Macroeconomic Theory
Dirk Krueger1
Department of Economics
University of Pennsylvania
January1,2015
1I am grateful to my teachers in Minnesota,V.V Chari,Timothy Kehoe and Ed-ward Prescott,my ex-colleagues at Stanford,Robert Hall,Beatrix Paal and Tom Sargent,my colleagues at UPenn Hal Cole,Jeremy Greenwood,Randy Wright and Iourii Manovski and my co-authors Juan Carlos Conesa,Jesus Fernandez-Villaverde, Felix Kubler and Fabrizio Perri as well as Victor Rios-Rull for helping me to learn and teach modern macroeconomic theory.The notes were tried out on numerous students at Stanford,UPenn,Frankfurt and Mannheim,who many uful comments I appreciate.Alexander Bick,Kaiji Chen,Antonio Doblas-Madrid and Weilong Zhang provided many important corrections to the notes.
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Contents
1Overview and Summary1 2A Simple Dynamic Economy5
2.1General Principles for Specifying a Model (5)
2.2An Example Economy (6)
内眼角疼2.ition of Competitive Equilibrium.. (8)
2.2.2Solving for the Equilibrium (9)
2.2.3Pareto Optimality and the First Welfare Theorem (11)
2.2.4Negishi’s(1960)Method to Compute Equilibria (14)
2.2.5Sequential Markets Equilibrium (19)
2.3Appendix:Some Facts about Utility Functions (26)
2.3.1Time Separability (26)
2.3.2Time Discounting (27)
2.3.3Standard Properties of the Period Utility Function (27)
2.3.4Constant Relative Risk Aversion(CRRA)Utility (27)
2.3.5Homotheticity and Balanced Growth (30)
3The Neoclassical Growth Model in Discrete Time33
3.1Setup of the Model (33)
3.2Optimal Growth:Pareto Optimal Allocations (34)
3.2.1Social Planner Problem in Sequential Formulation (35)
3.2.2Recursive Formulation of Social Planner Problem (37)
3.2.3An Example (39)
3.2.4The Euler Equation Approach and Transversality Condi-
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3.2.5Steady States and d Golden Rule. (55)
3.2.6A Remark About Balanced Growth (56)
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3.3Competitive Equilibrium Growth (58)
3d显示器3.ition of Competitive Equilibrium.. (59)
3.3.2Characterization of the Competitive Equilibrium and the
Welfare Theorems (61)
3.3.3Sequential Markets Equilibrium (67)
3.3.4Recursive Competitive Equilibrium (68)
3.4Mapping the Model to Data:Calibration (70)
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iv CONTENTS 4Mathematical Preliminaries75
4.1Complete Metric Spaces (76)
4.2Convergence of Sequences (77)
4.3The Contraction Mapping Theorem (81)
4.4The Theorem of the Maximum (87)
5Dynamic Programming89
5.1The Principle of Optimality (89)
5.2Dynamic Programming with Bounded Returns (96)tmp是什么文件
6Models with Risk99
6.1Basic Reprentation of Risk (99)
itions of Equilibrium. (101)
6.2.1Arrow-Debreu Market Structure (102)
6.2.2Pareto E¢ciency (104)
6.2.3Sequential Markets Market Structure (105)
商铺出租广告6.2.4Equivalence between Market Structures (106)
6.2.5Ast Pricing (106)
6.3Markov Process (108)
6.4Stochastic Neoclassical Growth Model (110)
6.4.1Social Planner Problem in Recursive Formulation (111)
6.4.2Recursive Competitive Equilibrium (112)
7The Two Welfare Theorems115
7.1What is an Economy? (115)
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7.2Dual Spaces (118)
ition of Competitive Equilibrium (120)
7.4The Neoclassical Growth Model in Arrow-Debreu Language (121)
7.5A Pure Exchange Economy in Arrow-Debreu Language (123)
7.6The First Welfare Theorem (125)
7.7The Second Welfare Theorem (126)
7.8Type Identical Allocations (134)
8The Overlapping Generations Model135
8.1A Simple Pure Exchange Overlapping Generations Model (136)
8.1.1Basic Setup of the Model (137)
8.1.2Analysis of the Model Using O¤er Curves (142)
8.1.3Ine¢cient Equilibria (149)
8.1.4Positive Valuation of Outside Money (154)
8.1.5Productive Outside Asts (156)
8.1.6Endogenous Cycles (158)
8.1.7Social Security and Population Growth (160)
8.2The Ricardian Equivalence Hypothesis (165)
8.ite Lifetime Horizon and Borrowing Constraints (166)
8.2.2Finite Horizon and Operative Bequest Motives (175)
8.3Overlapping Generations Models with Production (180)
CONTENTS v
8.3.1Basic Setup of the Model (181)
8.3.2Competitive Equilibrium (181)
8.3.3Optimality of Allocations (188)
8.3.4The Long-Run E¤ects of Government Debt (192)
9Continuous Time Growth Theory197
9.1Stylized Growth and Development Facts (197)
9.1.1Kaldor’s Growth Facts (198)
9.1.2Development Facts from the Summers-Heston Data Set.198
9.2The Solow Model and its Empirical Evaluation (203)
9.2.1The Model and its Implications (206)
9.2.2Empirical Evaluation of the Model (208)
9.3The Ramy-Cass-Koopmans Model (218)
9.3.1Mathematical Preliminaries:Pontryagin’s Maximum Prin-
活着的观后感ciple (219)
9.3.2Setup of the Model (219)
9.3.3Social Planners Problem (221)
9.3.4Decentralization (229)
9.4Endogenous Growth Models (234)
9.4.1The Basic AK-Model (235)
9.4.2Models with Externalities (239)
9.4.3Models of Technological Progress Bad on Monopolistic
Competition:Variant of Romer(1990) (251)
10References263
vi CONTENTS
