What is Sustainability?

Graciela Chichilnisky

Columbia University, New York

Cass School of Business, London

October 15th 2010

The goal of this presentation is to provide a formal

concept of sustainability and to suggest how to make

it operational while discussing and illustrating the new

results with examples of (i) renewable resources, (ii)

business strategies and (iii) public policies.

Support and Collaborating Institutions

Air Force O�ce of Scienti�c Research, Arlington VA

Columbia Consortium for Risk Management (CCRM)

Columbia University, New York

Alliance of Small Island States (AOSIS)

Intergovernmental Renewable Energy Organization (IREO)

Groupement de Recherche en Economie Quantitative

d'Aix Marseille (GREQAM) Institut D'Economie Publique

(IDEP), Universite De Montpellier, France

Institute for Advanced International Studies, Geneva,

Switzerland

East Carolina University (ECU), North Carolina

To simplify presentation, summary de�nitions and

results are provided.

Recent publications were circulated containing

de�nitions and proofs.

Sustainable Development

Pentagon's recent report on Climate Change

A recent Pentagon report �nds that climate change

over the next 20 years could result in a global catastro-

phe costing millions of lives in wars and natural dis-

asters. Potentially most important national security

risk. Sustainable Development comes to the fore.

http://www.guardian.co.uk/environment/2004/feb/22/usnews.theobserver#att-

most-commented

http://www.nytimes.com/2009/08/09/science/earth/09climate.html? r=2&pagewanted=1

http://wwfblogs.org/climate/content/climate-change-climbs-ranks-

pentagon-and-cia-0

Our research provides new foundations for decision

making over time, for risk management and econo-

metrics, probability and statistics that de�ne sustain-

abilty and illustrate how to implement it, improving

the measurement, management and mitigation of time

dependent decisions and catastrophic risks.

The research updates Mathematical and Economic

tools for optimal statistical decisions, and decisions

over time.

Examples of the new criteria

Finance:

Maximize expected returns while minimizing the dropin a portfolio's value in case of a market downturn

Network optimization:

Electric grids: Maximize expected electricity through-put in the grid, while minimizing the probability of a"black out"

Stochastic Systems:

Jump - Di�ussion Processes (Merton, 1985)

These are not consistent with current decision makingover time or under uncertainty, leading to perceived"irrationality". The issue is not lack of rationality- but a di�erent type of rationality that gives moreweight to the future - as we normally do.

In the midst of a turbulent global economy

G-20 leaders voiced a challenge last year:

We need a Sustainable form of EconomicDevelopment

We must achieve sustainable business practices &public policy

The G-20 Meeting took place in Pittsburgh, USA, September

24{25, 2009. The G-20 Leaders' Statement can be found in

http://www.pittsburghsummit.gov/mediacenter/129639.htm.

Here are relevant quotes from the G-20 Leaders' Statement: \As

we commit to implement a new, sustainable growth model, we

should encourage work on measurement methods so as to bet-

ter take into account the social and environmental dimensions

of economic development." and \Modernizing the international

�nancial institutions and global development architecture is es-

sential to our e�orts to promote global �nancial stability, foster

sustainable development, and lift the lives of the poorest." These

statements substantiate the extent to which sustainable devel-

opment has become a mainstream international priority.

What is Sustainability?

� Sustainability means addressing the needs of thepresent without undermining the the needs of the

future

Going beyond good intentions

� Is there a way to make this operational?

� If so, exactly how?

� And how will this change economics & public pol-icy?

The Present and the Future

Sustainability is about time

It is not just what we do today but the e�ect it will

have tomorrow

In economics, it means how we rank economic

opportunities over time

Examples

Public policy examples:

Sustainable Debt and Sustainable De�cit Spending

Example 1: Sustainable debt: The criterion used here

is to only accept \debt provisions made today that can

be met by future surpluses".

Example 2: De�cit spending: The criterion for sus-

tainable de�cit spending is \not to use new money to

pay the interest for the old".

Business Examples: Sustainable Business Plans

Example 3 Sustainable business plans: The sustain-

able criterion used here is to seek to maximize pro�ts

while ensuring the long-run feasibility or survival of

the enterprise.

Renewable resources examples

Sustainable Fisheries, Forests, and Land Products

Example 4: Sustainable exploitation or sustainable use

of resources over time: The criterion used here is to

maximize the value of production today while ensuring

long-run survival of the stock.

Sustainable Portfolio Management

Private decisions about Investment

Example 5 Sustainable portfolio management: A

sustainable criterion suggested is to maximize the present

discounted value of investment while limiting total

losses to the portfolio at any point in time.

Networks: Energy Supplies

Example 6 A sustainable electrical network: A sus-

tainable criterion suggested is to maximize average

electricity throughput, while minimizing the e�ects of

a `black out'.

None of the criteria listed above is consistent with neo-

classic cost-bene�t analysis. To evaluate an economic

project over time in a sustainable fashion { indeed, to

evaluate any business plan or any public policy that

requires sustainability { we need new economic foun-

dations that update classical economic thinking and

are clear, simple, general, and analytically tractable.

Providing these is the purpose of the article.

Sustainable Business & Public Policy

Debt, De�cit Spending and Business Plans

Sustainable debt means `debt provisions that can be

met by future surpluses'

De�cit spending: sustainable de�cits means that `we

do not use new money to pay the interest for the old'

Business plans: to maximize pro�ts while ensuring

long-run feasibility or survival of the enterprise.

Sustainable use of Renewable Natural Resources

Renewable resources such as �sheries, forests, land

products: sustainable use means to maximize the value

of production today while ensuring long-run survival

of the stock

Sustainable Portolio Management

Portofolio Management: maximize present discounted

value of investment while limiting total losses to the

portfolio at any point in time

Networks (Electricity) Maximize average electricity

throughput, while minimizing the e�ects of a `black

out'

These are all "constraints" on economic decisions

over time

None of these criteria are consistent with classic

cost-bene�t analysis

None are consistent with classic orneo-classic economics

Neoclassical economics o�ers no de�nition of

sustainable decisions

Economic decisions over time use cost-bene�t

analysis - with no "constraint" on sustainability

To evaluate any economic project over time, any

business plan or any public that require sustainability

{ we need new economic foundations that are clear,

simple, general and analytically tractable.

This is the purpose of the presentation

Theory & Policy

Economic actions over time - business, portfolio man-

agement, public policy - are based on cost bene�t

analysis and present discounted value and based on

T. Koopman's axioms for economics over time:

Impatience is Koopman's fundamental axiom

� Impatience leads to present discounted value witha `�xed discount factor'

This is not just theory

� By law, it must be used by the US Congress beforefunding large projects

� It determines Public Policy, US De�cits and Debt

� It permeates all Business Plans

� Determines the valuation of business projects, �rms'valuations and thus the value of portfolios

� I will show that Koopman's impatience axiom is a

dictatorship of the present and clashes with sus-

tainability.

� This was not a problem in his time

� It became a problem now - because we are us-

ing world resources to the limit, facing massive

extinction 1,000x of fossil records, and causing

global warming.

� It is a problem now because of "Ponzi schemes"

(e.g. Mado�)

� It became a problem now because our short term

values and economic strategies paved the way to

global economic crisis

� Public policy is in crisis too.

� We need to change economic in a way that is sus-tainable, consistent with economic development

and with pro�t maximization.

� How to achieve that?

� The following provides an alternative.

What is the problem?

Discount factors underestimate the importance of

the future

Discounting the Future makes it irrelevant

| A Ponzi scheme pushes to permanently the future

the moment of reckoning

| "Consumption loan" models used everywhere in

macroeconomics allow ballooning de�cits and debt -

forever.

| Experimental work with bonds pricing (short and

long term) shows that traders do not discount the

future using �xed discount factors

| Many care about massive biodiversity extinction

that will a�ect our grandchildren

| The Kyoto Protocol and its carbon makret that I

created - now international law and trading US$165

billion annually { is a demostration that the nations

care about the future climate

| We undervalue the future when using discount

rates that decrease the value of the problem over time

by 5-10%, a coumpound factor that leads to neglect

the future,

| Posner (2004) argues that present discounted value

does not capture the true impact of a catastrophe in

the future, and that something else is at stake.

| Because of his loyalty to the concept of present

value, he argues that `rationality' does not work for

catastrophes, that we cannot deal rationally with events

in the future that may cause large and irreversible

damage.

| A similar issue is raised in Behavioral Finance.

| A similar issue leads us to neglect environmental

risks - the use of resources | It leads us to neglect

the risk of global warming.

The problem is NOT rationality.

There may be a di�erent perspective of rationality

when considering the long range future of the species.

Expected value is a good measure for evaluating risks

that have a good chance to occur today and tomor-

row, but not for evaluating risks that are important

but have a low chance to occur while we are alive.

For such risks we may need another approach for the

present and the future

In our current state of evolution we may oppose a

human tendency to give preference to immediate out-

comes as opposed to more distant and dangerous ones.

I re-considered the foundations of economics over time

Step 1: I showed that Koopman's axioms are `biased'

against the future, Chichilnisky, 1992, 1996.

Discounting is biased against the future { favors projects

that have high returns today against those who have

higher returns in the future, a bias against many im-

portant long term environmental projects.

Step 2: I introduced new economic axioms requiring

more symmetry in the treatment of the present and

the future

Step 3. I characterized in simple terms all the sus-

tainable criteria that the axioms imply. They agree

with experimental work on bonds pricing.

Step 4: Provided simple and general examples of sus-

tainable economics: with renewable resources, experi-

mental validation, for public policy, and econometrics

Step 3. I showed that the new axioms coincide with

Koopman's with `normal' events likely to occur rea-

sonably soon - an extension of classic economics

� The two sets of axioms are consistent with eachother for `normal' events but are quite di�erent on

events involving a long run future or catastrophic

events.

� How can this be?

Example:

Classical mechanics and general relativity

Classic mechanics applies to `normal scales' closer to

our daily reality. Relativity applies to large scale phe-

nomena involving astral bodies.

Both are correct in their respective scales. Neither

contradicts the other.

The same is the case with the Koopmans' axioms and

the new axioms.

New Axiomsfor Valuing Welfare over Time

(i) No dictatorship of the present

(ii) No dictatorship of the future

(iii) Continuity in L1 and linearity, standard condi-

tions.

For each t = 1; 2; :::; �t 2 R represents the utility of

generation t:

� = �t and � = �t , are paths of utility across time.

Paths are bounded: �; � 2 L1:

The ranking is represented by a real valued function

W : L1 �! R:

A ranking is a `dictatorship of the present' when for

every �; �

W (�) > W (�),W (�0) > W (�0)

where �0 and �0 are arbitrary modi�cations of � and� beyond a period T = T (�; �):

Axiom (i) rules out dictatorship of the present.

A ranking is a `dictatorship of the future' when

W (�) > W (�),W (�0) �W (�0)

where �0 and �0 are obtained by modifying arbitrarily

� and � in any �nite number of periods.

Axioms (ii) rules out dictatorships of the future.

Examples

1. Lemma: Present discounted utility functions

W (�) =1Xt=1

��t�t

are dictatorships of the present.

Proof:

Let d�(s) denote e��tdt as in proper discounted util-ity { or more generally any other L1 measure used for

discounting utility over time.

Then

RR u(x(t))d�(t) >

RR u(y(t))d�(t), 9� > 0 :

RR u(x(t))d�(t) >

RR u(y(t))d�(t) + �:

Now let " = �=6K where

K = supx2L; s2R

j u(x(t)) j

and recall that u 2 L1:

Then if a path x0 = x and another y0 = y a.e. on anyset Sc where �(S) < ";

jZRu(x0(t))d�(t)�

ZRu(x(t))d�(t) j

� 2K�(t) < 2K:�=6K = �=3:

Therefore y � x)RR u(y

0(t))d�(t) <RR u(x

0(t))d�(t)

so that

y0 � x0 i.e.

W (x) > W (y))W (x0) > W (y0)

as we wished to prove.

Reciprocally,

W (x0) > W (y0))W (x) > W (y);

which shows that Koopman's axioms lead to dictator-

ships of the present.�

Example: The rankingW (�) = lim inft2R �t is a `dic-tatorship of the future', and is ruled out by our axioms.

We know what is 'ruled out' { but what remains?

Can we provide a complete characterization of all the

functionals that satisfy our axioms?

Representation Theorem

Theorem 1 (Chichilnisky 1992, 1996)

� No welfare criteria used until now satis�es our

axioms.

� There exist rankings : L1 ! R which satisfy

our axioms.

� All such rankings are convex combinations of dic-tatorships of the present and dictatorships of the

future.

� In technical terms, the two terms are (1) count-ably additive and (2) purely �nitely additive mea-

sures on R.

For example, if time is discrete, indexed by the integers

Z, there exists �; 0 < � < 1; such that : l1 ! R

is:

(�) = �1Xt=1

��t�t + (1� �)( limt!1

(�t)):

where limt!1(�t) is well de�ned for all sequenceswith limits, and extended to all others using Hahn Ba-

nach's theorem. More general substitute limt!1(�t)by � which denotes a `purely �nite measure' on Z:

How to Implement Sustainability

Equal Treatment of the Present and the Future

Theorem 2 (Chichilnisky, 2009): All sustainable cri-

teria in Theorem 1 are equivalent to optimizing pre-

sented discounted value plus a constraint at in�nity.

The lower bound is the 'sustainability contraint' - a

perpetuity - and it assumes di�erent forms depending

on the dynamics of the economy

Equivalence with the Axiom of Choice

The �rst part is an integral operator with a countably

additive kernel f��sgs2Z and emphasizing the weightof the present.

The second part is an extension of the function �(f) =

limx!1 f(x)

(which is de�ned only on functions that have limits,

a closed subspace of L1):

We extend this function � to all of L1 using Hahn

Banach - or free ultra�lters. Both are equivalent to

the Axiom of Choice.

Heavy Tails

The second purely �nitely additive part � assigns pos-

itive weight to the future. It is the equivalent of a

"heavy tail".

Because both parts are present, is sensitive to the

present and the future.

The optimization of functionals such as rquires new

tools of calculus of variations. Optimization theory

must be redeveloped in new directions. Some result

already exist, see Chichilnisky (1996) and Heal (1996).

Who is the future?

Sustainability and Global Consciousness

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G.Chichilnisky `Updating Von Neumann Morgenstern

Axioms for Choice under Uncertainty' The Fields In-

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G. Chichilnisky, `An Axiomatic Approach to Choice

under Uncertainty with Catastrophic Risks' Resource

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G. Heal `Valuating the Future', Columbia University

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G. Chichilnisky `The Foundations of Statistics with

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G. Chichilnisky `The Topology of Fear" J. Math Eco-

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G. Chichilnisky `The Limits of Econometrics: NP Es-

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G. Chichilnisky `Avoiding Extinction: Equal Treat-

ment of the Present and the Future' e-Economics

Journal, March 2009

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