Lecture

Accounting for the environment

Lecturer: Dr. Justus Wesseler, Wageningen UniversityLiterature: Perman et al. (2003), Ch.18

Why Measuring Sustainability?

Nobel laureate economist Robert Solow suggested that ‘an innovation in social accounting practice could contribute to more rational debate and perhaps more rational action in the economics of non-renewable resources and the approach to a sustainable economy.’

OECD (1994)

Driving Force-Pressure-State-Impact-Response Framework

The Driving Force - Pressure - State - Impact - Response Framework (DPSIR) provides an overall mechanism for analysing environmental problems.

Driving forces, such as industry and transport, produce

Pressures on the environment, such as polluting emissions, which then degrade the

State of the environment, which then

Impacts on human health and eco-systems, causing society to

Respond with various policy measures, such as regulations, information and taxes, which can be directed at any other part of the system.

OECD: Towards Environmental pressure Indicators for the EU - First Edition 1998.

Important question: How to measure depreciation on natural capital?

We start with a simple economy, where one good will be produced and either consumed or added to the capital stock:

0

tt

T

t

Max U C e dt

Objective function:

Constraints: t t tK Q K C

: costate variabletC t t t t

t

H U C Q K C

current-value Hamiltonian:

Important question: How to measure depreciation on natural capital?

necessary conditions for optimum:

: costate variabletC t t t t

t

H U C Q K C

current-value Hamiltonian:

0 C

k

HU

CH

QK

*

*

t

t

c t t t

c t C t

H U C K

H U C U K

maximized current-value Hamiltonian:

or

Important question: How to measure depreciation on natural capital?

*

tc t C tH U C U K maximized current-value Hamiltonian:

• Ct and dK/dt are the OPTIMAL values of the utility maximization process

• instantaneous national income measured in utils*

tcH

• if the utility function is linearlized by using U(Ct) = UCCt:

* * t tc C t C t c C t tH U C U K H U C I

Important question: How to measure depreciation on natural capital?

• if the utility function is linearlized by using U(Ct) = UCCt:

* * t tc C t C t c C t tH U C U K H U C I

• if we assume that capital K does not depreciate, the RHS is just net national income, and we can write:

*

tt c C t tNDP H U C I

Important question: How to measure depreciation on natural capital?

We can go back to our problem and now include a non-renewable resource:

0

tt

T

t

Max U C e dt

Objective function:

Constraints: ,t t t tK Q K R C ,t tS R

, : costate variables

tC t t t t t t

t t

H U C P R Q C

P

After substituting from the PF the current-value Hamiltonian:

Necessary conditions for a maximum with control variables C and R and dropping t:

,tC t t t t t t tH U C P R Q K R C

0 0

0

C R

k

H HU P Q

C RH

P PSH

QK

We can also write: 1.)

0

2.)

3.)

4.)

C

R R R

R R

R R

k

U

P dt Q dt P Q Q

P P Q P Q P

P P Q Q

Q

P P

: 0C

Hremember U

C

(differentiating by time)

We can also write:

1.)

2.)

3.)

4.)

t C

R R

k

U

P P Q Q

Q

P P

C CIf we consider constant consumption, U =0 and =U :

3.)

and we also get from this:k C

R R K

Q U U

Q Q Q

We can also linearise the Hamiltonian and using the equation of motions:

,

,

C C C

C R

C R R

H U C PS K

H U C PS K U U

H U C I P S P Q S R

H U C I Q R NDP Q R EDP

NDP is the conventionally measured national income and EDP, national income properly measured given the use of the natural resource in production.

QRR is the rent in the extraction of the resource, where the rent is the measure of the depreciation of the asset which is the resource stock.

Depreciation is the amount extracted valued at the marginal product of the resource, which in this model with costless extraction is the unit rent.

EDP C I P R We can also write:

• P/ is the relative (to the price of the numeraire commodity which is the consumption/capital good) price of the extracted resource, which in a model with costless extraction is the same as the price of the resource in situ. (in a fully competitive economy)

We can differentiate the Hamiltonian by time. In this case we get for EDP:

KEDP W Q W

W is the current wealth of the economy. Since the marginal product of capital is the interest rate in the economy, EDP is the return on the economy’s total stock of wealth: EDP= i W.

or R REDP C I Q R NDP Q R

Measuring depreciation:

KEDP W Q W

This looks familiar!

In a model economy where resource extraction involves cost, and new known reserves can be established at some cost:

R REDP NDP Q G R N

• N: additions to the known stock as the result of exploration;

• F{N, S}: costs of exploration;

• G{R, S}: costs of extraction;

• GR: marginal extraction cost;

• QR-GR: marginal rent.

, , ,CH U C P R N Q K R C G R S F N S

Measuring depreciation:

Consider a renewable resource as an argument in the production function:

R REDP NDP Q G R F S

• GR: marginal cost of harvesting;

• F{S}: growth function of the resource stock with size St.

Note: for sustainable yield exploitation of the renewable resource, R = F{S}, there is no depreciation to account for, and EDP = NDP

, ,CH U C P F S R Q K R C G R S

Measuring depreciation:

Consider a renewable resource as an argument in the utility function:

R C REDP NDP U U G R F S

, ,CH U C R P F S R Q K C G R S

Consider a renewable resource as an argument in the utility and production function:

S C R REDP NDP U U S Q G R F S

, , ,CH U C S P F S R Q K R C G R S

Definition of Sustainable Development, SD:Development that meet the needs of the present without comprising the ability of future generations to meet their own needs. (World Commission on Environment and Development, WCED)

Weak Sustainability, WS:Natural Capital is not singled out for special treatment. It is another form of capital. Therefore, what is required for SD is the transfer of an aggregate capital stock no less than the one that exists now.

Strong Sustainability, SS:Perfect substitution between different forms of capital is not a valid assumption to make. Some elements of the natural capital stock cannot be substituted for (except on a very limited basis) by man – made capital. These assets are critical natural capital and since they are not easily substitutable, the rule requires to protect them.

Different Welfare Measures

Definition of GDP: The total market value of all final goods and services produced within a nation’s borders in a given time period.

Definition of NDP:GDP less depreciation.

Definition of depreciation:The consumption of capital in the production process; the wearing out of plant and equipment.

Measuring Sustainability:

Net National Welfare

NNW = Total Output – Costs of Growth - Depreciation= GDP + Nonmarket Output- Externality Costs- Pollution Abatement and Cleanup Costs- Depreciation of Created Capital- Depreciation of Natural Capital

Genuine Saving (World Bank):

GS = Gross Domestic Investment- Net Foreign Borrowing = Gross Saving- Depreciation of Created Capital = Net Saving- Depreciation of Natural Capital

IPAT equation, developed by Paul Ehrlich:

environmental Impact = Population * Affluence * Technology

Example: emissions of carbon dioxide from cars in 1995

I = P A TCO2 emissions = 6 mio. people 0.1 cars/person 5.4 t CO2 / car and year = 3.45 billion tons

CO2/year

The Daly RuleNever reduce the stock of natural capital below a level that generates a sustained yield unless good substitutes are currently available for the services generated.

Measuring Sustainability:

• Dutch disease The deindustrialization of a nation's economy that occurs when the discovery of a natural resource raises the value of that nation's currency, making manufactured goods less competitive with other nations, increasing imports and decreasing exports. The term originated in Holland after the discovery of North Sea gas. This represents a problem if the manufacturing and other tradeables sector is characterized by economies of scale.

Natural resource curse:

Being richly endowed with natural resources can threaten a countries long-term prosperity as natural resource-intensive economies grow slower over time than economies that are less natural resource-intensive.

Major explanations offered (exogenous factors):

Are Natural Resources Always A Blessing?

• terms-of-trade effect TOT: the relative price of a country's exports compared to its imports. The relative price of exports compared to imports decrease over time of resource rich countries. Because it represents a decrease in what the country gets in return for what it gives up, this is associated with a decrease in the country's welfare.

Major explanations offered (exogenous factors):

• misguided industrial policies in the form of protectionist barriers for import-substitution, which has been typical for many natural resource-intensive economies.

• resource booms allows resource-intensive economies to sustain economically harmful policies longer than less resource-intensive economies that started out with similarly unproductive policies.

Major explanations offered (endogenous factors):

• resource abundance might lead to a rentier economy with a predatory state: corruption, political conflict and inequalities are rampant, economic institutions are poorly developed, human capital accumulation, entrepeneurship and innovative activity are crowded out and policy makers are more interested in resource transfers than developing and modernizing the countries economy.

• unsustainable consumption boom, countries do not reinvest a sufficiently high amount of their resource income.

Major explanations offered (endogenous factors):