| Zero Lower Bound andMonetary Policy in the Euro AreaOptimal Monetary Policy in aLow Inflation Environment | 1 |
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| Table of contents | 3 |
| 1. Introduction | 7 |
| 2. Literature | 8 |
| 3. The Model | 12 |
| 3.1 Households | 12 |
| 3.1.1 Utility maximization | 13 |
| 3.1.2 Optimality condition | 15 |
| 3.1.3 Demand for consumption goods | 18 |
| 3.2 Firms | 19 |
| 3.2.1 Fully flexible prices | 19 |
| 3.2.2 Price stickiness | 21 |
| 3.3 Monetary Authority | 23 |
| 3.3.1 Money supply and the nominal interest rate | 23 |
| 3.3.2 Assets bought by the central bank | 25 |
| 3.4 Fiscal authority | 27 |
| 3.5 General rational expectation equilibrium | 28 |
| 3.6 New Conditions without money and portfolio shares | 30 |
| 3.7 Log Linearization | 34 |
| 3.7.2 New Keynesian Phillips curve | 35 |
| 3.8 Optimal Policy | 37 |
| 3.8.1 The welfare criterion | 37 |
| 3.8.3 Optimal solution under commitment | 42 |
| 3.9 Implementing optimal policy | 44 |
| 3.9.1 The optimal rule | 45 |
| 3.9.2 A simpler rule with a similar outcome | 48 |
| 3.9.3 What is the result of the model | 49 |
| 4. Modelling the euro area economy | 52 |
| 4.1 The situation in the euro area | 52 |
| 4.1.1 Inflation dynamics | 53 |
| 4.1.1.1 Taylor contracting | 53 |
| 4.1.1.2 Fuhrer-Moore contracting | 55 |
| 4.1.1.3 Interest rate rules | 57 |
| 4.1.1.4 Frequency of bind | 58 |
| 4.1.1.5 Results from other studies | 60 |
| 4.1.2 Distortions with a Taylor rule | 62 |
| 4.1.2.1 Inflation distortions | 63 |
| 4.1.2.2 Output distortions | 64 |
| 4.1.3 Distortions with a forecast based first difference rule | 65 |
| 4.1.3.1 Inflation distortions | 65 |
| 4.1.3.2 Output distortions | 66 |
| 4.1.3 Comparing the risk in the major economies | 67 |
| 4.1.4 The role of the target for the rate of inflation | 69 |
| 4.2 Avoiding or escaping the negative consequences | 71 |
| 4.2.1 Exchange rate policy | 71 |
| 4.2.1.1 The exchange rate mechanism | 72 |
| 4.2.1.2 How strong is the effect? | 73 |
| 4.2.2 Quantitative easing | 74 |
| 4.2.3 Portfolio balance effects | 76 |
| 4.2.4 Purchasing real assets | 77 |
| 4.2.5 Pre-emptive strike | 79 |
| 4.2.6 Carry tax on money | 81 |
| 4.2.7 Fiscal policy | 83 |
| 4.3 Results | 84 |
| 5. How severe is the zero bound in the euro area? | 85 |
| 6. Discussion | 86 |
| 6.1 Some points of critique about the model | 87 |
| 6.2 Critique about alternative policy instruments in a zero interest rate period | 89 |
| 6.3 Rational expectations | 90 |
| 6.4 Is the zero bound really zero? | 91 |
| 7. Conclusions | 92 |
| Appendix | 93 |
| Literature | 171 |