Table of Contents
Preface x
I Getting Started 1
1 Info-Gap Theory in Plain English 3
1.1 Can Models Help? 3
1.2 Elements of Info-Gap Theory 6
1.3 Implications of Info-Gap Theory 9
1.4 Applications of Info-Gap Theory 11
2 A First Look: Stylized Example 15
2.1 Problem Formulation 16
2.2 Robustness 17
2.2.1 Formulation and Derivation 17
2.2.2 Trade-Off and Zeroing 19
2.2.3 Preference Reversal 20
2.2.4 What Do the Numbers Mean? 21
2.3 Opportuneness 22
2.3.1 Formulation 22
2.3.2 Interpretation 23
II Economic Decisions 27
3 Monetary Policy 29
3.1 Taylor Rule for Interest Rates 29
3.1.1 Policy Preview 30
3.1.2 Operational Preview 30
3.1.3 Formulation 31
3.1.4 Uncertainty, Performance and Robustness 33
3.1.5 Policy Exploration 35
3.2 Expectations, Communication and Credibility 41
3.2.1 Policy Preview 43
3.2.2 Operational Preview 44
3.2.3 Dynamics and Expectations 45
3.2.4 Uncertainty and Robustness 47
3.2.5 Policy Exploration 49
3.3 Shocks, Expectations and Credibility 56
3.3.1 Policy Preview 56
3.3.2 Operational Preview 57
3.3.3 Dynamics and Expectations 58
3.3.4 Uncertainty and Robustness 59
3.3.5 Policy Exploration 61
3.4 Credibility and Interacting Agents 65
3.4.1 Policy Preview 66
3.4.2 Operational Preview 67
3.4.3 Dynamics and Expectations 68
3.4.4 Uncertainty and Robustness 70
3.4.5 Policy Exploration 72
3.5 Extensions 77
3.6 Appendix: Auto-Regressive Representation of the Rudebusch-Svensson Model 78
3.7 Appendix: Derivation of Expectation Coefficients 79
3.8 Appendix: Derivation of Inverse 1-Step Robustnesses 80
4 Financial Stability 87
4.1 Structured Securities: Simple Example 87
4.1.1 Policy Preview 88
4.1.2 Operational Preview 88
4.1.3 Formulation 89
4.1.4 Uncertainty Model 90
4.1.5 Robustness Functions 91
4.1.6 Policy Exploration 92
4.1.7 Extensions 94
4.2 Value at Risk in Financial Economics 95
4.2.1 Policy Preview 97
4.2.2 Operational Preview 98
4.2.3 Value at Risk: Formulation 98
4.2.4 Uncertainty Model: Fat Tails 99
4.2.5 Performance and Robustness 101
4.2.6 Safety Factor and Incremental VaR 103
4.2.7 Policy Exploration 104
4.2.8 Robustness with Uncertain Normal Distributions 110
4.2.9 Extensions 113
4.3 Stress Testing: Suite of Models 115
4.3.1 Suite of Models and their Uncertainties 116
4.3.2 Shocks and their Uncertainties 118
4.3.3 Embedding a Stress Test 119
4.4 Strategic Asset Allocation 120
4.4.1 Policy Preview 121
4.4.2 Operational Preview 121
4.4.3 Budget Constraint 122
4.4.4 Uncertainty 123
4.4.5 Performance and Robustness 124
4.4.6 Opportuneness Function 125
4.4.7 Policy Exploration 127
4.4.8 Extensions 131
4.5 Appendix: Derivation of an Info-Gap Model 132
5 Topics in Public Policy 135
5.1 Emissions Compliance 135
5.1.1 Policy Preview 136
5.1.2 Operational Preview 137
5.1.3 Welfare Loss: Formulation 137
5.1.4 Uncertainty 139
5.1.5 Robustness 140
5.1.6 Policy Exploration 142
5.1.7 Extensions 149
5.2 Enforcing Pollution Limits 150
5.2.1 Policy Preview 150
5.2.2 Operational Preview 151
5.2.3 Economic Model 152
5.2.4 Uncertainty and Robustness 156
5.2.5 Policy Exploration 158
5.2.6 Extensions 164
5.3 Climate Change 165
5.3.1 Policy Preview 166
5.3.2 Operational Preview 166
5.3.3 System Model 167
5.3.4 Performance Requirement 168
5.3.5 Uncertainty Models 169
5.3.6 Robustness 170
5.3.7 Policy Exploration 172
5.3.8 Extensions 176
5.4 Appendix: Derivation of Eq.(5.19) 177
5.5 Appendix: Derivation of Eq.(5.22) 178
6 Estimation and Forecasting 179
6.1 Regression Prediction 179
6.1.1 Policy Preview 181
6.1.2 Operational Preview 181
6.1.3 Regression and Robustness 182
6.1.4 Policy Exploration 185
6.1.5 Extensions 188
6.2 Auto-Regression and Data Revision 189
6.2.1 Policy Preview 190
6.2.2 Operational Preview 190
6.2.3 Auto-Regression 190
6.2.4 Uncertainty and Robustness 191
6.2.5 Policy Exploration 193
6.3 Confidence Intervals 197
6.3.1 Policy Preview 197
6.3.2 Operational Preview 197
6.3.3 Formulating the Confidence Interval 198
6.3.4 Uncertainty and Robustness 200
6.3.5 Policy Exploration 202
6.3.6 Extension 208
6.4 Appendix: Least Squares Regression Coefficients for Section 6.1 209
6.5 Appendix: Mean Squared Error for Section 6.2 209
III Wrapping Up 211
7 The Art of Uncertainty Modelling 213
7.1 Uncertain Parameters 214
7.1.1 Certainty 214
7.1.2 Fractional Error 214
7.1.3 Fractional Error with Bounds 217
7.1.4 Calibrated Fractional Error 218
7.1.5 Discrete Probability Distributions 219
7.2 Uncertain Function 220
7.2.1 Envelope Bound 221
7.2.2 Slope Bound 222
7.2.3 Auto-Regressive Functions 225
7.3 Extensions 226
8 Positivism, F-twist, and Robust-Satisficing 227
8.1 Friedman and Samuelson 228
8.2 Shackle-Popper Indeterminism 230
8.3 Methodological Implications 231
References 233
Author Index 241
Subjec Index 244
