3.3.2 The Savings Rate, the Golden Rule, and Dynamic Inefficiency
3.3.3 The Elasticity of Steady State Output with Respect to the Savings Rate
3.4 Total Factor Productivity and Population Growth
3.4.1 Dynamic Effects of Total Factor Productivity in the Solow Model
3.4.2 Dynamic Effects of Population Growth in the Solow Model
3.5 Speed of Convergence toward the Balanced Growth Path
3.6 The Process of Economic Growth and the Solow Model
3.6.1 The Kaldor Stylized Facts of Economic Growth
3.6.2 Differences in Per Capita Output and Income between Developed and Less Developed Economies
3.6.3 Conditional Convergence
3.7 Convergence with a Cobb-Douglas Production Function
3.8 Dynamic Simulations of a Calibrated Solow Model
3.8.1 The Solow Model in Discrete Time
3.8.2 The Calibrated Solow Model
3.8.3 Dynamic Simulations of the Model
3.9 Conclusion
4 The Representative Household Model of Optimal Growth
4.1 The Optimal Intertemporal Path of Consumption
4.2 The Ramsey Model of Economic Growth
4.2.1 The Production Function
4.2.2 The Utility Function of the Representative Household
4.2.3 The Accumulation of Capital and the Optimality of the Decentralized Competitive Equilibrium
4.2.4 Conditions for Utility Maximization by the Representative Household
4.2.5 The Euler Equation for Consumption
4.2.6 The Intertemporal Budget Constraint of the Representative Household
4.2.7 The Transversality Condition with an Infinite Time Horizon
4.2.8 The Consumption Function of the Representative Household with an Infinite Horizon
4.3 Dynamic Adjustment and the Balanced Growth Path
4.3.1 Dynamic Adjustment toward the Balanced Growth Path
4.3.2 The Balanced Growth Path and the Modified Golden Rule
4.3.3 Effects of a Permanent Increase in the Pure Rate of Time Preference
4.3.4 Effects of a Permanent Increase in Total Factor Productivity
4.3.5 Effects of a Permanent Increase in the Rate of Growth of Population
4.4 Properties of the Adjustment Path and the Speed of Convergence
4.5 Dynamic Simulations of a Calibrated Ramsey Model
4.5.1 The Ramsey Model in Discrete Time
4.5.2 The Calibrated Ramsey Model
4.5.3 Dynamic Simulations of the Model
4.6 Conclusion
5 Overlapping Generations Models of Growth
5.1 The Diamond Model
5.1.1 Definitions
5.1.2 The Production Function
5.1.3 The Intertemporal Utility Function of Households
5.1.4 Markets and the Behavior of Households
5.1.5 Capital Accumulation and the Dynamic Adjustment of the Economy
5.1.6 A Simplified Diamond Model with Logarithmic Preferences and Cobb-Douglas Technology
5.1.7 The Speed of Adjustment in the Simplified Diamond Model
5.1.8 Welfare Implications of the Diamond Model and the Possibility of Dynamic Inefficiency
5.1.9 Dynamic Simulations of a Calibrated Diamond Model
5.2 The Blanchard-Weil Model
5.2.1 Definitions
5.2.2 The Production Function
5.2.3 The Intertemporal Utility Function of Households and Household Consumption
5.2.4 Aggregation across Generations
5.2.5 The Model in Terms of Efficiency Units of Labor
5.2.6 The Balanced Growth Path and the Adjustment Path
5.3 Dynamic Simulations of a Calibrated Blanchard-Weil Model
5.3.1 The Blanchard-Weil Model in Discrete Time
5.3.2 Dynamic Simulations of the Model
5.4 Conclusion
6 Fiscal Policy and Economic Growth
6.1 The Government Budget Constraint
6.1.1 Government Deficits, Debt, and Solvency
6.2 Ricardian Equivalence and the Ramsey Model
6.2.1 Ricardian Equivalence between Government Debt and Taxes
6.2.2 Government Expenditure, Taxes, and Debt in the Ramsey Model
6.3 Dynamic Effects of Fiscal Policy in the Blanchard-Weil Model
6.3.1 The Blanchard-Weil Model with Government Expenditure and Debt
6.3.2 Government Debt, Taxes, and Redistribution across Generations
6.3.3 Dynamic Simulations of Fiscal Policy in a Calibrated Blanchard-Weil Model
6.4 Dynamic Effects of Distortionary Taxation
6.4.1 Distortionary and Nondistortionary Taxes
6.4.2 Dynamic Effects of Capital Income and Business Gross Profits Taxation
6.4.3 Dynamic Simulations of Increases in Capital Income and Business Gross Profits Taxation
6.5 Conclusion
7 Money, Inflation, and Economic Growth
7.1 Private Consumption and Money Demand in a Representative Household Model
7.1.1 Money in the Utility Function of Households
7.1.2 Nominal and Real Interest Rates and the Opportunity Cost of Real Money Balances
7.1.3 First-Order Conditions for an Optimum
7.1.4 The Money Demand Function
7.1.5 Growth Rate of the Money Supply and Inflation
7.1.6 The Euler Equation for Consumption
7.2 Aggregate Capital Accumulation in a Ramsey Model with Money
7.2.1 The Production Function, the Real Interest Rate, and the Real Wage
7.2.2 The Inflation Tax and the Accumulation of Capital
7.3 Effects of the Growth Rate of the Money Supply in the Ramsey Monetary Model
7.3.1 The Balanced Growth Path in the Ramsey Model with Money
7.3.2 The Superneutrality of Money and Inflation
7.3.3 The Welfare Costs of Inflation in a Ramsey Model
7.4 Effects of Monetary Growth in an OLG Model
7.4.1 The Blanchard-Weil Model with Money
7.4.2 Real Effects of the Growth Rate of the Money Supply
7.4.3 A Dynamic Simulation of the Effects of a Rise in the Growth Rate of the Money Supply in a Calibrated Blanchard-Weil Model
7.5 Conclusion
8 Externalities, Human Capital, and Technical Progress
8.1 Externalities from Capital Accumulation and Economic Growth
8.1.1 Definitions
8.1.2 The Production Function
8.1.3 Externalities from the Accumulation of Capital
8.1.4 Determination of the Real Interest Rate and the Real Wage
8.1.5 The Savings Rate and the Endogenous Growth Rate
8.1.6 Externalities and Endogenous Growth in the Ramsey Model
8.1.7 The Suboptimality of the Competitive Equilibrium with Externalities Due to Capital Accumulation
8.1.8 Externalities and Endogenous Growth in the Blanchard-Weil Model
8.1.9 Fiscal Policy and Endogenous Growth
8.1.10 Convergence in Exogenous and Endogenous AK Growth Models
8.2 Investment in Human Capital and Economic Growth
8.2.1 The Extended Solow Model and the Share of Spending on Education and Training
8.2.2 The Balanced Growth Path in the Extended Solow Model
8.2.3 Endogenous Growth in the Extended Solow Model
8.2.4 The Jones Model of Human Capital Accumulation
8.2.5 The Lucas Model of Human Capital Accumulation and Endogenous Growth
8.2.6 A Detailed Analysis of the Lucas Model
8.3 Ideas, Innovations, and Technical Progress
8.3.1 Key Features of Ideas and Innovations
8.3.2 Key Elements of an Ideas-and-Innovations Growth Model
8.3.3 Endogenous Determination of the Rate of Technical Progress
8.3.4 The Balanced Growth Path with Endogenous Technical Progress
8.4 Unified Growth Theory and the Transition from Stagnation to Growth
8.5 Institutions and Long-Run Growth
8.6 The New Stylized Facts of Economic Growth
8.7 Conclusion
9 Dynamic Stochastic Models under Rational Expectations
9.1 A Stochastic Expectational Model of a Competitive Market
9.1.1 Absence of Uncertainty and Perfect Foresight
9.1.2 Uncertainty and Adaptive Expectations
9.1.3 The Rational Expectations Hypothesis
9.2 Rational Expectations for Linear Autoregressive Processes
9.3 First-Order Linear Expectational Models
9.3.1 The Method of Repeated Substitutions
9.3.2 The Method of Factorization
9.3.3 The Method of Undetermined Coefficients
9.3.4 Two Additional Economic Examples
9.3.5 Alternative Assumptions about the Evolution of Exogenous Variables
9.3.6 The Expectational Competitive Market Model Revisited
9.4 Second-Order Linear Expectational Models
9.4.1 The Method of Factorization
9.4.2 The Method of Undetermined Coefficients
9.4.3 An Economic Example of a Second-Order System
9.5 Multivariate Linear Models with Rational Expectations
9.5.1 The Blanchard-Kahn Method
9.5.2 Other Solution Methods
9.5.3 A Second-Order Example of the Blanchard-Kahn Method
9.6 Rational Expectations and Learning
9.7 Conclusion
10 Consumption and Portfolio Choice under Uncertainty
10.1 Consumption and Portfolio Choice
10.1.1 The Random Walk Model of Consumption
10.1.2 The Consumption Capital Asset Pricing Model
10.2 Full Analysis of Consumption and Portfolio Choice
10.2.1 The Case of Logarithmic Preferences
10.2.2 Quadratic Preferences and Certainty Equivalence
10.2.3 The Permanent-Income Hypothesis with Quadratic Preferences
10.2.4 The Consumption CAPM with Quadratic Preferences
10.2.5 The Efficient Markets Hypothesis
10.3 Precautionary Savings and Borrowing Constraints
10.4 Conclusion
11 Investment and the Cost of Capital
11.1 Optimal Investment with Convex Adjustment Costs
11.1.1 The Choice of Optimal Investment
11.1.2 The Case of Zero Adjustment Costs
11.1.3 The Investment Function with Convex Adjustment Costs
11.1.4 The Determinants of q
11.1.5 Dynamic Adjustment of q and the Capital Stock K
11.2 Optimal Investment under Uncertainty
11.2.1 The Value of a Firm under Uncertainty
11.2.2 The Lucas-Prescott Model of Investment under Uncertainty
11.2.3 Rational Expectations Equilibrium and Aggregate Investment in the Lucas-Prescott Model
11.3 Conclusion
12 Money, Interest, and Prices
12.1 The Functions of Money
12.2 The Supply of Money and Central Banks
12.2.1 Central Banks and Their Functions
12.2.2 Central Banks and the Money Supply
12.3 The Demand for Money
12.4 Nominal Interest Rates and Short-Run Equilibrium in the Money Market
12.5 The Long-Run Neutrality of Money
12.5.1 Monetary Growth, Inflation, and Nominal Interest Rates in the Long Run
12.5.2 The Welfare Cost of Inflation
12.5.3 The Long-Run Neutrality of Money and Monetary Reforms
12.6 Money and the Price Level in Dynamic General Equilibrium Models
12.6.1 The Samuelson OLG Model
12.6.2 Money in the Utility Function of a Representative Household
12.6.3 Cash in Advance in a Representative Household Model
12.6.4 Cash in Advance in an OLG Model
12.7 Nominal and Real Interest Rates and the Money Supply
12.7.1 Money in the Utility Function of a Representative Household
12.7.2 Cash in Advance in a Representative Household Model
12.7.3 Cash in Advance in an OLG Model
12.7.4 The Liquidity Effect in Representative Household Models
12.8 Interest Rate Pegging and Price Level Indeterminacy
12.8.1 Interest Rate Pegging and Price Level Indeterminacy in Representative Household Models
12.8.2 The Wicksell Solution to the Problem of Price Level Indeterminacy
12.8.3 The Fiscal Theory of the Price Level
12.8.4 The Pigou Effect and Price Level Determinacy in OLG Models
12.9 Money Growth, Seigniorage, and Inflation
12.9.1 Relations between Monetary Growth, Seigniorage, and Inflation
12.9.2 The Seigniorage Laffer Curve
12.9.3 The Demand for Seigniorage and Equilibrium with High Inflation
12.9.4 The Transition to Hyperinflation
12.9.5 How Can High Inflation and Hyperinflation Be Tackled?
12.10 Conclusion
13 The Stochastic Growth Model of Aggregate Fluctuations
13.1 The Stochastic Growth Model
13.1.1 Extending the Ramsey Model to Account for Aggregate Fluctuations
13.1.2 The Representative Firm
13.1.3 The Representative Household
13.1.4 Exogenous Population Growth, Efficiency of Labor, and Government Expenditure
13.1.5 Labor Supply of the Representative Household
13.1.6 Intertemporal Substitution in Labor Supply
13.1.7 Uncertainty and the Behavior of the Representative Household
13.2 A Simplified Version of the Stochastic Growth Model
13.2.1 Fluctuations of Output in the Simplified Stochastic Growth Model
13.2.2 The Simplified Stochastic Growth Model and the Evidence on Aggregate Fluctuations
13.3 A Log-Linear Approximation to the General Stochastic Growth Model
13.3.1 The Steady State
13.3.2 Log-Linearizing the Model around the Steady State
13.4 Solving the Log-Linear Stochastic Growth Model
13.4.1 Aggregate Fluctuations around the Steady State
13.4.2 A Dynamic Simulation of the Log-Linear Stochastic Growth Model
13.5 Conclusion
14 Perfectly Competitive Models with Flexible Prices
14.1 A Perfectly Competitive Model without Capital
14.1.1 The Representative Household
14.1.2 The Representative Firm
14.1.3 General Equilibrium
14.2 Monetary Factors in a Perfectly Competitive Model
14.2.1 An Exogenous Path for the Money Supply
14.2.2 An Exogenous Path for the Nominal Interest Rate
14.2.3 An Inflation-Based Nominal Interest Rate Rule
14.2.4 Optimal Monetary Policy
14.3 Imperfect Information and the Nonneutrality of Money
14.3.1 Competitive Equilibrium under Imperfect Information about the Price Level
14.3.2 The Determination of Output and Employment
14.3.3 The Real Effects of Monetary Shocks in a Rational Expectations Equilibrium
14.3.4 Optimal Monetary Policy in the Lucas Model
14.3.5 The New Classical Model and the Great Depression
14.3.6 Models of Informational Frictions and Rational Inattention
14.4 Conclusion
15 Keynesian Models and the Phillips Curve
15.1 The Original Keynesian Models
15.1.1 The Keynesian Cross
15.1.2 The IS-LM Model
15.1.3 The AD-AS Model
15.1.4 The Impact of Aggregate Demand Policies
15.2 The Samuelson Multiplier Accelerator Model
15.3 The Theory of Discretionary Monetary and Fiscal Policy
15.3.1 The Tinbergen-Theil Theory of Discretionary Aggregate Demand Policies
15.3.2 Monetary and Fiscal Policy with a Full Employment Target
15.3.3 Monetary and Fiscal Policy with a Full Employment Target and a Price Level Target
15.4 The Phillips Curve and Inflationary Expectations
15.4.1 The Phillips Curve and the Trade-off between Inflation and Unemployment
15.4.2 Instability of the Phillips Curve and Inflationary Expectations
15.5 The Natural Rate of Unemployment and Aggregate Demand Policies
15.5.1 The Path of Inflation and Unemployment under Adaptive Expectations
15.5.2 Rules versus Discretion in Aggregate Demand Policy
15.5.3 Inflation and Unemployment under Rational Expectations
15.6 Conclusion
16 A Model of Imperfect Competition and Staggered Pricing
16.1 An Imperfectly Competitive Model of Aggregate Fluctuations
16.1.1 The Representative Household
16.1.2 The Representative Firm and Optimal Pricing
16.1.3 Full Price Flexibility and the Natural Rate
16.1.4 Inefficiency of the Natural Rate
16.2 Staggered Price Adjustment and Aggregate Fluctuations
16.2.1 Optimal Pricing with Staggered Price Adjustment
16.2.2 Equilibrium in the Market for Goods and Services and the New Keynesian IS curve
16.2.3 Labor Market Equilibrium and the New Keynesian Phillips Curve
16.2.4 The Imperfectly Competitive Model with Staggered Pricing and the Taylor Rule
16.2.5 Real and Monetary Shocks and Aggregate Fluctuations
16.2.6 The Divine Coincidence and Optimal Monetary Policy in the New Keynesian Model with Staggered Pricing
16.2.7 A Dynamic Simulation of the Model
16.3 The Rotemberg Model of Convex Costs of Price Adjustment
16.4 Conclusion
17 A Model of Unemployment and Nominal Wage Contracts
17.1 Alternative Views of the Labor Market and Equilibrium Unemployment
17.2 Households and Optimal Consumption and Money Demand
17.3 Firms and Optimal Pricing and Production
17.4 Wage Setting and Employment in a Model with Insiders and Outsiders
17.4.1 Wage Determination, Unemployment Persistence, and the Phillips Curve
17.4.2 The Relation between Output and Unemployment Persistence
17.4.3 The Phillips Curve in Terms of Deviations of Output from Its Natural Rate
17.5 The Implications of Staggered Pricing
17.5.1 Optimal Pricing with Staggered Price Adjustment
17.5.2 Inflation and Unit Labor Costs under Staggered Pricing
17.6 An Extended New Keynesian Phillips Curve: Combining Staggered Pricing with Periodic Nominal Wage Contracts
17.7 Inflation and Aggregate Fluctuations under a Taylor Rule
17.7.1 New Neoclassical Synthesis IS-LM Functions
17.7.2 The Natural and Equilibrium Real Interest Rate
17.7.3 Equilibrium Fluctuations with Exogenous Preference and Productivity Shocks
17.7.4 Does Staggered Pricing Matter for Inflation Persistence?
17.7.5 Inflation Stabilization and the Divine Coincidence
17.8 The Optimal Taylor Rule
17.8.1 Optimal Inflation Policy
17.9 A Dynamic Simulation of the Effects of Monetary and Real Shocks
17.10 Conclusion
18 Matching Frictions and Equilibrium Unemployment
18.1 The Matching Function
18.1.1 The Probability of Filling a Vacancy and Labor Market Tightness
18.1.2 The Probability of the Unemployed Finding a Job
18.2 Flows into and out of Employment, Equilibrium Unemployment, and the Beveridge Curve
18.3 Firms and the Creation of Vacancies
18.3.1 The Present Value of Net Expected Profits from an Existing Job
18.3.2 The Present Value of Net Expected Profits from a Vacancy and the Creation of Vacancies
18.3.3 Free Entry and the Job Creation Condition
18.4 The Behavior of Unemployed Job Seekers
18.4.1 The Permanent Income of an Unemployed Job Seeker
18.4.2 The Permanent Income of an Employed Worker
18.4.3 Comparing the Permanent Income of the Employed and the Unemployed
18.5 Wage Bargaining and the Wage Equation
18.6 Wage Determination and Equilibrium Unemployment
18.7 Determinants of Equilibrium Unemployment, Real Wages, and Labor Market Tightness
18.7.1 An Increase in Labor Productivity
18.7.2 An Increase in Unemployment Benefits
18.7.3 An Increase in the Real Interest Rate
18.7.4 An Increase in the Probability of Job Destruction
18.8 Dynamic Adjustment to the Steady State
18.8.1 The Dynamic Adjustment of Unemployment and Vacancies
18.8.2 Numerical Simulations of the Model
18.9 Matching Models and Nominal Rigidities
18.10 Conclusion
19 The Macroeconomic Implications of Financial Frictions
19.1 The Role of Finance and Financial Markets
19.1.1 Financial Frictions and Financial Intermediation
19.1.2 The Risks of Financial Intermediation, Leverage, and the External Finance Premium
19.1.3 The Links between the Financial Sector and Real Activity in the Presence of Frictions
19.2 Financial Frictions in a New Keynesian Model with Staggered Pricing
19.3 Financial Frictions in a Model with Unemployment Persistence and Nominal Wage Contracts
19.4 Conclusion
20 The Role of Monetary Policy
20.1 Rules versus Discretion in Monetary Policy
20.2 Rules, Discretion, and Credibility in a New Keynesian Model
20.2.1 The Social Welfare Loss from Inflation and Unemployment
20.2.2 Monetary Policy under Discretion: The Problem of Credibility
20.2.3 Monetary Policy under a Fixed Inflation Rule
20.2.4 Central Bank Constitutions
20.2.5 Reputation as a Solution to the Problem of Inflationary Bias
20.3 Optimal Monetary Policy in the Presence of Stochastic Shocks
20.4 The Mechanics of Monetary Policy
20.4.1 Financial Markets and Open Market Operations
20.4.2 The Term Structure of Interest Rates
20.5 Optimal Monetary Policy and the Taylor Rule
20.6 Monetary Policy Shocks and the Optimal Policy Rule
20.7 Monetary Policy, Financial Frictions, and the Zero Lower Bound on Interest Rates
20.7.1 The Liquidity Trap
20.7.2 Monetary Policy at the Zero Lower Bound
20.7.3 The Zero Lower Bound and Unconventional Monetary Policy
20.8 Conclusion
21 Fiscal Policy and Government Debt
21.1 Tax Smoothing and Government Debt Accumulation
21.1.1 The Barro Tax-Smoothing Model
21.1.2 Steady State Implications of Tax Smoothing
21.2 Keynesian Stabilization Policy, Automatic Stabilizers, and Fiscal Implications of the Zero Lower Bound
21.3 Optimal Dynamic Ramsey Taxation
21.4 Fiscal Policy and Politics
21.4.1 Distributional Considerations and Politics
21.4.2 Electoral Factors and Partisan Differences
21.5 The Burden of High Government Deficits and Debt
21.6 A Model of Government Debt Crises
21.6.1 The Calvo Model
21.6.2 Multiple Equilibria and Self-Fulfilling Prophecies
21.7 Conclusion
22 Bubbles, Multiple Equilibria, and Sunspots
22.1 Bubbles in Linear Rational Expectations Models
22.1.1 Bubbles versus Fundamentals
22.1.2 Deterministic versus Stochastic Bubbles
22.1.3 Bubbles as Self-Fulfilling Prophecies in Inherently Unstable Models
22.1.4 Higher-Order Linear Models
22.2 Bubbles in Models of Stock and Money Markets
22.2.1 Stock Market Bubbles
22.2.2 Money Market Bubbles, the Price Level, and Inflation
22.3 Ruling Out Unstable Bubbles
22.4 Indeterminacy, Self-Fulfilling Prophecies, and Sunspots
22.4.1 The Samuelson OLG Model with Money, Revisited
22.4.2 Other Models of Indeterminacy and Sunspots in Macroeconomics
22.5 Conclusion
23 The Interaction of Events and Ideas in Dynamic Macroeconomics
23.1 The Financial Crisis and Recent Developments in Dynamic Macroeconomics
23.2 The Interaction of Events and Ideas and the Role of Empirical Macroeconomics
23.3 Policy Evaluation and DSGE Models
23.4 Conclusion
Appendixes
A Variables, Functions, and Optimization
A.1 Models, Variables, and Functions
A.1.1 Functions
A.1.2 Derivatives and Partial Derivatives of Functions
A.1.3 Maxima and Minima of Functions
A.2 Mathematical Optimization under Constraints
A.2.1 Constrained Optimization in the Case of a Function of One Variable
A.2.2 Optimal Consumption under an Income Constraint
A.2.3 The Lagrange Method
A.3 Some Useful Functional Forms
A.3.1 The Two-Factor CES Production Function and the Elasticity of Substitution
A.3.2 Special Cases of the CES Production Function
A.3.3 The CES Production Function and the Solow Model of Economic Growth
A.3.4 The CES Utility Function
A.3.5 Additively Separable Utility and the CEIS Utility Function
B Linear Models and Linear Algebra
B.1 Linear Models
B.2 Elements of Linear Algebra
B.2.1 Matrix Addition, Subtraction, and Multiplication
B.2.2 The Inverse of a Square Matrix
B.3 An Example with Two Endogenous Variables
B.3.1 Cramer’s Rule
B.3.2 The Augmented Matrix and Gauss-Jordan Elimination
B.3.3 Diagonalization, Eigenvalues, and Eigenvectors
B.3.4 Solving a System with Two Endogenous and Two Exogenous Variables
C Ordinary Differential Equations
C.1 Definitions
C.2 First-Order Linear Differential Equations
C.2.1 Constant Coefficients
C.2.2 Variable Right-Hand Side
C.2.3 Variable Coefficients
C.2.4 Homogeneous and Nonhomogeneous Differential Equations
C.2.5 Convergence and Stability of First-Order Differential Equations
C.3 Second-Order Linear Differential Equations
C.3.1 Homogeneous Equations with Constant Coefficients
C.3.2 Nonhomogeneous Equations with Constant Coefficients
C.4 A Pair of First-Order Linear Differential Equations
C.4.1 The Method of Substitution
C.4.2 The Method of Eigenvalues
C.5 A System of n First-Order Linear Differential Equations
C.5.1 Eigenvalues and Eigenvectors
C.5.2 Solving the nth-Order System of Linear Differential Equations
D Difference Equations
D.1 Lag Operators and Difference Equations
D.2 First-Order Linear Difference Equations
D.3 Second-Order Linear Difference Equations
D.4 A Pair of First-Order Linear Difference Equations
D.5 A System of n First-Order Linear Difference Equations
E Methods of Intertemporal Optimization
E.1 The Form of Dynamic Optimization Problems
E.2 The Method of Optimal Control
E.3 The Optimal Control Method in Continuous Time
E.4 Dynamic Programming and the Bellman Equation
E.5 An Example Based on Optimal Savings in Continuous Time
F Random Variables and Stochastic Processes
F.1 Probability
F.2 Random Variables and Probability Distributions
F.2.1 Discrete Probability Distributions
F.2.2 Continuous Probability Distributions
F.2.3 Mathematical Expectation, Variance, and Higher Moments
F.2.4 Some Useful Probability Distributions
F.2.5 Convergence of Random Variables
F.2.6 The Law of Large Numbers
F.2.7 The Central Limit Theorem
F.2.8 Joint Probability Distributions
F.3 Stochastic Processes
F.4 Univariate Linear Stochastic Processes in Discrete Time
F.4.1 The White Noise Process
F.4.2 Moving Average Stochastic Processes
F.4.3 Autoregressive Stochastic Processes
F.4.4 Autoregressive Moving Average Stochastic Processes
F.5 Vector Stochastic Processes and Vector Autoregressions
References
Index