Monetary Policy
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Abstract/Syllabus:
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Monetary Policy
Paul S¨oderlind
October 2003
1University of St. Gallen and CEPR. Address: s/bf-HSG, Rosenbergstrasse 52, CH-9000 St.
Gallen, Switzerland. E-mail: Paul.Soderlind@unisg.ch. Document name: MonAll.TeX.
Contents
1 Traditional Models of Monetary Policy 4
1.1 The IS-LM Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
1.2 The Barro-Gordon Model . . . . . . . . . . . . . . . . . . . . . . . . 7
2 Microfoundations of Monetary Policy Models 14
2.1 Money Demand . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
2.2 The Effect of Money vs the Effect of Price Stickiness . . . . . . . . . 18
2.3 Dynamic Models of Sticky Prices . . . . . . . . . . . . . . . . . . . 21
2.4 Aggregate Demand . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
2.5 Recent Models for Studying Monetary Policy . . . . . . . . . . . . . 28
3 Looking into Some Recent Models of Monetary Policy 36
3.1 A Baseline Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
3.2 Model Extension 1: Predetermined Prices . . . . . . . . . . . . . . . 43
3.3 Model Extension 2: More Output Dynamics . . . . . . . . . . . . . . 46
3.4 Appendix: Derivation of the Aggregate Demand Equation . . . . . . . 48
4 Solving Linear Expectational Difference Equations 50
4.1 The Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
4.2 Matrix Decompositions . . . . . . . . . . . . . . . . . . . . . . . . . 51
4.3 Solving . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
4.4 Singular Dynamic Equations . . . . . . . . . . . . . . . . . . . . . 58
5 A “Simple” Policy Rule 58
5.1 Model and Solution . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
5.2 Time Series Representation . . . . . . . . . . . . . . . . . . . . . . . 59
5.3 Value of Loss Function . . . . . . . . . . . . . . . . . . . . . . . . . 60
5.4 Optimal Simple Rule . . . . . . . . . . . . . . . . . . . . . . . . . . 62
5.5 Singular Dynamic Equations . . . . . . . . . . . . . . . . . . . . . 63
6 Optimal Policy under Commitment 63
6.1 Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
6.2 Solving . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
6.3 Alternative Expression when R is Invertible . . . . . . . . . . . . . 69
6.4 Singular Dynamic Equations . . . . . . . . . . . . . . . . . . . . . 71
7 Simple Rules with Singular Dynamic Equations 71
8 Discretionary Solution 72
8.1 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72
8.2 The Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73
8.3 Optimization in Period t . . . . . . . . . . . . . . . . . . . . . . . . 73
8.4 A Recursive Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . 78
8.5 The Time Invariant Solution . . . . . . . . . . . . . . . . . . . . . . 79
8.6 Dynamics in Terms of x1t and x2t . . . . . . . . . . . . . . . . . . . 79
8.7 Singular Dynamic Equations . . . . . . . . . . . . . . . . . . . . . 80
9 Monetary Policy in VAR Systems 82
9.1 VAR System, Structural Form, and Impulse Response Function . . . . 82
9.2 Fully Recursive Structural Form . . . . . . . . . . . . . . . . . . . . 83
9.3 Some Controversies . . . . . . . . . . . . . . . . . . . . . . . . . . . 87
9.4 Interpretation of the VAR Results . . . . . . . . . . . . . . . . . . . . 88
9.5 “The Federal Funds Rate and the Channels of Monetary Transmission”
by Bernanke and Blinder . . . . . . . . . . . . . . . . . . . . . 91
9.6 “The Effects of Monetary Policy Shocks: Evidence from the Flow of
Funds” by Christiano, Eichenbaum, and Evans . . . . . . . . . . . . . 92
9.7 “Do Measures of Monetary Policy in a VAR Make Sense” by Rudebusch 93
9.8 “What Does Monetary Policy Do?” by Leeper, Sims. and Zha . . . . 95
9.9 “Identifying Monetary Policy in a Small Open Economy under Flexible
Exchange Rates” by Cushman and Zha . . . . . . . . . . . . . . . 95
9.10 “What Does the Bundesbank Target?” by Bernanke and Mihov . . . . 96
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