Intergenerational and inter-

regional equity in a warming

planet*

By John E. Roemer Yale University

John.roemer@yale.edu

*Based upon work by H. Llavador , J. Roemer and J. Silvestre

Evidence is overwhelming that man-made greenhouse gas (GHG)

emissions account for the rapid rise in atmospheric carbon, a

negative global externality of huge import

Main welfare effect will be a rise in global temperature, causing the

death of species, flooding of coastal zones, storms, desertification,

and drought

Concentration in 2008: 385ppm

Last Ice Age

Currently concentration is 385 ppm CO2. Pre-industrial was 280 ppm.

If we stabilize at 500 ppm, the 0.9 confidence interval of temp increase is[1.5o, 5.2o]

An increase of 5o would eliminate one-half Earth’s species

At present, concentration is increasing at 1-2 ppm per annum. By mid-century we will be at 500 ppm without changing what we do

Atmospheric carbon is a true ‘public bad.’ The actions of each affect

all. Reducing the rate of GHG emissions requires international

cooperation

The Intergovernmental Panel on Climate Change (IPCC) has issued

four reports. In the latest, they propose levels of GHG emissions

that will stabilize concentration at 450 ppm by 2050.

Scientific opinion is leaning heavily towards a goal of 350 ppm. This

would require reducing the carbon in the atmosphere. The next

IPCC report is due in 2013.

Global 4.4 tons per capita

United States 19.0

Canada 16.7

China 4.62

Russia 10.92

Japan 10.11

Germany 9.74

S. Arabia 15.78

UAR 32.8

France 6.24 (nuclear energy)

India 1.31

Mexico 4.14

By 2050, global population will be 9.2 billion

To keep global temperature rising at most 2 degrees Celsius we must

emit no more than 18 billion tons of carbon (18 GtC) or 2 tons per

person per capita

US will have to cut its emissions by 90%

Rapid reduction

In emissions per Dollar of prod’n

1. What is the equitable way to share the scarce global commons

between the present and future generations?

2. Given the present generation’s allotment, what is the equitable/

politically feasible way to share the scarce global commons among

countries/ regions of the world?

We design a model with two persons at each date (generation): an

adult and a child. A representative family.

The child is educated by the adult, and becomes an adult with a child

at the next date

This ‘society’ goes on forever.

How can we organize production and consumption to optimize human

welfare, and stabilize atmos. carbon at 450 ppm?

Consists in five inputs:

Consumption of a produced commodity

Education

Leisure time

The stock of human knowledge

The quality of the biosphere ( inverse of atmospheric carbon concentration)

Commodities produced by educated labor, capital, knowledge.

Production causes emissions which degrade biosphere

Children are educated by the adult; level of skill of child is

proportional to teacher’s level of skill (education)

Knowledge depreciates over time, but is augmented by workers

producing knowledge(researchers, professors, artists)

A feasible path consists in a specification of all the stocks and flows

through time: of labor into four uses at each date, of commodities

into two uses. The intergenertional links are provided by

Capital formation

Education of children

Evolution of biospheric quality

Knowledge creation

Feasible Paths

There are an infinitude of possible paths which are feasible given the

constraint that we stay within the emissions guidelines of the IPCC IV,

and so stabilize carbon concentration at 450 ppm

Each such path entails an evolution of human welfare through time.

• We model human welfare as

•

• feasible path entails values for all variables at every date, where all

the production equations are satisfied, AND emissions stay within

prescribed levels

c.32 (s ).65(S

n ).02 (S Sm ).01

To maximize the level of human welfare that can be sustained

forever:

We include as a constraint a path of emissions which stabilizes at 450

ppm. We do not optimize over the emissions path.

This concept of sustainability is anthropomorphic. It is

distinguished from green sustainability which preserves the

biospheric assets just as they are today.

max

s.t. ( t)(ut

)

(u1,u

2,...)

To solve this problem requires specifying precisely what

all the economic parameters are: the production

function for commodities, the educational production function, the knowledge production function.

We do this using US data: not due to ethical

parochialism, but rather because the data are available

and are of high quality. So our computations are really concerning the

sustainability of welfare of the average US citizen forever

The IPCC IV specifies global emissions over time for

the 450 ppm path. How shall we decide upon the share

permitted for US emissions in our computation?

Two scenarios:

Scenario 1. The US continues to emit 24% of

global emissions

Scenario 2. The US emits its per capita share (approximately 4% of global emissions)

7

Postulated Path for CO2 Emissions

Implied Path for CO2 Concentrations

In this alternative we fix a rate of growth of Quality of Life g–

say 2% per annum ,which is 64% per generation. Then we ask:

What is the path that maximizes the Quality of Life of Generation one Subject to guaranteeing a rate of growth of g thereafter?

Trade-off: If we insist on positive growth, the first generation will be worse Off than under pure sustainability.

max

s.t. ( t)(ut

(1+ g)t 1 )

(u1,u

2,...)

(1)Sustainable welfare at levels noticeably higher than 2000 reference

level

(2) Small trade-off between utility of Gen 1 and moderate growth rates

thereafter; it is therefore attractive to advocate positive growth of

welfare

(3)The most important change required by the implementation of the

desirable paths is the (more than) doubling the reference fraction of labor

devoted to the creation of knowledge, whereas the fractions of labor

allocated to consumption and leisure are similar to those of the reference

year 2000

(4) Higher growth rates require substantial increases in the fraction of

labor devoted to education (of the order of a 30% increase for each

additional 1% of annual growth), together with moderate increases in

the fractions of labor devoted to knowledge and the investment in

physical capital (of the order of a 5% increase for each additional 1%

of annual growth)

Most climate-change economists use the social welfare function

There are two justifications for this choice:

(1) society is ethically equivalent to an infinitely lived agent

(2) a utilitarian Ethical Observer (EO) facing the possible extinction

of homo sapiens

W (u

1,u

2,...) = t 1

ut, 0 < <1

t=1

Suppose a consumer discounts her own future utility at rate . If the consumer lives an infinite number of periods, her utility of a stream of consumption z is

where is her discount factor and is her rate of time preference.

This is the justification of DU of Nordhaus & Weitzman. But there is no ethical equivalence between an infinitely lived consumer and a society with many generations. Why should we discount future generations’ welfare because an I.L. consumer would discount her welfare in later periods?

u(z1)+ u(z2 )+2u(z3)+ ...

=1

1+

Suppose there is a prob. p that each generation, should it be born, will be the last. Then the probability that the species survives exactly T dates is

Suppose a utilitarian Ethical Observer (EO) has vNM preferences over events of the form .His vNM utility function on events is

Then he will max expected utility, that is, choose u to:

(T ) = (1 p)T 1p

(u,T ) where u = (u

1,u

2,...)

WT (u) = u

t

1

T

max (t)ut s.t. u

1

A little algebra shows this is equivalent to

This is the justification of DU used by N. Stern.

I find this justification logically consistent…..if one is a utilitarian!

max

t 1u

t where = 1 p

Nordhaus takes and uses the Ramsey Equation to estimate

from market interest rates. He sets

Stern takes p=.001 per annum (pretty large) and therefore uses

Consequently, Stern discounts the welfare of those living a century from now by about 10%, and Nordhaus discounts it by about 80%!

The debate is not really over discount factors: it is over the justification of discounted utilitarianism. Unfortunately, S. & N. have not been clear about this in their jousting.

=1

1+

0.98

= 0.999

“An individual’s lifetime well-being is an aggregate of the flow of well-being she experiences, while intergenerational well-being is an aggregate of the lifetime well-beings of all who appear on the scene. It is doubtful that the two aggregates have the same functional form. (My italics- JR) On the other hand, I know of no evidence that suggests we would be way off the mark in assuming they do have the same form. As a matter of practical ethics, it helps enormously [my italics- JR] to approximate by not distinguishing the functional form of someone’s well-being through time from that of intergenerational well-being.”

An honest and indefensible justification!!

“How much and how fast should we react to the threat of global

warming? The Stern Review argues that the damages from climate

change are large, and that nations should undertake sharp and

immediate reductions in greenhouse gas emissions. An examination

of the Review's radical revision of the economics of climate change

finds, however, that it depends decisively on the assumption of a

near-zero time discount rate [ i.e., ] combined with a specific utility

function. The Review's unambiguous conclusions about the need for

extreme immediate action will not survive the substitution of

assumptions that are consistent with today's marketplace real interest rates

and savings rates. (my italics-JR)”

“One point should perhaps be emphasized more particularly;

it is assumed that we do not discount later enjoyments in

comparison with earlier ones, a practice which is ethically

indefensible and arises merely from weakness of the imagination;

we shall, however, in Section II, include a rate of discount in some

of our investigations.”

So why did Ramsey discount? To get convergence! Often the

undiscounted utilitarian program diverges, so the utilitarian ethic

cannot make a reccomendation.

But this is like looking for the lost keys under the streetlamp….

As I’ve said, we (Llavador, Roemer & Silvestre) are sustainabilitarians.

I did not discount earlier. But we should discount. The

sustainabilitarian EO has a vNM utility function

So if the world ends with prob. p at each date, he/she must solve:

W

T (u) = min1 t T

ut

max (t)W t (u), u

1

Consider these two problems:

A. where

B.

Theorem If program A diverges on then the solution of program B is identical to the solution of the undiscounted sustainabilitarian program

In other words, if DU diverges, then the sustainabilitarian EO does not need to discount!

max (t)W t (u)

1

max (t)W t (u)

1

max min

t

ut, u

(t) = (1 p)tp

Now consider the fixed path of emissions that we used in our

analysis, that according to IPPC IV , stabilizes CO2 concentration at

450 ppm. Suppose this path implies a certain probability of homo

sapiens extinction, of the form here discussed, and suppose that

(per annum).

Then program A diverges on our set of feasible paths, and therefore, by the

theorem just stated, the sustainabilitarian need not discount!

Therefore, the optimal path I presented earlier is the solution to the

discounted sustainabilitarian problem.

p .132

The ‘elephant in the room’ today is how to share the responsibility

among nations.

US and China each emit approx one-quarter of global emissions.

An agreement between them is necessary and (I think) sufficient to

enable an international global agreement

How should China and the US (think : the global South and North)

share the emissions quotas of IPCC IV?

Copenhagen conference was essentially a failure. No international

agreement. On final day, an ‘agreement’ to limit emissions to the 2

degrees Celsius limit: but no details, no plans, no enforcement

mechanism

Hopefully, these details will come forth in Cancun.

Failure in large part due to Pres. Obama’s focus on health care, and

neglect of global warming, in first year of administration

Various proposals:

• The North is responsible for the present carbon concentration. Hence

the South should have the lion’s share of permits henceforth

• Allocate permits on population basis to countries

• Note that ‘cap and trade’ is no answer to the question of basic principle. Cap and trade is a mechanism for trading permits AFTER the first,

international allocation of permits had been made. We are concerned

with the solution of that problem.

Imagine the world consists of China and the US (for simplicity).

Suppose we could agree that absent the problem of global warming

Chinese GDP per capita would converge to US GDP in n years (say : n

=75, i.e., three generations)

Propose: With the emissions constraint, we should still converge in n

years

To see this, imagine, on the contrary, that an agreement was

proposed in which China-US convergence occurs in less than 75

years. Then the US negotiators will say: “Why should you, China,

benefit vis-à-vis US because of global warming?”

Or imagine an agreement in which convergence occurs in more than

75 years. China will say: “Why should China lose vis-à-vis the US

because of global warming?

gdpUS = $47.4; gdpCH=$ 5.97 (2008)

Convergence in approximately 3 generations.

1+ gUS

1.02 1+ gCH

1.05

Solve the equation:

(1+ gCH )t

gnpCH

(1+ gUS )t

gnpUS=1 t = 71.5 years

We assume that the focal point of bargaining is to maintain the date of convergence of GDP per capita of Ch and US

Suppose China and the US reduce their growth factors by the same factor. Then the date of convergence remains unchanged:

We propose that China & the US reduce their growth factors by the same fraction, and stay within the emission constraints required to maintain suitably low global temperature

( r (1+ gCH ))t

gnpCH

( r (1+ gUS ))t

gnpUS= 1 t = 71.5 years

We propose a model with a Chinese rep. hh and a US rep.

household: they have different capital stocks, human capital stocks,

knowledge stocks. We parameterize the model using available data.

There is a global emissions constraint identical to our earlier one: the

IPCC IV inspired path that converges to 450 ppm concentration.

In addition, there are knowledge spillovers between the households

(countries) and there is the possibility of transfers of the good between

the countries

Problem: To find an ‘optimal’ path s.t. the emissions constraint in

which China converges to the US in welfare at date 3. (75 years)

We tried a number of formulations of the optimizandum. We

finally decided upon this one:

Maximize the welfare of the second generation of China subject to :

(1) Satisfying the global emissions constraint

(2) Guaranteeing US welfare growth of at least 1% per annum

(3) Convergence to identical endowments per capita between the

countries at date 2 – and hence equal welfare from date 3 onward,

under the sustainabilitarian program.

Transfers of the good go from the South to the North for generations 1

and 2. And knowledge goes, unsurprisingly, from the North to the

South.

Intuition: In the transition, the South has comparative advantage in

producing commodities and the North, in producing knowledge. If we

relaxed the requirement that the North grow at 28% each generation

(1% p.a.), we conjecture that there would be no transfers from South to

North.

The fly in the ointment is US national politics. A bill in the US Senate

to impose emission cutbacks has recently died. The Republican Party

is preaching ‘skepticism’ about CC

Ignorance of American citizens + linking by the Republicans of

global-warming fears with the Left

Obama administration would like to take action, but they do not

possess the political capital to fight on this front at this time. Health

care reform, finance reform, the stimulus have each been used by the

RP to build populist opposition to Obama.

It is perfectly feasible to sustain human welfare at levels higher than

today and live within the constraints required to preserve global

temperature below 2 degrees C. Even less than that is possible.

Moderate growth of welfare is probably ethically preferable to pure

sustainability (zero growth). This, too, is feasible: a 2% annual rate of

growth of welfare requires only a very small reduction of utility of

Generation 1 compared to pure sustainability

Reasonable negotiating principle is to cut back the growth factors of all countries (which are sufficiently rich) by the same factor. Special allowances for very poor countries until a specified level of GDP per capita is reached

The stumbling block is political; in particular, it is the ignorance of US citizenry, abetted by populist propaganda that global warming is a left-wing plot.

My own view is that China is not the stumbling block. They are reticent to make serious proposals due to American sluggishness.

We have calculated feasible paths exist whereby China and US converge in three generations

There is a crisis of ideology in the US. The right-wing’s sole goal

has been to destroy the Obama administration. Partly due to

racism, partly to extreme individualistic, anti-state, anti-tax ideology

which has grown in influence in the last 30 years.

Obama won the 2008 election because many voters were disgusted

with the GW Bush administration, not because of a progressive

resurgence:

Bush’s mendacity about WMD and the Iraq war

Unrepentant torture of terror suspects

Financial crisis

What happens in the US is the key. At this point, I

have no prediction. I think the success of President

Obama in countering the right-wing attack is of

utmost importance for the eventual positive

resolution of control of GHGs.

It is perhaps not too extreme to say that the quality

of the lives of future generations depends on

Obama’s overcoming the right-wing attack.

This will require engaging in some ‘justice talk’ about

our responsibility to generations yet unborn.

“A dynamic analysis of human welfare in a warming planet”

“Intergenerational resource allocation when the existence of future

worlds is uncertain” (in press, J. Math. Econ.)

“The ethics of inter-temporal distribution in a warming planet” (in

press, Environmental and Resource Econ.)

“North-South convergence and the allocation of emissions”

Available at: http://pantheon.yale.edu/~jer39/climatechange.html

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