Info-Gap Economics: An Operational Introduction

257 Pages·2010·2.308 MB·English

by  Yakov Ben-Haim (auth.)

Ben-Haim’s “theories and presentation of how to calculate what one
needs to know are, or should be, must reading for anyone seriously
involved in any aspect of today’s economic world, from the trader on
a desk to a Central Bank head. It is much too easy, given the stresses
of today’s world, to skip past missing information so as to act quickly
in the market, but that is exactly the path which leads to significant
errors, as we have all unfortunately witnessed. A method of calculating the
‘info gap’ is certainly vital in setting policy.” Lew Weston, Retired Partner,
Goldman, Sachs & Co.
“In an economic world where complexity defines the system and the
underlying models are at best simplistic and incomplete, it is imperative
that policy decisions be taken on the assumption of (disappointingly)
incomplete knowledge. Now, more than ever, is the economics profession
confronted with the truth of it all. This is the time for info-gap and
decisions under fundamental uncertainty.” Dr Maria Demertzis, Research
Department, De Nederlandsche Bank.
“The work by Yakov Ben-Haim is always inspiring. It is impressive how
many scientists already apply his theory. With his enthusiasm, Yakov
has made uncertainty issues a topic in a variety of disciplines and thus
promoted interdisciplinary work, which is most welcome. It is particu-
larly important to consider uncertainty in economic decision-making,
as the current financial crisis shows. For me, as a forest scientist and
forest economist, uncertainty is a key topic to be addressed by any
sustainable management strategy for ecosystems. This book provides an
excellent overview on opportunities for economic applications of the
Information-Gap Theory. The manifold practical examples make it easy
for all to understand and to follow, including persons who are yet not
familiar with uncertainty issues.” Dr Thomas Knoke, Institute of Forest
Management, Technical University of Munich.
“Much of the recent economic crisis can be traced to over-reliance on
simple mathematical models that take no account of the fact that real
economies are subject to significant Knightian uncertainty. Ben-Haim
shows how Info-Gap Theory can be used to model this uncertainty with
carefully chosen, relevant and important economic examples. A must-read
for serious economic decision makers.” Prof. Colin J. Thompson, Maths
and Stats Department, University of Melbourne.
Also by Yakov Ben-Haim:
INFO-GAP DECISION THEORY: Decisions Under Severe Uncertainty,
2nd edition
ROBUST RELIABILITY IN THE MECHANICAL SCIENCES
CONVEX MODELS OF UNCERTAINTY IN APPLIED MECHANICS,
with I. Elishakoff
THE ASSAY OF SPATIALLY RANDOM MATERIAL
Info-Gap Economics
An Operational Introduction
Yakov Ben-Haim
© Yakov Ben-Haim 2010
Softcover reprint of the hardcover 1st edition 2010 978-0-230-22804-7
All rights reserved. No reproduction, copy or transmission of this
publication may be made without written permission.
No portion of this publication may be reproduced, copied or transmitted
save with written permission or in accordance with the provisions of the
Copyright, Designs and Patents Act 1988, or under the terms of any licence
permitting limited copying issued by the Copyright Licensing Agency,
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Any person who does any unauthorized act in relation to this publication
may be liable to criminal prosecution and civil claims for damages.
The author has asserted his right to be identified as the author of this
work in accordance with the Copyright, Designs and Patents Act 1988.
First published 2010 by
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registered in England, company number 785998, of Houndmills,
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Palgrave Macmillan in the US is a division of St Martin’s Press LLC,
175 Fifth Avenue, New York, NY 10010.
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Palgrave® and Macmillan® are registered trademarks in the United States,
the United Kingdom, Europe and other countries.
ISBN 978-1-349-30991-7 ISBN 978-0-230-27732-8 (eBook)
DOI 10.1057/9780230277328
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10 9 8 7 6 5 4 3 2 1
19 18 17 16 15 14 13 12 11 10
To contact the author:
Prof. Yakov Ben-Haim
Yitzhak Moda'i Chair in Technology and Economics
Technion – Israel Institute of Technology
Haifa 32000 Israel
[email protected]
http://info-gap.com
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
v
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
vi
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
vii
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
viii
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
Subject Index 244
ix