Dynamic Macroeconomics
by Alogoskoufis
ISBN: 9780262043014  Copyright 2019
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An advanced treatment of modern macroeconomics, presented through a sequence of dynamic equilibrium models, with discussion of the implications for monetary and fiscal policy.
This textbook offers an advanced treatment of modern macroeconomics, presented through a sequence of dynamic general equilibrium models based on intertemporal optimization on the part of economic agents. The book treats macroeconomics as applied and policyoriented general equilibrium analysis, examining a number of models, each of which is suitable for investigating specific issues but may be unsuitable for others.
After presenting a brief survey of the evolution of macroeconomics and the key facts about longrun economic growth and aggregate fluctuations, the book introduces the main elements of the intertemporal approach through a series of twoperiod competitive general equilibrium modelsâ€”the simplest possible intertemporal models. This sets the stage for the remainder of the book, which presents models of economic growth, aggregate fluctuations, and monetary and fiscal policy. The text focuses on a full analysis of a limited number of key intertemporal models, which are stripped down to essentials so that students can focus on the dynamic properties of the models. Exercises encourage students to try their hands at solving versions of the dynamic models that define modern macroeconomics. Appendixes review the main mathematical techniques needed to analyze optimizing dynamic macroeconomic models. The book is suitable for advanced undergraduate and graduate students who have some knowledge of economic theory and mathematics for economists.
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Contents (pg. vii)  
List of Figures and Table (pg. xxi)  
Preface (pg. xxvii)  
1. Introduction (pg. 1)  
1.1 The Nature and Evolution of Macroeconomics (pg. 2)  
1.1.1 PreKeynesian Macroeconomics (pg. 2)  
1.1.2 Classical and Keynesian Macroeconomics (pg. 4)  
1.1.3 Microeconomic Foundations of Macroeconomics (pg. 6)  
1.1.4 Deterministic and Stochastic Dynamic General Equilibrium Models (pg. 7)  
1.2 Key Facts about LongRun Economic Growth (pg. 11)  
1.2.1 CrossCountry Differences in Per Capita Output and Income (pg. 11)  
1.2.2 Evolution of Per Capita Output and Income over Time (pg. 13)  
1.2.3 Economic Growth and Convergence since 1820 (pg. 14)  
1.3 Key Facts about Aggregate Fluctuations (pg. 18)  
1.3.1 Frequency, Severity, and Duration of Recessions (pg. 18)  
1.3.2 Unemployment in Booms and Recessions (pg. 20)  
1.3.3 Trends and Fluctuations in the Price Level and Inflation (pg. 22)  
1.3.4 Monetary Policy and Government Debt (pg. 26)  
1.3.5 Monetary Policy and Inflation in the Postwar Period (pg. 31)  
1.4 Conclusion (pg. 32)  
2. The Intertemporal Approach (pg. 33)  
2.1 Models, Variables, and Functions (pg. 34)  
2.2 General Equilibrium in a OnePeriod Competitive Model (pg. 36)  
2.2.1 Endowments, Preferences, and the Optimal Behavior of Households (pg. 36)  
2.2.2 The Production Function and the ProfitMaximizing Behavior of Firms (pg. 38)  
2.2.3 The CobbDouglas Production Function (pg. 40)  
2.2.4 General Equilibrium in the OnePeriod Model (pg. 40)  
2.3 Savings and Investment in a TwoPeriod Competitive Model (pg. 42)  
2.3.1 The Representative Household in a TwoPeriod Model (pg. 42)  
2.3.2 Implications of the Euler Equation for Consumption (pg. 45)  
2.3.3 The Case of a Constant Elasticity of Intertemporal Substitution (pg. 46)  
2.3.4 Firms, Technology, and the Optimal Output Path (pg. 48)  
2.3.5 General Equilibrium in the TwoPeriod Model (pg. 49)  
2.3.6 Diagrammatic Exposition of the Intertemporal Equilibrium (pg. 53)  
2.3.7 Implications for Growth and Business Cycle Theory (pg. 55)  
2.4 Consumption and Labor Supply in a OnePeriod Competitive Model (pg. 56)  
2.4.1 The Optimal Choice of Consumption and Labor Supply (pg. 56)  
2.4.2 Income and Substitution Effects on Labor Supply (pg. 58)  
2.4.3 The Frisch Elasticity of Labor Supply (pg. 60)  
2.4.4 The Production Function and the Optimal Decisions of Firms (pg. 61)  
2.4.5 General Equilibrium and the Determination of Output and Employment (pg. 61)  
2.5 Consumption and Labor Supply in a TwoPeriod Competitive Model (pg. 62)  
2.5.1 Optimal Consumption and Labor Supply in a TwoPeriod Model (pg. 63)  
2.5.2 Intertemporal Substitution in Consumption and Labor Supply (pg. 64)  
2.5.3 Optimal Production Decisions of Firms (pg. 65)  
2.5.4 General Equilibrium and the Determination of Output and Employment (pg. 66)  
2.5.5 Implications for Business Cycle Theory (pg. 68)  
2.6 Money, Prices, and Inflation in a TwoPeriod Competitive Model (pg. 69)  
2.6.1 The Representative Household and the Demand for Money (pg. 69)  
2.6.2 The Classical Dichotomy and the Neutrality of Money (pg. 71)  
2.6.3 The TwoPeriod Competitive Model and Classical Monetary Theory (pg. 74)  
2.7 Fiscal Policy in a TwoPeriod Competitive Model (pg. 74)  
2.7.1 Government Expenditure and Taxes in a OnePeriod Economy (pg. 74)  
2.7.2 Income Taxes and Labor Supply (pg. 76)  
2.7.3 Government Expenditure, Taxes, and Debt in a TwoPeriod Economy (pg. 77)  
2.7.4 Ricardian Equivalence between Tax and Debt Finance (pg. 78)  
2.7.5 Income Taxation and Aggregate Savings and Investment (pg. 81)  
2.7.6 Implications for Fiscal Policy and Government Debt (pg. 81)  
2.8 The Treatment of Time and the Intertemporal Approach (pg. 82)  
2.9 Conclusion (pg. 84)  
3. Savings, Investment, and Economic Growth (pg. 85)  
3.1 The Solow Growth Model (pg. 87)  
3.1.1 The Neoclassical Production Function (pg. 87)  
3.1.2 The CobbDouglas Production Function (pg. 89)  
3.1.3 Population Growth and Technical Progress (pg. 90)  
3.1.4 Savings, Capital Accumulation, and Economic Growth (pg. 90)  
3.1.5 The Balanced Growth Path and the Convergence Process (pg. 92)  
3.1.6 The Rate of Growth of Capital and Output (pg. 93)  
3.1.7 Significance of the Inada Conditions (pg. 95)  
3.2 Competitive Markets, the Real Interest Rate, and Real Wages (pg. 96)  
3.3 The Savings Rate and the Golden Rule (pg. 97)  
3.3.1 The Savings Rate and the Balanced Growth Path (pg. 98)  
3.3.2 The Savings Rate, the Golden Rule, and Dynamic Inefficiency (pg. 99)  
3.3.3 The Elasticity of Steady State Output with Respect to the Savings Rate (pg. 101)  
3.4 Total Factor Productivity and Population Growth (pg. 102)  
3.4.1 Dynamic Effects of Total Factor Productivity in the Solow Model (pg. 103)  
3.4.2 Dynamic Effects of Population Growth in the Solow Model (pg. 104)  
3.5 Speed of Convergence toward the Balanced Growth Path (pg. 104)  
3.6 The Process of Economic Growth and the Solow Model (pg. 106)  
3.6.1 The Kaldor Stylized Facts of Economic Growth (pg. 107)  
3.6.2 Differences in Per Capita Output and Income between Developed and Less Developed Economies (pg. 108)  
3.6.3 Conditional Convergence (pg. 110)  
3.7 Convergence with a CobbDouglas Production Function (pg. 110)  
3.8 Dynamic Simulations of a Calibrated Solow Model (pg. 111)  
3.8.1 The Solow Model in Discrete Time (pg. 112)  
3.8.2 The Calibrated Solow Model (pg. 113)  
3.8.3 Dynamic Simulations of the Model (pg. 114)  
3.9 Conclusion (pg. 117)  
4. The Representative Household Model of Optimal Growth (pg. 119)  
4.1 The Optimal Intertemporal Path of Consumption (pg. 121)  
4.2 The Ramsey Model of Economic Growth (pg. 124)  
4.2.1 The Production Function (pg. 124)  
4.2.2 The Utility Function of the Representative Household (pg. 125)  
4.2.3 The Accumulation of Capital and the Optimality of the Decentralized Competitive Equilibrium (pg. 126)  
4.2.4 Conditions for Utility Maximization by the Representative Household (pg. 128)  
4.2.5 The Euler Equation for Consumption (pg. 129)  
4.2.6 The Intertemporal Budget Constraint of the Representative Household (pg. 130)  
4.2.7 The Transversality Condition with an Infinite Time Horizon (pg. 132)  
4.2.8 The Consumption Function of the Representative Householdwith an Infinite Horizon (pg. 133)  
4.3 Dynamic Adjustment and the Balanced Growth Path (pg. 135)  
4.3.1 Dynamic Adjustment toward the Balanced Growth Path (pg. 135)  
4.3.2 The Balanced Growth Path and the Modified Golden Rule (pg. 138)  
4.3.3 Effects of a Permanent Increase in the Pure Rate of Time Preference (pg. 139)  
4.3.4 Effects of a Permanent Increase in Total Factor Productivity (pg. 141)  
4.3.5 Effects of a Permanent Increase in the Rate of Growth of Population (pg. 142)  
4.4 Properties of the Adjustment Path and the Speed of Convergence (pg. 143)  
4.5 Dynamic Simulations of a Calibrated Ramsey Model (pg. 146)  
4.5.1 The Ramsey Model in Discrete Time (pg. 146)  
4.5.2 The Calibrated Ramsey Model (pg. 148)  
4.5.3 Dynamic Simulations of the Model (pg. 149)  
4.6 Conclusion (pg. 152)  
5. Overlapping Generations Models of Growth (pg. 153)  
5.1 The Diamond Model (pg. 154)  
5.1.1 Definitions (pg. 155)  
5.1.2 The Production Function (pg. 155)  
5.1.3 The Intertemporal Utility Function of Households (pg. 155)  
5.1.4 Markets and the Behavior of Households (pg. 156)  
5.1.5 Capital Accumulation and the Dynamic Adjustment of the Economy (pg. 157)  
5.1.6 A Simplified Diamond Model with Logarithmic Preferences and CobbDouglas Technology (pg. 159)  
5.1.7 The Speed of Adjustment in the Simplified Diamond Model (pg. 163)  
5.1.8 Welfare Implications of the Diamond Model and the Possibility of Dynamic Inefficiency (pg. 164)  
5.1.9 Dynamic Simulations of a Calibrated Diamond Model (pg. 165)  
5.2 The BlanchardWeil Model (pg. 169)  
5.2.1 Definitions (pg. 169)  
5.2.2 The Production Function (pg. 170)  
5.2.3 The Intertemporal Utility Function of Households and Household Consumption (pg. 170)  
5.2.4 Aggregation across Generations (pg. 172)  
5.2.5 The Model in Terms of Efficiency Units of Labor (pg. 173)  
5.2.6 The Balanced Growth Path and the Adjustment Path (pg. 173)  
5.3 Dynamic Simulations of a Calibrated BlanchardWeil Model (pg. 177)  
5.3.1 The BlanchardWeil Model in Discrete Time (pg. 178)  
5.3.2 Dynamic Simulations of the Model (pg. 178)  
5.4 Conclusion (pg. 182)  
6. Fiscal Policy and Economic Growth (pg. 183)  
6.1 The Government Budget Constraint (pg. 185)  
6.1.1 Government Deficits, Debt, and Solvency (pg. 185)  
6.2 Ricardian Equivalence and the Ramsey Model (pg. 187)  
6.2.1 Ricardian Equivalence between Government Debt and Taxes (pg. 187)  
6.2.2 Government Expenditure, Taxes, and Debt in the Ramsey Model (pg. 188)  
6.3 Dynamic Effects of Fiscal Policy in the BlanchardWeil Model (pg. 191)  
6.3.1 The BlanchardWeil Model with Government Expenditure and Debt (pg. 191)  
6.3.2 Government Debt, Taxes, and Redistribution across Generations (pg. 192)  
6.3.3 Dynamic Simulations of Fiscal Policy in a Calibrated BlanchardWeil Model (pg. 194)  
6.4 Dynamic Effects of Distortionary Taxation (pg. 201)  
6.4.1 Distortionary and Nondistortionary Taxes (pg. 201)  
6.4.2 Dynamic Effects of Capital Income and Business Gross Profits Taxation (pg. 203)  
6.4.3 Dynamic Simulations of Increases in Capital Income and Business Gross Profits Taxation (pg. 205)  
6.5 Conclusion (pg. 206)  
7. Money, Inflation, and Economic Growth (pg. 209)  
7.1 Private Consumption and Money Demand in a Representative Household Model (pg. 211)  
7.1.1 Money in the Utility Function of Households (pg. 211)  
7.1.2 Nominal and Real Interest Rates and the Opportunity Cost of Real Money Balances (pg. 212)  
7.1.3 FirstOrder Conditions for an Optimum (pg. 212)  
7.1.4 The Money Demand Function (pg. 213)  
7.1.5 Growth Rate of the Money Supply and Inflation (pg. 214)  
7.1.6 The Euler Equation for Consumption (pg. 215)  
7.2 Aggregate Capital Accumulation in a Ramsey Model with Money (pg. 216)  
7.2.1 The Production Function, the Real Interest Rate, and the Real Wage (pg. 216)  
7.2.2 The Inflation Tax and the Accumulation of Capital (pg. 216)  
7.3 Effects of the Growth Rate of the Money Supply in the Ramsey Monetary Model (pg. 218)  
7.3.1 The Balanced Growth Path in the Ramsey Model with Money (pg. 219)  
7.3.2 The Superneutrality of Money and Inflation (pg. 220)  
7.3.3 The Welfare Costs of Inflation in a Ramsey Model (pg. 221)  
7.4 Effects of Monetary Growth in an OLG Model (pg. 222)  
7.4.1 The BlanchardWeil Model with Money (pg. 223)  
7.4.2 Real Effects of the Growth Rate of the Money Supply (pg. 224)  
7.4.3 A Dynamic Simulation of the Effects of a Rise in the Growth Rate of the Money Supply in a Calibrated BlanchardWeil Model (pg. 227)  
7.5 Conclusion (pg. 229)  
8. Externalities, Human Capital, and Technical Progress (pg. 231)  
8.1 Externalities from Capital Accumulation and Economic Growth (pg. 232)  
8.1.1 Definitions (pg. 233)  
8.1.2 The Production Function (pg. 233)  
8.1.3 Externalities from the Accumulation of Capital (pg. 234)  
8.1.4 Determination of the Real Interest Rate and the Real Wage (pg. 237)  
8.1.5 The Savings Rate and the Endogenous Growth Rate (pg. 238)  
8.1.6 Externalities and Endogenous Growth in the Ramsey Model (pg. 239)  
8.1.7 The Suboptimality of the Competitive Equilibrium with ExternalitiesDue to Capital Accumulation (pg. 241)  
8.1.8 Externalities and Endogenous Growth in the BlanchardWeil Model (pg. 242)  
8.1.9 Fiscal Policy and Endogenous Growth (pg. 245)  
8.1.10 Convergence in Exogenous and Endogenous AK Growth Models (pg. 247)  
8.2 Investment in Human Capital and Economic Growth (pg. 248)  
8.2.1 The Extended Solow Model and the Share of Spending on Educationand Training (pg. 249)  
8.2.2 The Balanced Growth Path in the Extended Solow Model (pg. 250)  
8.2.3 Endogenous Growth in the Extended Solow Model (pg. 251)  
8.2.4 The Jones Model of Human Capital Accumulation (pg. 252)  
8.2.5 The Lucas Model of Human Capital Accumulation and Endogenous Growth (pg. 253)  
8.2.6 A Detailed Analysis of the Lucas Model (pg. 254)  
8.3 Ideas, Innovations, and Technical Progress (pg. 258)  
8.3.1 Key Features of Ideas and Innovations (pg. 258)  
8.3.2 Key Elements of an IdeasandInnovations Growth Model (pg. 259)  
8.3.3 Endogenous Determination of the Rate of Technical Progress (pg. 261)  
8.3.4 The Balanced Growth Path with Endogenous Technical Progress (pg. 261)  
8.4 Unified Growth Theory and the Transition from Stagnation to Growth (pg. 262)  
8.5 Institutions and LongRun Growth (pg. 263)  
8.6 The New Stylized Facts of Economic Growth (pg. 265)  
8.7 Conclusion (pg. 266)  
9 Dynamic Stochastic Models under Rational Expectations (pg. 269)  
9.1 A Stochastic Expectational Model of a Competitive Market (pg. 271)  
9.1.1 Absence of Uncertainty and Perfect Foresight (pg. 272)  
9.1.2 Uncertainty and Adaptive Expectations (pg. 273)  
9.1.3 The Rational Expectations Hypothesis (pg. 275)  
9.2 Rational Expectations for Linear Autoregressive Processes (pg. 277)  
9.3 FirstOrder Linear Expectational Models (pg. 279)  
9.3.1 The Method of Repeated Substitutions (pg. 279)  
9.3.2 The Method of Factorization (pg. 281)  
9.3.3 The Method of Undetermined Coefficients (pg. 282)  
9.3.4 Two Additional Economic Examples (pg. 282)  
9.3.5 Alternative Assumptions about the Evolution of Exogenous Variables (pg. 284)  
9.3.6 The Expectational Competitive Market Model Revisited (pg. 286)  
9.4 SecondOrder Linear Expectational Models (pg. 286)  
9.4.1 The Method of Factorization (pg. 287)  
9.4.2 The Method of Undetermined Coefficients (pg. 288)  
9.4.3 An Economic Example of a SecondOrder System (pg. 290)  
9.5 Multivariate Linear Models with Rational Expectations (pg. 291)  
9.5.1 The BlanchardKahn Method (pg. 291)  
9.5.2 Other Solution Methods (pg. 293)  
9.5.3 A SecondOrder Example of the BlanchardKahn Method (pg. 293)  
9.6 Rational Expectations and Learning (pg. 295)  
9.7 Conclusion (pg. 295)  
10. Consumption and Portfolio Choice under Uncertainty (pg. 297)  
10.1 Consumption and Portfolio Choice (pg. 298)  
10.1.1 The Random Walk Model of Consumption (pg. 301)  
10.1.2 The Consumption Capital Asset Pricing Model (pg. 302)  
10.2 Full Analysis of Consumption and Portfolio Choice (pg. 303)  
10.2.1 The Case of Logarithmic Preferences (pg. 303)  
10.2.2 Quadratic Preferences and Certainty Equivalence (pg. 305)  
10.2.3 The PermanentIncome Hypothesis with Quadratic Preferences (pg. 306)  
10.2.4 The Consumption CAPM with Quadratic Preferences (pg. 307)  
10.2.5 The Efficient Markets Hypothesis (pg. 308)  
10.3 Precautionary Savings and Borrowing Constraints (pg. 310)  
10.4 Conclusion (pg. 311)  
11. Investment and the Cost of Capital (pg. 313)  
11.1 Optimal Investment with Convex Adjustment Costs (pg. 315)  
11.1.1 The Choice of Optimal Investment (pg. 315)  
11.1.2 The Case of Zero Adjustment Costs (pg. 317)  
11.1.3 The Investment Function with Convex Adjustment Costs (pg. 317)  
11.1.4 The Determinants of q (pg. 317)  
11.1.5 Dynamic Adjustment of q and the Capital Stock K (pg. 318)  
11.2 Optimal Investment under Uncertainty (pg. 320)  
11.2.1 The Value of a Firm under Uncertainty (pg. 321)  
11.2.2 The LucasPrescott Model of Investment under Uncertainty (pg. 323)  
11.2.3 Rational Expectations Equilibrium and Aggregate Investment in the LucasPrescott Model (pg. 325)  
11.3 Conclusion (pg. 327)  
12. Money, Interest, and Prices (pg. 329)  
12.1 The Functions of Money (pg. 331)  
12.2 The Supply of Money and Central Banks (pg. 332)  
12.2.1 Central Banks and Their Functions (pg. 332)  
12.2.2 Central Banks and the Money Supply (pg. 333)  
12.3 The Demand for Money (pg. 336)  
12.4 Nominal Interest Rates and ShortRun Equilibrium in the Money Market (pg. 339)  
12.5 The LongRun Neutrality of Money (pg. 343)  
12.5.1 Monetary Growth, Inflation, and Nominal Interest Rates in the Long Run (pg. 345)  
12.5.2 The Welfare Cost of Inflation (pg. 346)  
12.5.3 The LongRun Neutrality of Money and Monetary Reforms (pg. 346)  
12.6 Money and the Price Level in Dynamic General Equilibrium Models (pg. 347)  
12.6.1 The Samuelson OLG Model (pg. 347)  
12.6.2 Money in the Utility Function of a Representative Household (pg. 351)  
12.6.3 Cash in Advance in a Representative Household Model (pg. 353)  
12.6.4 Cash in Advance in an OLG Model (pg. 355)  
12.7 Nominal and Real Interest Rates and the Money Supply (pg. 357)  
12.7.1 Money in the Utility Function of a Representative Household (pg. 357)  
12.7.2 Cash in Advance in a Representative Household Model (pg. 359)  
12.7.3 Cash in Advance in an OLG Model (pg. 359)  
12.7.4 The Liquidity Effect in Representative Household Models (pg. 360)  
12.8 Interest Rate Pegging and Price Level Indeterminacy (pg. 361)  
12.8.1 Interest Rate Pegging and Price Level Indeterminacy in Representative Household Models (pg. 361)  
12.8.2 The Wicksell Solution to the Problem of Price Level Indeterminacy (pg. 362)  
12.8.3 The Fiscal Theory of the Price Level (pg. 363)  
12.8.4 The Pigou Effect and Price Level Determinacy in OLG Models (pg. 364)  
12.9 Money Growth, Seigniorage, and Inflation (pg. 364)  
12.9.1 Relations between Monetary Growth, Seigniorage, and Inflation (pg. 365)  
12.9.2 The Seigniorage Laffer Curve (pg. 367)  
12.9.3 The Demand for Seigniorage and Equilibrium with High Inflation (pg. 368)  
12.9.4 The Transition to Hyperinflation (pg. 368)  
12.9.5 How Can High Inflation and Hyperinflation Be Tackled? (pg. 371)  
12.10 Conclusion (pg. 372)  
13. The Stochastic Growth Model of Aggregate Fluctuations (pg. 375)  
13.1 The Stochastic Growth Model (pg. 376)  
13.1.1 Extending the Ramsey Model to Account for Aggregate Fluctuations (pg. 377)  
13.1.2 The Representative Firm (pg. 377)  
13.1.3 The Representative Household (pg. 378)  
13.1.4 Exogenous Population Growth, Efficiency of Labor, and Government Expenditure (pg. 378)  
13.1.5 Labor Supply of the Representative Household (pg. 380)  
13.1.6 Intertemporal Substitution in Labor Supply (pg. 381)  
13.1.7 Uncertainty and the Behavior of the Representative Household (pg. 382)  
13.2 A Simplified Version of the Stochastic Growth Model (pg. 383)  
13.2.1 Fluctuations of Output in the Simplified Stochastic Growth Model (pg. 384)  
13.2.2 The Simplified Stochastic Growth Model and the Evidence on Aggregate Fluctuations (pg. 385)  
13.3 A LogLinear Approximation to the General Stochastic Growth Model (pg. 386)  
13.3.1 The Steady State (pg. 387)  
13.3.2 LogLinearizing the Model around the Steady State (pg. 388)  
13.4 Solving the LogLinear Stochastic Growth Model (pg. 390)  
13.4.1 Aggregate Fluctuations around the Steady State (pg. 391)  
13.4.2 A Dynamic Simulation of the LogLinear Stochastic Growth Model (pg. 391)  
13.5 Conclusion (pg. 393)  
14. Perfectly Competitive Models with Flexible Prices (pg. 395)  
14.1 A Perfectly Competitive Model without Capital (pg. 396)  
14.1.1 The Representative Household (pg. 396)  
14.1.2 The Representative Firm (pg. 397)  
14.1.3 General Equilibrium (pg. 398)  
14.2 Monetary Factors in a Perfectly Competitive Model (pg. 400)  
14.2.1 An Exogenous Path for the Money Supply (pg. 400)  
14.2.2 An Exogenous Path for the Nominal Interest Rate (pg. 401)  
14.2.3 An InflationBased Nominal Interest Rate Rule (pg. 401)  
14.2.4 Optimal Monetary Policy (pg. 402)  
14.3 Imperfect Information and the Nonneutrality of Money (pg. 403)  
14.3.1 Competitive Equilibrium under Imperfect Information about the Price Level (pg. 403)  
14.3.2 The Determination of Output and Employment (pg. 406)  
14.3.3 The Real Effects of Monetary Shocks in a Rational Expectations Equilibrium (pg. 407)  
14.3.4 Optimal Monetary Policy in the Lucas Model (pg. 410)  
14.3.5 The New Classical Model and the Great Depression (pg. 410)  
14.3.6 Models of Informational Frictions and Rational Inattention (pg. 411)  
14.4 Conclusion (pg. 411)  
15. Keynesian Models and the Phillips Curve (pg. 413)  
15.1 The Original Keynesian Models (pg. 415)  
15.1.1 The Keynesian Cross (pg. 416)  
15.1.2 The ISLM Model (pg. 419)  
15.1.3 The ADAS Model (pg. 422)  
15.1.4 The Impact of Aggregate Demand Policies (pg. 424)  
15.2 The Samuelson Multiplier Accelerator Model (pg. 427)  
15.3 The Theory of Discretionary Monetary and Fiscal Policy (pg. 429)  
15.3.1 The TinbergenTheil Theory of Discretionary Aggregate Demand Policies (pg. 431)  
15.3.2 Monetary and Fiscal Policy with a Full Employment Target (pg. 431)  
15.3.3 Monetary and Fiscal Policy with a Full Employment Target and a Price Level Target (pg. 432)  
15.4 The Phillips Curve and Inflationary Expectations (pg. 435)  
15.4.1 The Phillips Curve and the Tradeoff between Inflation and Unemployment (pg. 435)  
15.4.2 Instability of the Phillips Curve and Inflationary Expectations (pg. 437)  
15.5 The Natural Rate of Unemployment and Aggregate Demand Policies (pg. 439)  
15.5.1 The Path of Inflation and Unemployment under Adaptive Expectations (pg. 440)  
15.5.2 Rules versus Discretion in Aggregate Demand Policy (pg. 444)  
15.5.3 Inflation and Unemployment under Rational Expectations (pg. 446)  
15.6 Conclusion (pg. 447)  
16. A Model of Imperfect Competition and Staggered Pricing (pg. 449)  
16.1 An Imperfectly Competitive Model of Aggregate Fluctuations (pg. 451)  
16.1.1 The Representative Household (pg. 452)  
16.1.2 The Representative Firm and Optimal Pricing (pg. 454)  
16.1.3 Full Price Flexibility and the Natural Rate (pg. 455)  
16.1.4 Inefficiency of the Natural Rate (pg. 456)  
16.2 Staggered Price Adjustment and Aggregate Fluctuations (pg. 457)  
16.2.1 Optimal Pricing with Staggered Price Adjustment (pg. 459)  
16.2.2 Equilibrium in the Market for Goods and Services and the New Keynesian IS Curve (pg. 461)  
16.2.3 Labor Market Equilibrium and the New Keynesian Phillips Curve (pg. 462)  
16.2.4 The Imperfectly Competitive Model with Staggered Pricing and the Taylor Rule (pg. 463)  
16.2.5 Real and Monetary Shocks and Aggregate Fluctuations (pg. 464)  
16.2.6 The Divine Coincidence and Optimal Monetary Policy in the New Keynesian Model with Staggered Pricing (pg. 468)  
16.2.7 A Dynamic Simulation of the Model (pg. 469)  
16.3 The Rotemberg Model of Convex Costs of Price Adjustment (pg. 470)  
16.4 Conclusion (pg. 473)  
17. A Model of Unemployment and Nominal Wage Contracts (pg. 475)  
17.1 Alternative Views of the Labor Market and Equilibrium Unemployment (pg. 477)  
17.2 Households and Optimal Consumption and Money Demand (pg. 478)  
17.3 Firms and Optimal Pricing and Production (pg. 481)  
17.4 Wage Setting and Employment in a Model with Insiders and Outsiders (pg. 483)  
17.4.1 Wage Determination, Unemployment Persistence, and the Phillips Curve (pg. 485)  
17.4.2 The Relation between Output and Unemployment Persistence (pg. 487)  
17.4.3 The Phillips Curve in Terms of Deviations of Output from Its Natural Rate (pg. 488)  
17.5 The Implications of Staggered Pricing (pg. 489)  
17.5.1 Optimal Pricing with Staggered Price Adjustment (pg. 490)  
17.5.2 Inflation and Unit Labor Costs under Staggered Pricing (pg. 491)  
17.6 An Extended New Keynesian Phillips Curve: Combining Staggered Pricing with Periodic Nominal Wage Contracts (pg. 492)  
17.7 Inflation and Aggregate Fluctuations under a Taylor Rule (pg. 494)  
17.7.1 New Neoclassical Synthesis ISLM Functions (pg. 494)  
17.7.2 The Natural and Equilibrium Real Interest Rate (pg. 494)  
17.7.3 Equilibrium Fluctuations with Exogenous Preference and Productivity Shocks (pg. 495)  
17.7.4 Does Staggered Pricing Matter for Inflation Persistence? (pg. 500)  
17.7.5 Inflation Stabilization and the Divine Coincidence (pg. 501)  
17.8 The Optimal Taylor Rule (pg. 502)  
17.8.1 Optimal Inflation Policy (pg. 502)  
17.9 A Dynamic Simulation of the Effects of Monetary and Real Shocks (pg. 504)  
17.10 Conclusion (pg. 506)  
18. Matching Frictions and Equilibrium Unemployment (pg. 509)  
18.1 The Matching Function (pg. 510)  
18.1.1 The Probability of Filling a Vacancy and Labor Market Tightness (pg. 511)  
18.1.2 The Probability of the Unemployed Finding a Job (pg. 511)  
18.2 Flows into and out of Employment, Equilibrium Unemployment,and the Beveridge Curve (pg. 512)  
18.3 Firms and the Creation of Vacancies (pg. 513)  
18.3.1 The Present Value of Net Expected Profits from an Existing Job (pg. 514)  
18.3.2 The Present Value of Net Expected Profits from a Vacancy and the Creation of Vacancies (pg. 515)  
18.3.3 Free Entry and the Job Creation Condition (pg. 516)  
18.4 The Behavior of Unemployed Job Seekers (pg. 517)  
18.4.1 The Permanent Income of an Unemployed Job Seeker (pg. 518)  
18.4.2 The Permanent Income of an Employed Worker (pg. 518)  
18.4.3 Comparing the Permanent Income of the Employed and the Unemployed (pg. 518)  
18.5 Wage Bargaining and the Wage Equation (pg. 519)  
18.6 Wage Determination and Equilibrium Unemployment (pg. 521)  
18.7 Determinants of Equilibrium Unemployment, Real Wages, and Labor Market Tightness (pg. 523)  
18.7.1 An Increase in Labor Productivity (pg. 523)  
18.7.2 An Increase in Unemployment Benefits (pg. 525)  
18.7.3 An Increase in the Real Interest Rate (pg. 527)  
18.7.4 An Increase in the Probability of Job Destruction (pg. 527)  
18.8 Dynamic Adjustment to the Steady State (pg. 527)  
18.8.1 The Dynamic Adjustment of Unemployment and Vacancies (pg. 530)  
18.8.2 Numerical Simulations of the Model (pg. 532)  
18.9 Matching Models and Nominal Rigidities (pg. 534)  
18.10 Conclusion (pg. 535)  
19. The Macroeconomic Implications of Financial Frictions (pg. 539)  
19.1 The Role of Finance and Financial Markets (pg. 539)  
19.1.1 Financial Frictions and Financial Intermediation (pg. 541)  
19.1.2 The Risks of Financial Intermediation, Leverage, and the External Finance Premium (pg. 542)  
19.1.3 The Links between the Financial Sector and Real Activity in the Presence of Frictions (pg. 543)  
19.2 Financial Frictions in a New Keynesian Model with Staggered Pricing (pg. 544)  
19.3 Financial Frictions in a Model with Unemployment Persistenceand Nominal Wage Contracts (pg. 546)  
19.4 Conclusion (pg. 548)  
20. The Role of Monetary Policy (pg. 551)  
20.1 Rules versus Discretion in Monetary Policy (pg. 552)  
20.2 Rules, Discretion, and Credibility in a New Keynesian Model (pg. 554)  
20.2.1 The Social Welfare Loss from Inflation and Unemployment (pg. 555)  
20.2.2 Monetary Policy under Discretion: The Problem of Credibility (pg. 556)  
20.2.3 Monetary Policy under a Fixed Inflation Rule (pg. 559)  
20.2.4 Central Bank Constitutions (pg. 559)  
20.2.5 Reputation as a Solution to the Problem of Inflationary Bias (pg. 560)  
20.3 Optimal Monetary Policy in the Presence of Stochastic Shocks (pg. 562)  
20.4 The Mechanics of Monetary Policy (pg. 564)  
20.4.1 Financial Markets and Open Market Operations (pg. 565)  
20.4.2 The Term Structure of Interest Rates (pg. 566)  
20.5 Optimal Monetary Policy and the Taylor Rule (pg. 567)  
20.6 Monetary Policy Shocks and the Optimal Policy Rule (pg. 569)  
20.7 Monetary Policy, Financial Frictions, and the Zero Lower Bound onInterest Rates (pg. 571)  
20.7.1 The Liquidity Trap (pg. 572)  
20.7.2 Monetary Policy at the Zero Lower Bound (pg. 573)  
20.7.3 The Zero Lower Bound and Unconventional Monetary Policy (pg. 574)  
20.8 Conclusion (pg. 576)  
21. Fiscal Policy and Government Debt (pg. 579)  
21.1 Tax Smoothing and Government Debt Accumulation (pg. 581)  
21.1.1 The Barro TaxSmoothing Model (pg. 581)  
21.1.2 Steady State Implications of Tax Smoothing (pg. 583)  
21.2 Keynesian Stabilization Policy, Automatic Stabilizers, and Fiscal Implicationsof the Zero Lower Bound (pg. 585)  
21.3 Optimal Dynamic Ramsey Taxation (pg. 586)  
21.4 Fiscal Policy and Politics (pg. 589)  
21.4.1 Distributional Considerations and Politics (pg. 589)  
21.4.2 Electoral Factors and Partisan Differences (pg. 590)  
21.5 The Burden of High Government Deficits and Debt (pg. 592)  
21.6 A Model of Government Debt Crises (pg. 593)  
21.6.1 The Calvo Model (pg. 593)  
21.6.2 Multiple Equilibria and SelfFulfilling Prophecies (pg. 598)  
21.7 Conclusion (pg. 600)  
22. Bubbles, Multiple Equilibria, and Sunspots (pg. 601)  
22.1 Bubbles in Linear Rational Expectations Models (pg. 602)  
22.1.1 Bubbles versus Fundamentals (pg. 603)  
22.1.2 Deterministic versus Stochastic Bubbles (pg. 604)  
22.1.3 Bubbles as SelfFulfilling Prophecies in Inherently Unstable Models (pg. 605)  
22.1.4 HigherOrder Linear Models (pg. 607)  
22.2 Bubbles in Models of Stock and Money Markets (pg. 607)  
22.2.1 Stock Market Bubbles (pg. 607)  
22.2.2 Money Market Bubbles, the Price Level, and Inflation (pg. 609)  
22.3 Ruling Out Unstable Bubbles (pg. 611)  
22.4 Indeterminacy, SelfFulfilling Prophecies, and Sunspots (pg. 612)  
22.4.1 The Samuelson OLG Model with Money, Revisited (pg. 614)  
22.4.2 Other Models of Indeterminacy and Sunspots in Macroeconomics (pg. 619)  
22.5 Conclusion (pg. 620)  
23. The Interaction of Events and Ideas in Dynamic Macroeconomics (pg. 623)  
23.1 The Financial Crisis and Recent Developments in Dynamic Macroeconomics (pg. 624)  
23.2 The Interaction of Events and Ideas and the Role of Empirical Macroeconomics (pg. 626)  
23.3 Policy Evaluation and DSGE Models (pg. 628)  
23.4 Conclusion (pg. 629)  
Appendixes (pg. 631)  
A. Variables, Functions, and Optimization (pg. 633)  
A.1 Models, Variables, and Functions (pg. 633)  
A.2 Mathematical Optimization under Constraints (pg. 644)  
A.3 Some Useful Functional Forms (pg. 651)  
B. Linear Models and Linear Algebra (pg. 659)  
B.1 Linear Models (pg. 659)  
B.2 Elements of Linear Algebra (pg. 660)  
B.3 An Example with Two Endogenous Variables (pg. 663)  
C. Ordinary Differential Equations (pg. 667)  
C.1 Definitions (pg. 667)  
C.2 FirstOrder Linear Differential Equations (pg. 669)  
C.3 SecondOrder Linear Differential Equations (pg. 673)  
C.4 A Pair of FirstOrder Linear Differential Equations (pg. 675)  
C.5 A System of n FirstOrder Linear Differential Equations (pg. 678)  
D. Difference Equations (pg. 683)  
D.1 Lag Operators and Difference Equations (pg. 683)  
D.2 FirstOrder Linear Difference Equations (pg. 686)  
D.3 SecondOrder Linear Difference Equations (pg. 687)  
D.4 A Pair of FirstOrder Linear Difference Equations (pg. 689)  
D.5 A System of n FirstOrder Linear Difference Equations (pg. 690)  
E. Methods of Intertemporal Optimization (pg. 693)  
E.1 The Form of Dynamic Optimization Problems (pg. 693)  
E.2 The Method of Optimal Control (pg. 694)  
E.3 The Optimal Control Method in Continuous Time (pg. 696)  
E.4 Dynamic Programming and the Bellman Equation (pg. 697)  
E.5 An Example Based on Optimal Savings in Continuous Time (pg. 700)  
F. Random Variables and Stochastic Processes (pg. 703)  
F.1 Probability (pg. 703)  
F.2 Random Variables and Probability Distributions (pg. 704)  
F.3 Stochastic Processes (pg. 715)  
F.4 Univariate Linear Stochastic Processes in Discrete Time (pg. 716)  
F.5 Vector Stochastic Processes and Vector Autoregressions (pg. 720)  
References (pg. 723)  
Index (pg. 743) 
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