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National Accounts and Measures of Sustainability. Rui Mota Tel. 21 841 9440 Ext. 3440 Tiago Domingos October 2011. National Accounts Identity. C. I. X. M. Main Aggregates. Subtract CFC. Main Aggregates. National (Residence). + Primary income flows from ROW.

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national accounts and measures of sustainability

National Accounts and Measures of Sustainability

Rui Motarmota@ist.utl.ptTel. 21 841 9440 Ext. 3440

Tiago Domingos

October 2011


Main Aggregates

Subtract CFC


Main Aggregates



+ Primary income flows from ROW

- Primary income flows to ROW

Product / Income




+ Consumption Fixed Capital (CFC)

- Consumption of Fixed Capital (CFC)

Aggregate X


X – Domestic produc, Income, Saving, Disposable income, ...

GNI = GDP + Y’RM . Where Y’RM = Netincome payable to non-resident units for production factors.

Domestic Product vs. National Income

Source: AMECO database


GDP growth rate

Source: AMECO database


Net Saving in Portugal [Mrd euros 2000]

  • Net savings are negative when consumption is higher than net disposable income

Source: AMECO database


Sustainable Development

  • “Development that meets the needs of the present without compromising the ability of future generations to meet their own need.”
    • Intra- and inter-generational equity
    • Anthropocentric
  • Sustainability of what?
    • non-declining aggregate output or consumption,
    • non-declining utility,
    • non-declining aggregate resources (productive base),
    • non-increasing pollution, …
  • Weak vs. Strong Sustainability
    • Limits to substitution,
      • Is the combined value of all assets remain constant, that is, it is possible to substitute one form of capital for another, so natural capital can be depleted or the environment degraded as long as there are compensating investments in other types of capital?
    • Critical levels of natural capital.

International Efforts

  • World Bank’s Adjusted Net Savings (Genuine Savings)
    • Rate of savings after taking into account investment in human capital, depletion of natural resources and damage caused by pollution. Time series (1970 - …) for 140 countries. (
  • European Commission (
    • Indices to measure progress integrated into the decision-making and public debate?
    • “We cannot face the challenges of the future with the tools of the past. It's time to go beyond GDP.” Durão Barroso
    • Extending European National Accounts to environmental and social issues.
  • OECD work on alternative measures of welfare (
    • Extending GDP to include leisure time and inequality. Changes in country rankings
  • Stiglitz Commission (
    • Identify the limits of GDP as an indicator of economic performance and social progress.
  • SEEA 2003, United Nations (
    • Satellite system of the SNA including economic and environmental information in a single framework to measure the contribution of the environment to the economy and vice-versa.

World Bank’s Genuine Savings

  • Resource Curse: Countries dependent on natural resources tend to depict unsustainable development (negative GS).

Sustainability vs Optimality

  • A Sustainable Economic path at time t is one that obeyswhere is the maximum sustainable utility, defined as
  • A Present Value Optimal path is one that results from the maximization of Present Value (PV):
  • Future utility is being discounted with a constant discount rate
  • Hicks (1946) : Individual’s income “maximum amount of money which the individual can spend this week, and still expect to be able to spend the same amount in real terms in each ensuing week".

Sustainability vs Optimality (DH economy)

  • If C(t) > Cm(t) then C(t) must decline to below Cm(t) at some future time.
  • For low enough discount rates, the path is sustainable.
  • For high enough discount rates, the path is unsustainable.
  • These conclusions also depend on the assumption that man-made capital is more important to production than the resource.
dynamic optimization cake eating economy
Dynamic Optimization: Cake-Eating Economy

What is the optimal path for an economy “eating” a cake?

Optimal System:

Optimal and sustainable?

subject to


Dasgupta-Heal Model

  • Capital resource economy with no technological progress:
  • Production can be used to consume or invest:
  • Extraction of a non-renewable resource used in production
  • Optimal Path:
  • Hotelling’s rule
  • Ramsey’s rule
  • Optimal and sustainable?

subject to



  • Capital resourceeconomywithCobb-Douglasproduction:
  • Factorsofproduction are essential. Butwithdifferentimportance (factor elasticities).
  • Elasticityofsubstitution: Provides a measure of how easy it is to substitute one input for another in production (curvature of isoquants).

Constant Elasticity of Substitution (CES)







 = 1








 = 0

 = 





 = 1




 < 1







Sustainability vs Optimality (Cobb-Douglas)

  • Consumption tends to zero (resources are essential).
  • Since K is more important to production than R, then Cm(t) is positive.
  • Consumption becomes unsustainable (C >Cm) before it becomes unsustained (C >F).

Sustainability vs Optimality

  • For low enough discount rates, the path is sustainable.
  • For high enough discount rates, the path is unsustainable.
  • These conclusions also depend on the assumption that man-made capital is more important to production than the resource.

Hartwick’s Rule

  • Can this economy maintain constant consumption even though the resource is being depleted?
  • What is the role of substitution between man-made capital K and the natural resource R in the production of the composite good?
  • If then
  • Net investments = value of the ‘revenues’ from exploitation
  • If the accumulation of man-made capital always exactly compensates in value for the resource depletion, then consumption remains constant at the maximum sustainable level.

To Sum Up

  • In Cobb-Douglas, consumption declines to zero (with no tech. progress).
  • If the elasticity of substitution is > 1 (man-made capital is more important than exhaustible capital), such resources are not essential for production, so consumption may not decline to zero.
  • If consumers are sufficiently patient (low discount rates – high value to the future), then consumption will be sustained in the optimal path.
  • If there is technological progress, it is possible to sustain consumption even if inputs are complements (no substitution).
  • The effect of essential resources may be offset by sufficient substitution possibilities and technological progress.
m-dimensional consumption bundle, including everything that influences well-being.

Includes all market and non-market commodities, e.g, produced at home, environmental services, …

n-dimensional capital vector:

Includes man-made capital, natural resources, human capital (education and knowledge) and foreign capital. Time is included as a capital, to depict technological progress in production.

Attainable production possibilities

The model

Green Accounting Theory



Green Accounting Theory

  • Green Net National Income
  • Genuine Savings
  • Changes in Green Net National Product measure changes in welfare.
  • Genuine Savings measure changes in welfare.
  • Define sustainable development as:
    • - non-decreasing utility.
  • Then, a one-sided sustainability test is (Pezzey, 2004)
  • un-sustainable development.

stocks of commercial forests,

welfare costs of air emissions,

The capital stocks are :

Domestic man-made capital,

Net foreign capital held privately or by the government,

Stock of commercial natural resources

Human capital


Small Open Economy

Households’ utility function depends on material consumption rate and (negatively) on the flow of emissions

The vector of emissions depends on production and abatement expenditure.

Maximize welfare subject to the dynamics of the forms of capital considered.

Green Net National Income:

Genuine Saving:

The value technological progress (TFP):

Small Open Economy

Starting from conventional SNA aggregates:

Deduct the damage from flow pollution emissions,

Deduct (add) the value of rents from resource depletion (or not),

GNNI and GS in Portugal

Impacts considered:

Exposure to PM2.5 and ozone

Health damages of PM2.5 (both acute and chronic effects) and ozone, O3 (only acute). Both long-term (chronic) and short-term (acute). Both mortality (i.e. deaths) and morbidity (i.e. illness)

Marginal cost of emission per emitted pollutant [€2000/ton]:

GNNI and GS in Portugal – Air Emissions


GNNI and GS in Portugal – Air Emissions

  • The damages from air emissions are around 8% of Portuguese GNI: - [4, 11]% GNI

GNNI and GS in Portugal – Forests

The depreciation of commercial forests in Portugal is on average 10% of the contribution of forestry to national product (around 4%).

Without the value of time – Decreasing tendency throughout the period and negative GS after 2002.

With the value of time – Decreasing tendency until 2001, but GS are always positive.

Genuine Savings


Sustainability Message

  • In 1993, SO2 costs of emissions, which represent around 30% of total emission costs, decreased substantially. Increases welfare but does not counteract the loss of production.
The depletion of water resources.

The depletion of biodiversity.

Depletion of stocks of fish.

Inclusion of the value of ecosystem services.

Soil quality.

Distributional issues (intragenerational concerns).

Looking at an extended but incomplete range of assets may produce a result further from the truth

Indicators need to be treated with caution as tests for sustainable development and guides to policy.


What’s Missing?