A Course in Monetary Economics: Sequential Trade, Money, and Uncertainty

Preface xiii

Part I: Introduction to Monetary Economics 1

1 Overview 5

1.1 Money, Inflation, and Output: Some Empirical Evidence 5

1.2 The Policy Debate 8

1.3 Modeling Issues 13

1.4 Background Material 14

1.4.1 The Fisherian diagram 15

1.4.2 Efficiency and distortive taxes 18

1.4.3 Asset pricing 21

2 Money in the Utility Function 26

2.1 Motivating the Money in the Utility Function Approach: The Single-period, Single-agent Problem 26

2.2 The Multi-period, Single-agent Problem 28

2.3 Equilibrium with Constant Money Supply 33

2.4 The Social and Private Cost for Accumulating Real Balances 34

2.5 AdministrativeWays of Getting to the Optimum 36

2.6 Once and for All Changes in M 36

2.7 Change in the Rate of Money Supply Change: Technical Aspects 37

2.8 Change in the Rate of Money Supply Change: Economics 38

2.9 Steady-state Equilibrium (SSE) 41

2.10 Transition from One Steady State to Another 41

2.11 Regime Changes 43

2.12 Introducing Physical Capital and Bonds 45

2.13 The Golden Rule and the Modified Golden Rule 47

Appendix 2A A dynamic programming example 53

3 The Welfare Cost of Inflation in a Growing Economy 57

3.1 Steady-state Equilibrium in a Growing Economy 57

3.2 Generalizing the Model in Chapter 2 to the Case of Growth 58

3.3 Money Substitutes 64

Appendix 3A A dynamic programming formulation 69

4 Government 72

4.1 The Revenues from Printing Money 72

4.1.1 Steady-state revenues 72

4.1.2 Out of the steady-state revenues 73

4.1.3 The present value of revenues 75

Appendix 4A Non-steady-state equilibria 76

4.2 The Government’s “Budget Constraint” 78

4.2.1 Monetary and fiscal policy: Who moves first? 81

4.2.2 The fiscal approach to the price level 81

4.3 Policy in the Absence of Perfect Commitment: A Positive Theory of Inflation 82

5 More Explicit Models of Money 86

5.1 A Cash-in-advance Model 86

5.1.1 A two-goods model 87

5.1.2 An analogous real economy 89

5.1.3 Money super-neutrality in a one-good model 92

5.2 An Overlapping Generations Model 94

5.3 A Baumol–Tobin Type Model 96

Appendix 5A 98

6 Optimal Fiscal and Monetary Policy 100

6.1 The Second-best Allocation 100

6.2 The Second Best and the Friedman Rule 103

6.3 Smoothing Tax Distortions 109

6.4 A Shopping Time Model 112

7 Money and the Business Cycle: Does Money Matter? 123

7.1 VAR and Impulse Response Functions: An Example 125

7.2 Using VAR Impulse Response Analysis to Assess the Money–Output Relationship 127

7.3 Specification Search 135

7.4 Variance Decomposition 142

8 Sticky Prices in a Demand-satisfying Model 147

9 Sticky Prices with Optimal Quantity Choices 155

9.1 The Production to Order Case 156

9.2 The Production to Market Case 161

10 Flexible Prices 170

10.1 Lucas’ Confusion Hypothesis 170

10.2 Limited Participation 174

Part II: An Introduction to the Economics of Uncertainty 179

11 Preliminaries 182

11.1 Trade in Contingent Commodities 185

11.2 Efficient Risk Allocation 190

12 Does Insurance Require Risk Aversion? 197

12.1 The Insurance-buying Gambler 200

12.2 Socially Harmful Information 201

13 Asset Prices and the Lucas “Tree Model” 202

Part III: An Introduction to Uncertain and Sequential Trade (UST) 207

14 Real Models 210

14.1 An Example 210

14.1.1 Downward sloping demand 215

14.1.2 Welfare analysis 218

14.1.3 Demand and supply analysis 221

14.2 Monopoly 224

14.2.1 Procyclical productivity 226

14.2.2 Estimating the markup 227

14.3 Relationship to the Arrow–Debreu Model 228

14.4 Heterogeneity and Supply Uncertainty 231

14.4.1 The model 233

14.5 Inventories 237

14.5.1 Temporary (partial) equilibrium 238

14.5.2 Solving for a temporary equilibrium 240

14.5.3 Full equilibrium 243

14.5.4 Efficiency 243

Appendix 14A The firm’s problem 247

Appendix 14B The planner’s problem 248

15 A Monetary Model 250

15.1 An Example 251

15.2 Working with the Money Supply as the Unit of Account 253

15.3 Anticipated and Unanticipated Money 255

15.4 Labor Choice, Average Capacity Utilization andWelfare 256

15.5 A Generalization to Many Potential Markets 256

15.6 Asymmetric Equilibria: A Perfectly Flexible Price Distribution is Consistent with Individual Prices That Appear to Be “Rigid” 258

15.7 Summary of the Implications of the Model 259

16 Limited Participation, Sticky Prices, and UST: A Comparison 261

16.1 Limited Participation 261

16.2 Sticky Prices 265

16.3 UST 268

16.4 A Real Business Cycle Model withWedges: Some Equivalence Results 274

16.5 Additional Tests Based on Unit Labor Cost and Labor Share 276

17 Inventories and the Business Cycle 280

17.1 Introducing Costless Storage 282

17.2 Adding Supply Shocks 288

17.3 Testing the Model with Detrended Variables 292

17.4 Using an Impulse Response Analysis with Non-detrended Variables to Test for Persistence 297

Appendix 17A The Hodrick–Prescott (H–P) filter 300

18 Money and Credit in the Business Cycle 302

18.1 A UST Model with Credit 302

18.2 Inventories Are a Sufficient Statistic for Past Demand Shocks 305

18.3 Estimating the Responses to a Money Shock 306

18.4 Estimating the Responses to an Inventories Shock 310

18.5 Concluding Remarks 312

19 Evidence from Micro Data 313

19.1 A Menu Cost Model 313

19.2 The Serial Correlation in the Nominal Price Change 315

19.3 A Two-Sided Policy 316

19.4 Relative Price Variability and Inflation 317

19.5 A Staggered Price Setting Model 319

20 The Friedman Rule in a UST Model 327

20.1 A Single-Asset Economy 327

20.2 Adding a Costless Bonds Market 330

20.3 Costly Transactions in Bonds 331

21 Sequential International Trade 333

21.1 A Real Model 334

21.2 A Monetary Model 341

21.3 Exchange Rates 348

Appendix 21A Proofs of the Claims in the Monetary Model 350

Appendix 21B Example 7 in detail 353

22 Endogenous Information and Externalities 356

22.1 A Real Model 356

22.2 A Monetary Model 361

22.3 Relationship to the New Keynesian Economics 367

23 Search and Contracts 369

23.1 Search over Time 369

23.2 Random Choice of Markets 371

23.3 Capacity Utilization Contracts and Carlton’s Observations 375

References 385

Index 395