Quantitative Macroeconomics: An Introduction

Dirk Krueger1
Professor of Macroeconomics
Johann Wolfgang Goethe-University Frankfurt am Main
Mertonstr. 17, PF 81
60054 Frankfurt am Main
Germany
http://www.wiwi.uni-frankfurt.de/professoren/krueger/
April 1, 2005

Contents

I Motivation and Data 1
1 Introduction 3
1.1 The Questions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.2 The Approach and the Structure of the Book . . . . . . . . . . . 3
2 Basic Business Cycle Facts 5
2.1 Decomposition of Growth Trend and Business Cycles . . . . . . . 5
2.2 Basic Facts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
II The Real Business Cycle (RBC) Model and Its Extensions
17
3 Set-Up of the Basic Model 21
3.1 Households . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
3.2 Firms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
3.3 Aggregate Resource Constraint . . . . . . . . . . . . . . . . . . . 27
3.4 Competitive Equilibrium . . . . . . . . . . . . . . . . . . . . . . . 27
3.5 Characterization of Equilibrium . . . . . . . . . . . . . . . . . . . 30
4 Social Planner Problem and Competitive Equilibrium 33
4.1 The Social Planner Problem . . . . . . . . . . . . . . . . . . . . . 33
4.2 Characterization of Solution . . . . . . . . . . . . . . . . . . . . . 34
4.3 The Welfare Theorems . . . . . . . . . . . . . . . . . . . . . . . . 35
4.4 Appendix: More Rigorous Math . . . . . . . . . . . . . . . . . . 36
5 Steady State Analysis 39
5.1 Characterization of the Steady State . . . . . . . . . . . . . . . . 39
5.2 Golden Rule and Modi…ed Golden Rule . . . . . . . . . . . . . . 40
6 Dynamic Analysis 43
6.1 An Example with Analytical Solution . . . . . . . . . . . . . . . 44
6.2 Linearization of the Euler Equation . . . . . . . . . . . . . . . . . 47
6.2.1 Preliminaries . . . . . . . . . . . . . . . . . . . . . . . . . 47
6.2.2 Doing the Linearization . . . . . . . . . . . . . . . . . . . 48
6.3 Analysis of the Results . . . . . . . . . . . . . . . . . . . . . . . . 54
6.3.1 Plotting the Policy Function . . . . . . . . . . . . . . . . 54
6.3.2 Impulse Response Functions . . . . . . . . . . . . . . . . . 54
6.3.3 Simulations . . . . . . . . . . . . . . . . . . . . . . . . . . 54
6.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56
7 A Note on Economic Growth 57
7.1 Preliminary Assumptions and De…nitions . . . . . . . . . . . . . 57
7.2 Reformulation of Problem in E¢ciency Units . . . . . . . . . . . 58
7.3 Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60
7.4 The Balanced Growth Path . . . . . . . . . . . . . . . . . . . . . 60
8 Calibration 63
8.1 Long Run Growth Rates . . . . . . . . . . . . . . . . . . . . . . . 63
8.2 Capital and Labor Share . . . . . . . . . . . . . . . . . . . . . . . 64
8.3 The Depreciation Rate . . . . . . . . . . . . . . . . . . . . . . . . 64
8.4 The Technology Constant A . . . . . . . . . . . . . . . . . . . . . 65
8.5 Preference Parameters . . . . . . . . . . . . . . . . . . . . . . . . 65
8.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66
9 Adding Labor Supply 67
9.1 The Modi…ed Social Planner Problem . . . . . . . . . . . . . . . 67
9.2 Labor Lotteries . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68
9.3 Analyzing the Model with Labor . . . . . . . . . . . . . . . . . . 69
9.4 A Note on Calibration . . . . . . . . . . . . . . . . . . . . . . . . 72
9.5 Intertemporal Substitution of Labor Supply: A Simple Example 73
9.6 A Remark on Decentralization . . . . . . . . . . . . . . . . . . . 74
10 Stochastic Technology Shocks: The Full RBC Model 77
10.1 The Basic Idea . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77
10.2 Specifying a Process for Technology Shocks . . . . . . . . . . . . 78
10.3 Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80
10.4 What are these Technology Shocks and How to Measure Them? . 82
III Evaluating the Model 85
11 Technology Shocks and Business Cycles 89
11.1 Impulse Response Functions . . . . . . . . . . . . . . . . . . . . . 89
11.2 Comparing Business Cycle Statistics of Model and Data . . . . . 92
11.3 Counterfactual Experiments . . . . . . . . . . . . . . . . . . . . . 94
IV Welfare and Policy Questions 95
12 The Cost of Business Cycles 99