What is Sustainability? Graciela Chichilnisky Columbia University, - - PDF document

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 Oce of Scientic 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 denitions and results are provided. Recent publications were circulated containing denitions and proofs.

Sustainable Development Pentagon's recent report on Climate Change A recent Pentagon report nds that climate change

• ver 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.theobserve most-commented http://www.nytimes.com/2009/08/09/science/earth/09climate.html? r=2 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 dene 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

• ver time.

Examples of the new criteria Finance: Maximize expected returns while minimizing the drop in 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 - Diussion Processes (Merton, 1985) These are not consistent with current decision making

• ver time or under uncertainty, leading to perceived

"irrationality". The issue is not lack of rationality

• but a dierent type of rationality that gives more

weight 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 Economic Development 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

• f economic development." and \Modernizing the international

nancial institutions and global development architecture is es- sential to our eorts to promote global nancial stability, foster sustainable development, and lift the lives of the poorest." These statements substantiate the extent to which sustainable devel-

• pment has become a mainstream international priority.

What is Sustainability?

Sustainability means addressing the needs of the present 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 eect it will have tomorrow In economics, it means how we rank economic

• pportunities over time

Examples Public policy examples: Sustainable Debt and Sustainable Decit 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: Decit spending: The criterion for sus- tainable decit 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 prots 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

• f 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 eects of a `black out'. None of the criteria listed above is consistent with neo- classic cost-benet 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, Decit Spending and Business Plans Sustainable debt means `debt provisions that can be met by future surpluses' Decit spending: sustainable decits means that `we do not use new money to pay the interest for the old' Business plans: to maximize prots 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

• f production today while ensuring long-run survival
• f 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 eects of a `black

• ut'

These are all "constraints" on economic decisions

• ver time

None of these criteria are consistent with classic cost-benet analysis

None are consistent with classic or neo-classic economics

Neoclassical economics oers no denition of sustainable decisions Economic decisions over time use cost-benet 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 benet 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 with a `xed discount factor' This is not just theory By law, it must be used by the US Congress before funding large projects It determines Public Policy, US Decits 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 prot 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 decits 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 aect 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 dierent 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 each

• ther for `normal' events but are quite dierent 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

• ur 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 modications 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() =

1

X

t=1

tt are dictatorships of the present.

Proof: Let d(s) denote etdt as in proper discounted util- ity { or more generally any other L1 measure used for discounting utility over time. Then

R

R u(x(t))d(t) >

R

R u(y(t))d(t) , 9 > 0 :

R

R u(x(t))d(t) >

R

R u(y(t))d(t) + :

Now let " = =6K where K = sup

x2L; 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 any set Sc where (S) < "; j

Z

R u(x0(t))d(t)

Z

R u(x(t))d(t) j

2K(t) < 2K:=6K = =3:

Therefore y x )

R

R u(y0(t))d(t) <

R

R u(x0(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 ranking W() = 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 satises our axioms. There exist rankings : L1 ! R which satisfy

• ur 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: () =

1

X

t=1

tt + (1 )( lim

t!1(t)):

where limt!1(t) is well dened for all sequences with 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 innity. The lower bound is the 'sustainability contraint' - a perpetuity - and it assumes dierent forms depending

• n the dynamics of the economy

Equivalence with the Axiom of Choice The rst part is an integral operator with a countably additive kernel fsgs2Z and emphasizing the weight

• f the present.

The second part is an extension of the function (f) = limx!1 f(x) (which is dened only on functions that have limits, a closed subspace of L1): We extend this function to all of L1 using Hahn Banach - or free ultralters. 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

G.Chichilnisky `An Axiomatic Approach to Sustain- able Development' Soc. Choice and Welfare (1996) 13:321-257. G.Chichilnisky `What is Sustainable Development' Land Economics, 1997 G.Chichilnisky `Updating Von Neumann Morgenstern Axioms for Choice under Uncertainty' The Fields In- stitute for Mathematical Sciences, 1996.

• G. Chichilnisky, `An Axiomatic Approach to Choice

under Uncertainty with Catastrophic Risks' Resource and Energy Economics, 22 (2000) 221-231.

• G. Heal `Valuating the Future', Columbia University

Press, 2002.

• G. Chichilnisky `The Foundations of Statistics with

Black Swans" J. of Probability and Statistics, 2010

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

nomics, December 2009

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

timation in Hilbert Spaces' Econometric Theory, De- cember 2009

• G. Chichilnisky `Avoiding Extinction:

Equal Treat- ment of the Present and the Future' e-Economics Journal, March 2009

• N. Hernstein and J. Milnor \An Axiomatic Approach

to Measurable Utility" Econometrica (1953) 21,:291- 297

• O. Chanel and G. Chichilnisky "Experimental Resources
• n Decisions over Time" Risk and Uncertainty, 2009