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Theoretical aspects of long-term evaluation in environmental economics [Elektronische Ressource] / vorgelegt von Christian P. Traeger

288 pages
Theoretical aspects of long-term evaluation inenvironmental economicsInaugural-Dissertation zur Erlangung der Wu¨rde einesDoktors der Wirtschaftswissenschaften (Dr. rer. pol.)an der Wirtschafts- und Sozialwissenschaftlichen Fakult¨atder Ruprecht-Karls-Universit¨at Heidelbergvorgelegt im August 2006 vonChristian P. Traegergeboren in Frankfurt am MainiiiAcknowledgementsFirst of all, I owe thanks to my advisor Prof. Dr. Hans Gersbach, now at the ETHZu¨rich. His always constructive comments on my work have been very motivating andhelpful. His willingness to support me, in particular, when pressing deadlines darkenedthe horizon, is very gratefully acknowledged. I thank Prof. Dr. Ju¨rgen Eichberger, atthe University of Heidelberg, for the interesting discussions on decision theory, and hiswillingness to evaluate this dissertation under quite unfavorable circumstances. Fur-thermore, I am deeply grateful to Prof. Larry Karp, who invited me for an exceptionallyinterestingyearofresearchtotheUniversityofCaliforniaatBerkeley. Larrywasalwaysopen for questions and I have benefited in many ways from his comments and help.I am most grateful to Dr. Ralph Winkler, who (tried his best to) introduce me tothe art of scientific working and writing. The discussions with Ralph have always beenvery inspiring and my economic understanding has benefited in many ways from hisanalytic expertise. I thank Prof. Dr.
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Theoretical aspects of long-term evaluation in
environmental economics
Inaugural-Dissertation zur Erlangung der Wu¨rde eines
Doktors der Wirtschaftswissenschaften (Dr. rer. pol.)
an der Wirtschafts- und Sozialwissenschaftlichen Fakult¨at
der Ruprecht-Karls-Universit¨at Heidelberg
vorgelegt im August 2006 von
Christian P. Traeger
geboren in Frankfurt am Mainiii
Acknowledgements
First of all, I owe thanks to my advisor Prof. Dr. Hans Gersbach, now at the ETH
Zu¨rich. His always constructive comments on my work have been very motivating and
helpful. His willingness to support me, in particular, when pressing deadlines darkened
the horizon, is very gratefully acknowledged. I thank Prof. Dr. Ju¨rgen Eichberger, at
the University of Heidelberg, for the interesting discussions on decision theory, and his
willingness to evaluate this dissertation under quite unfavorable circumstances. Fur-
thermore, I am deeply grateful to Prof. Larry Karp, who invited me for an exceptionally
interestingyearofresearchtotheUniversityofCaliforniaatBerkeley. Larrywasalways
open for questions and I have benefited in many ways from his comments and help.
I am most grateful to Dr. Ralph Winkler, who (tried his best to) introduce me to
the art of scientific working and writing. The discussions with Ralph have always been
very inspiring and my economic understanding has benefited in many ways from his
analytic expertise. I thank Prof. Dr. Malte Faber, who most influenced my interests in
economic research, and who always called attention to the limits of models and formal
representations. Furthermore, I owe special thanks to my office mates, collegues and
professorsattheGraduateSchoolforEnvironmentalandResourceEconomicsinHeidel-
berg, and the Department of Agricultural and Resource Economics at the University of
California at Berkeley. In these institutions, I have benefited from a multitude of inter-
esting talks and discussions. Let me express by name my thanks to Dr. Martin Quaas,
Prof. Michael Hanemann, Prof. Anthony Fisher, Prof. Alberto Garrido, Prof. Brian
Wright, Prof. Reimund Schwarze, Prof. Timo G¨oschl, Prof. Armin Schmutzler, Prof.
Hans Haller, Dr. Andreas Lange, Dr. Christian Becker, Maik Schneider, Grischa Perino,
Benjamin Lu¨nenbu¨rger, Dr. Sheila Wertz-Kanounnikoff, Hendrik Wolff and Elizaveta
Perova. Many of whom have also provided comments on this thesis or proof read chap-
ters. Moreover,Iexpressmythankstotheparticipantsofseveralconferences,workshops
and summer schools for comments on the first two parts of this study. In particular, I
owe thanks to Prof. Bernard Sinclair-Desgagn´e.
Last but not least, I thank my family and my roommates Andr´e Butz and Christoph
Eichhorn for supporting me mentally and physically during the years of my Ph.D. re-
search. To the latter, as to Martin Kaufmann and Marc-Thomas Eisele, I also owe
thanks for many interesting discussions on the (sometimes remote) connections to the
physics underlying the motivation for parts of my research, and their willingness to
proof read ‘strange’ economic thoughts. Financial support from the German ResearchFoundation (DFG) and the German Academic Exchange Service (DAAD) is gratefully
acknowledged, as is financial support from the European Association of Environmental
and Resource Economists for the participation in two summer schools.
Heidelberg, August 2006 Christian P. TraegerContents
Notation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ix
1 Introduction 1
1.1 Motivation: Environmental Change . . . . . . . . . . . . . . . . . . . . . 1
1.2 Conceptual Background . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.3 Key Issues . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
1.4 Methodology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
1.5 Outline. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
I Social Discounting and Limited Substitutability
in Welfare 13
2 Social Discounting 15
2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
2.2 Social Discount Rates and Factors . . . . . . . . . . . . . . . . . . . . . . 18
3 Sustainability and Limited Substitutability 23
3.1 A Preference for Weak versus Strong Sustainability . . . . . . . . . . . . 23
3.2 Limited Substitutability in Consumption and Social Discount Rates . . . 26
3.3 Social Discount Rates in a Stylized Growth Scenario. . . . . . . . . . . . 28
4 Discounting and Project Evaluation 41
4.1 Social Discounting in a Cost Benefit Analysis of a Small Project . . . . . 41
4.2 Relation to a Complete Market Evaluation . . . . . . . . . . . . . . . . . 45
4.3 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
vvi CONTENTS
II Intertemporal Risk Aversion and the
Precautionary Principle 51
5 Preliminaries 53
5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
5.2 The Precautionary Principle . . . . . . . . . . . . . . . . . . . . . . . . . 57
5.3 Uncertainty Aggregation Rules . . . . . . . . . . . . . . . . . . . . . . . 66
6 The Representation 71
6.1 Atemporal Uncertainty . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
6.2 Intertemporal Certainty . . . . . . . . . . . . . . . . . . . . . . . . . . . 76
6.3 Certain× Uncertain . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79
6.4 Gauging . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81
7 Discussion 85
7.1 Risk Aversion and Intertemporal Substitutability . . . . . . . . . . . . . 85
7.2 Intertemporal Risk Aversion . . . . . . . . . . . . . . . . . . . . . . . . . 92
7.3 Welfare and Precaution . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95
7.4 Measures of Intertemporal Risk Aversion . . . . . . . . . . . . . . . . . . 99
7.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105
III Extensions and Refinements of Part II 107
8 Multiperiod Extension 109
8.1 Multiperiod Extension of the Representation . . . . . . . . . . . . . . . . 109
8.2 Intertemporal Risk Aversion . . . . . . . . . . . . . . . . . . . . . . . . . 116
9 Stationarity 127
9.1 Certainty Stationarity . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127
9.2 Risk Stationarity I . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132
9.3 Risk Stationarity II . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135
9.4 Intertemporal Risk Aversion . . . . . . . . . . . . . . . . . . . . . . . . . 139
10 Temporal Resolution of Uncertainty 149
10.1 A Preference for the Timing of Uncertainty Resolution . . . . . . . . . . 14910.2 Indifference to the Timing of Uncertainty Resolution and Reduction of
Recursive Probabilites . . . . . . . . . . . . . . . . . . . . . . . . . . . . 158
10.3 Intertemporal Risk Aversion and Non-Recursive Uncertainty . . . . . . . 165
10.4 Implications for Discounting . . . . . . . . . . . . . . . . . . . . . . . . . 173
10.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 177
11 Conclusions 179
11.1 Summary of Conceptual Contributions . . . . . . . . . . . . . . . . . . . 179
11.2 Implications and Applications . . . . . . . . . . . . . . . . . . . . . . . . 181
11.3 Extensions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 184
A Proofs and Calculations for Part I 187
A.1 Calculations for Chapter 2 . . . . . . . . . . . . . . . . . . . . . . . . . 187
A.2 Calculations and Proofs for Chapter 3 . . . . . . . . . . . . . . . . . . . 189
B Proofs for Part II 195
B.1 Notation and lemma . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 195
B.2 Proofs for Chapter 5 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 196
B.3 Proofs for Chapter 6 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 197
B.4 Proofs for Chapter 7 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 202
C Proofs for Part III 207
C.1 Proofs for Chapter 8 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 207
C.2 Proofs for Chapter 9 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 226
C.3 Proofs for Chapter 10 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 249
List of Figures 263
Bibliography 265NOTATION
Notation in parts II and III
Symbol Explanation Page
weak preference relation 72, 77, 79
≻ strong preference relation 72
∼ indifference relation 72
preference relation in period t on P 110t t
| restriction of to the set of certain consumption paths 80X
≡ defining equality
A A ={a : IR→ IR :a(z) =az+b, a,b∈ IR,a = 0},
group of affine transformations 74
+ + + +A A ={a : IR→ IR :a (z) =az+b, a,b∈ IR,a> 0} 74
a a a aA A ={a : IR→ IR :a (z) =az+b,b∈ IR} 113
AIRA measure of absolute intertemporal risk aversion 100
AIRA measure of absolute intertemporal risk aversion in period t 123t
B set of Bernoulli utility functions for,
0 ′ ′ ′{u∈C (X) : [x] [x] ⇔u(x)≥u(x)∀x,x ∈X} 73, 77, 80, 1301 1
B set of Bernoulli utility functions, non-stationary settingt
0 ′ ′ ′{u ∈C (X) : [x] [x] ⇔u (x)≥u (x)∀x,x ∈X} 111t t t t t t
0C (X) space of all continuous functions from X to IR 66
Δ(Y) space of Borel probability measures on Y 66
ΔG ΔG =G −G 111t t t t
exp exponential function
−1 −1fg f◦g , composition
ˆ ˆf f ={af :a∈A} 91
−1 −1 −1ˆ ˆf f ={f a :a∈A} 91
G G =g(U) 76
G G =g(U) 76
G G = [G,G] 76
G G =g (U ) 111t t t t
G G =g (U ) 111t t t t
G G = [G ,G ] 111t t t t
Γ Γ = (G,G) 76
Γ Γ = (G ,G ) 111t t t t
ix
6NOTATION
Symbol Explanation Page
id identity
′ ′λx+(1−λ)x lottery over outcomes x and x with respective
′probabilities λ and 1−λ, λx+(1−λ)x ∈P 66
ln natural logarithm
fM uncertainty aggregation rule, R
f f0 −1M : Δ(Y)×C (Y)→ IR withM (p,u) =f f◦udp ,
Y
f : IR→ IR strictly monotonic and continuous 67
α 1R
α id α αM shorthand forM (p,u) = u dp 68
Y R
0 αM shorthand for lim M (p,u) = exp ln(u)dp 68α→0 Y
ftM uncertainty aggregation rule in period t 111
gN intertemporal aggregation rule, stationary, no discounting
g g −1 1 1N :U×U → IR withN (,) =g g()+ g() 78
2 2
g ,gt t+1N intertemporal aggregation rule, non-stationary 112
P space of Borel probability measures on X 66
p uncertain outcomes or lotteries, p∈P 66
P general choice space in period t 110t
p period t lottery, p ∈P 110t t t
xp reduced probability measure on certaint
txconsumption paths, p ∈ Δ(X ) 165t
IR IR ={z∈ IR :z≥ 0} 67+ +
IR IR ={z∈ IR :z > 0} 67++ ++
range range of a function
RIRA measure of relative intertemporal risk aversion 99
RIRA measure of relative intertemporal risk aversion in period t 123t
RRA Arrow-Pratt-measure of relative risk aversion 86
θ normalization constant, non-stationary representation 112t
ϑ normalization constant, non-stationary representation 112t
0u Bernoulli utility function, u∈C (X) 66, 73, 77
U min u(x) 66x∈X
U max u(x) 66x∈X
U range(u) = [U,U] 66
U min u (x) 111t x∈X t
U max u (x) 111t x∈X t
U [U ,U ] = range(u ) 111t t t t
welfu welfare, certainty additive Bernoulli utility function 96
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