Finding a Green Nudge: An Evolutionary Perspectiveblogs.cuit.columbia.edu/sdds/files/2013/04/... ·...
Transcript of Finding a Green Nudge: An Evolutionary Perspectiveblogs.cuit.columbia.edu/sdds/files/2013/04/... ·...
IntroductionThe Model
Conclusions
Finding a Green Nudge:An Evolutionary Perspective
Lorenzo Cerda Planas
Universite Paris 1 Pantheon-SorbonneVisiting Scholar at Columbia (Alliance Program)
Interdisciplinary Ph.D. Workshop in Sustainable DevelopmentColumbia University
April 13th, 2013
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IntroductionThe Model
Conclusions
MotivationGeneral Framework
Motivation
General questions which motivate this work:
Is it possible to obtain and sustain a good environment?
Meaning: Are we able to auto-regulate ourselves andachieve this objective in the long term?
Why do some countries behave ’green’, whereas othersbehave ’brown’? Are the Environmental Kuznets Curvesthe (only) explanation?
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IntroductionThe Model
Conclusions
MotivationGeneral Framework
Motivation
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Source: World Bank (2008)
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IntroductionThe Model
Conclusions
MotivationGeneral Framework
Motivation
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IntroductionThe Model
Conclusions
MotivationGeneral Framework
Motivation
$15,000
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20.0AUS
CAN
FIN
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NOR
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GBR
USA
GDP per Capita (PPP)
CO
2 em
issi
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s (t
on
s p
er y
ear,
per
cap
ita)
Source: World Bank (2008)
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IntroductionThe Model
Conclusions
MotivationGeneral Framework
Motivation
$15,000
$20,000
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$35,000
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$55,000
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$65,000
0.0
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20.0AUS
CAN
FIN
FRA
DEUJPN
NOR
RUS
SWE
GBR
USA
GDP per Capita (PPP)
CO
2 em
issi
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s (t
on
s p
er y
ear,
per
cap
ita)
Source: World Bank (2008)
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IntroductionThe Model
Conclusions
MotivationGeneral Framework
Motivation
Why similar countries (from an economic point of view) likethe U.S. and the Nordic countries can behave so differentlywith respect to the environment?
It looks like the environmental problem is not (only) atechnical one, but a socio-political one.
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IntroductionThe Model
Conclusions
MotivationGeneral Framework
Motivation
The aim of the present work is:
To analyse the possibility of having two similar countriesending up in different environmental conditions.
Try to understand the possible reasons of this phenomenon.
To find a way of shifting from a brown equilibrium (path) to agreen one (maybe through some tipping points? 1).
1Concept from Schelling’s book ’Micromotives and Macrobehavior’ (1978)and with ’The Tipping Point’, book by Malcolm Gladwell, 2000.Formal definition: Lamberson & Page (2012), ’Tipping Points’.)
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IntroductionThe Model
Conclusions
MotivationGeneral Framework
General Framework - The People
A society with types of people: Those who are concerned aboutthe environment and those who are not.
n → 2 (to keep it simple): The green and brown people.
Green people:
Their utility will derive not only from consumption.
But also from ’moral’ motivation,2 coming from:
Their contribution to the environment (r).Their awareness/worry about the environment (pt).
2As in from Brekke, Kverndokk & Nyborg (2001): ‘An economic model ofmoral motivation’.
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IntroductionThe Model
Conclusions
MotivationGeneral Framework
General Framework - The People
A society with types of people: Those who are concerned aboutthe environment and those who are not.
n → 2 (to keep it simple): The green and brown people.
Green people:
Their utility will derive not only from consumption.
But also from ’moral’ motivation,2 coming from:
Their contribution to the environment (r).Their awareness/worry about the environment (pt).
2As in from Brekke, Kverndokk & Nyborg (2001): ‘An economic model ofmoral motivation’.
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IntroductionThe Model
Conclusions
MotivationGeneral Framework
General Framework - The People
A society with types of people: Those who are concerned aboutthe environment and those who are not.
n → 2 (to keep it simple): The green and brown people.
Green people:
Their utility will derive not only from consumption.
But also from ’moral’ motivation,2 coming from:
Their contribution to the environment (r).Their awareness/worry about the environment (pt).
2As in from Brekke, Kverndokk & Nyborg (2001): ‘An economic model ofmoral motivation’.
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IntroductionThe Model
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MotivationGeneral Framework
General Framework - The Society
The society is compounded by a share of green people (qt) andbrown people (1− qt).
An ’evolving’ society.
The proportion of these people will change in time (asobserved in real life).
As seen in Sethi and Somanathan:3 It will evolve in favour ofthose groups getting higher benefits.
Which is based on replicator dynamics.4
3Sethi and Somanathan: ’Evolution of Social Norms’ (1996).4Taylor and Jonker: ’Evolutionarily Stable Strategies and Game Dynamics’
(1978).12 / 42
IntroductionThe Model
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MotivationGeneral Framework
General Framework - The Goods and Environment
There will be two types of goods in the society:
A ‘brown’ good:
Which pollutes.And is ’cheap’: price = 1.
A ‘green’ good:
Which does not pollute.But it is more expensive: price = 1 + ρ.
Pollution level answers a stock equation:
pt = −ηpt + γdt
(dt : Total brown product consumption)
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IntroductionThe Model
Conclusions
MotivationGeneral Framework
General Framework - The Goods and Environment
There will be two types of goods in the society:
A ‘brown’ good:
Which pollutes.And is ’cheap’: price = 1.
A ‘green’ good:
Which does not pollute.But it is more expensive: price = 1 + ρ.
Pollution level answers a stock equation:
pt = −ηpt + γdt
(dt : Total brown product consumption)
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MotivationGeneral Framework
General Framework
A government which answers to a simple majority rule:
If qt < 1/2 a brown government will be elected.
Otherwise, a green government will be elected.
A green government will implement a green policy.
The cycle:
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MotivationGeneral Framework
General Framework
A government which answers to a simple majority rule:
If qt < 1/2 a brown government will be elected.
Otherwise, a green government will be elected.
A green government will implement a green policy.
The cycle:
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The General FrameworkThe PeopleThe Evolution of SocietyFinal DynamicsSearching for a environmental nudge
The General Framework
A proportion qt of green people and conversely (1− qt) of brownpeople.
The society can consume two types of goods:
A green good (xi ): which does not pollute, but price = 1 + ρ.
A brown one (yi ): which does pollute, but cheaper: price = 1.
Each agent can consume both:
Green person: xG green prod + yG brown prod = cG products
Brown person: xB green prod + yB brown prod = cB products
They have a fixed income w :
Budget constraint: xi (1 + ρ) + yi = w i ∈ G ,B
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The General FrameworkThe PeopleThe Evolution of SocietyFinal DynamicsSearching for a environmental nudge
The People
The difference between green and brown people is:Brown people are pure homo-economicous:
UB = u(cB) → cB = yB = w
Green people get moral gain from helping the environment:
UG = m(r , pt) + u(cG )
m(r , pt): Moral gain coming from:
r : their contribution to the environment ≡ the share ofgreen products bought: r = xG/cG .
m3(pt): their awareness/worry about the environment.
m(r , pt)→← u(cG ): Trade-off between contributing and theconsumption level.
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The General FrameworkThe PeopleThe Evolution of SocietyFinal DynamicsSearching for a environmental nudge
The People
The difference between green and brown people is:Brown people are pure homo-economicous:
UB = u(cB) → cB = yB = w
Green people get moral gain from helping the environment:
UG = m(r , pt) + u(cG )
m(r , pt): Moral gain coming from:
r : their contribution to the environment ≡ the share ofgreen products bought: r = xG/cG .
m3(pt): their awareness/worry about the environment.
m(r , pt)→← u(cG ): Trade-off between contributing and theconsumption level.
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IntroductionThe Model
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The General FrameworkThe PeopleThe Evolution of SocietyFinal DynamicsSearching for a environmental nudge
The People
The difference between green and brown people is:Brown people are pure homo-economicous:
UB = u(cB) → cB = yB = w
Green people get moral gain from helping the environment:
UG = m(r , pt) + u(cG )
m(r , pt): Moral gain coming from:
r : their contribution to the environment ≡ the share ofgreen products bought: r = xG/cG .
m3(pt): their awareness/worry about the environment.
m(r , pt)→← u(cG ): Trade-off between contributing and theconsumption level.
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The General FrameworkThe PeopleThe Evolution of SocietyFinal DynamicsSearching for a environmental nudge
The green agent’s program
Lets recall that r = xG/cG
Amount of green product: xG = r cG
Amount of brown product: yG = (1− r)cG
So the budget constraint becomes: (1 + ρ)r cG + (1− r)cG = w
Giving the quantity of products consumed by the green person:
cG =w
(1 + rρ)= cG (r) → ∂cG
∂r< 0︸ ︷︷ ︸
the trade-off of being green
The more he contributes (r ↑), the less he consumes (cG ↓).
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Moral gain
m(r , pt) = α1m1(r)︸ ︷︷ ︸contribution
· m3(pt)︸ ︷︷ ︸awareness
Contribution:
I fell better when I contribute: m1(r) is an increasing function.
Awareness:
The idea: The worse the environment, the worrier or moreaware people get.
m3(pt) is an increasing function of pt .For simplicity: m3(pt) = Ω3ptΩ3 > 0 is the perception bias of the pollution level.
α1 > 0 being a weighting parameter.
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The green agent’s program
Therefore they solve the following maximization program:
maxr
m(r , pt) + u(cG (r))
s.t. 0 ≤ r ≤ 1 and qt , pt given.
Hence the optimal level of contribution for the agent r∗(pt) will be
given by solving ∂U(r ,pt)∂r = 0.
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The General FrameworkThe PeopleThe Evolution of SocietyFinal DynamicsSearching for a environmental nudge
The Evolution of Society
Using the replicator dynamics we have that the growth rate of atrait is proportional to the pay-off’s difference with respect to thepopulation. Generally speaking:
qi = qt(Ui − U)
(with U =∑
i qiUi )
In this case we have: qt = qt(1− qt)(UG − UB)
Where UG − UB = m(r∗, pt) + u(cG )− u(cB)︸ ︷︷ ︸∆u : the cost of being green
(Depending on the functional form of u(ci ), ∂∆u∂w T 0)
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The Evolution of Society
pt = −ηpt + γdt and qt = qt(1− qt)[m(r∗, pt) + ∆u]
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The Evolution of Society
The Governments:
If qt < 1/2, we will have a brown government: nothing willhappen.
If qt ≥ 1/2, we will have a green government, which willsubsidy the green product.5
This will lower ρ.Which in turn will change the dynamics equilibrium.
5Or equivalently, it will tax the brown product.26 / 42
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The General FrameworkThe PeopleThe Evolution of SocietyFinal DynamicsSearching for a environmental nudge
The Evolution of Society
qt < 1/2→ Brown government qt ≥ 1/2→ Green government→ usual ρ → subsided ρ
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The General FrameworkThe PeopleThe Evolution of SocietyFinal DynamicsSearching for a environmental nudge
The Evolution of Society
qt < 1/2→ Brown government qt ≥ 1/2→ Green government→ usual ρ → subsided ρ
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The General FrameworkThe PeopleThe Evolution of SocietyFinal DynamicsSearching for a environmental nudge
Final Dynamics
pt = −ηpt + γdt and qt = qt(1− qt)[m(r∗, pt) + ∆u]qt = 0 and pt = 0 → pt(qt) and pt(qt)
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Final Dynamics
pt = −ηpt + γdt and qt = qt(1− qt)[m(r∗, pt) + ∆u]qt = 0 and pt = 0 → pt(qt) and pt(qt)
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Final Dynamics
pt = −ηpt + γdt and qt = qt(1− qt)[m(r∗, pt) + ∆u]qt = 0 and pt = 0 → pt(qt) and pt(qt)
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The General FrameworkThe PeopleThe Evolution of SocietyFinal DynamicsSearching for a environmental nudge
Final Dynamics
pt = −ηpt + γdt and qt = qt(1− qt)[m(r∗, pt) + ∆u]qt = 0 and pt = 0 → pt(qt) and pt(qt)
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Final Dynamics
pt = −ηpt + γdt and qt = qt(1− qt)[m(r∗, pt) + ∆u]qt = 0 and pt = 0 → pt(qt) and pt(qt)
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The General FrameworkThe PeopleThe Evolution of SocietyFinal DynamicsSearching for a environmental nudge
Example of a limit trajectory
Example of a limit trajectory. Possibility of tipping points.34 / 42
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The General FrameworkThe PeopleThe Evolution of SocietyFinal DynamicsSearching for a environmental nudge
Example of a limit trajectory
Example of a limit trajectory. Possibility of tipping points.35 / 42
IntroductionThe Model
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The General FrameworkThe PeopleThe Evolution of SocietyFinal DynamicsSearching for a environmental nudge
Searching for a environmental nudge
Example of a limit trajectory. Possibility of tipping points.36 / 42
IntroductionThe Model
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The General FrameworkThe PeopleThe Evolution of SocietyFinal DynamicsSearching for a environmental nudge
Searching for a environmental nudge
Example of a limit trajectory. Possibility of tipping points.37 / 42
IntroductionThe Model
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The General FrameworkThe PeopleThe Evolution of SocietyFinal DynamicsSearching for a environmental nudge
Searching for a environmental nudge
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The General FrameworkThe PeopleThe Evolution of SocietyFinal DynamicsSearching for a environmental nudge
Searching for a environmental nudge
qt = 0→ pt(qt)
The limit trajectory can be ’defined’ by
limqt→1/2
pt(qt)
And we can make sensibility analysis (work in progress):How does it shift with Ω3 (perception bias of the pollution level)?
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Searching for a environmental nudge
For example: A (temporary) change in Ω3 could switch the systeminto the green path.
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Summing up - Conclusions
The present model is compatible with the fact that we canhave similar countries behaving differently with respect tothe environment.
Also people behave differently → possible explanation: amoral motivation.
Using this idea, we can find a way to switch from a browntrajectory into a green one.
Therefore we could find where to nudge in order to producethis change (work in progress).
Drawback: It is difficult to measure some of these variables(real behaviour, motivation).
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The End
Thank you
For your attention
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