Finding a Green Nudge: An Evolutionary Perspectiveblogs.cuit.columbia.edu/sdds/files/2013/04/... · green one (maybe through some tipping points?1). 1Concept from Schelling’s book

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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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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Conclusions


Motivation

$15,000

$20,000

$25,000

$30,000

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$40,000

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Source: World Bank (2008)

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Conclusions


Motivation

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$20,000

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$40,000

$45,000

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$55,000

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Conclusions


Motivation

$15,000

$20,000

$25,000

$30,000

$35,000

$40,000

$45,000

$50,000

$55,000

$60,000

$65,000

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2.0

4.0

6.0

8.0

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USA


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Conclusions


Motivation

$15,000

$20,000

$25,000

$30,000

$35,000

$40,000

$45,000

$50,000

$55,000

$60,000

$65,000

0.0

2.0

4.0

6.0

8.0

10.0

12.0

14.0

16.0

18.0

20.0AUS

CAN

FIN

FRA

DEUJPN

NOR

RUS

SWE

GBR

USA


CO

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Conclusions


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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Conclusions


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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Conclusions


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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Conclusions





Green people:





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Conclusions





Green people:





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Conclusions


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


Conclusions


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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Conclusions


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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Conclusions


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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Conclusions


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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Conclusions

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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Conclusions


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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Conclusions


The People




UG = m(r , pt) + u(cG )





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Conclusions


The People




UG = m(r , pt) + u(cG )





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Conclusions


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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Conclusions


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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Conclusions


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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Conclusions


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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Conclusions



pt = −ηpt + γdt and qt = qt(1− qt)[m(r∗, pt) + ∆u]

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Conclusions



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


Conclusions



qt < 1/2→ Brown government qt ≥ 1/2→ Green government→ usual ρ → subsided ρ

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Conclusions



qt < 1/2→ Brown government qt ≥ 1/2→ Green government→ usual ρ → subsided ρ

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Conclusions


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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Conclusions


Final Dynamics


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Conclusions


Final Dynamics


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Conclusions


Final Dynamics


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Conclusions


Final Dynamics


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Conclusions


Example of a limit trajectory

Example of a limit trajectory. Possibility of tipping points.34 / 42


Conclusions


Example of a limit trajectory



Conclusions


Searching for a environmental nudge



Conclusions





Conclusions



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Conclusions



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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Conclusions



For example: A (temporary) change in Ω3 could switch the systeminto the green path.

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ConclusionsConclusions

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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ConclusionsConclusions

The End

Thank you

For your attention

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Documents

Finding a Green Nudge: An Evolutionary Perspectiveblogs.cuit.columbia.edu/sdds/files/2013/04/... · green one (maybe through some tipping points?1). 1Concept from Schelling’s book