The theory of Green Accounting

1. The theory of Green Accounting Rui Motarmota@ist.utl.ptTel. 21 841 9442. Ext. 3442 Tiago Domingos May 2009

2. What is Sustainable Development? Brundtland report (1987) – “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 We choose non-declining utility as the criterion for sustainable development some call this Weak Sustainability, but we don’t agree  this still misses the intra-generational component What is green net national income (GNNI) and what does it measure? What is genuine saving and what does it measure?

3. Welfare in the Ramsey Model Assumptions: Discounted utilitarianism Closed economy with no government No technological progress No population growth Competitive economy What is the SNA’s conventional net product (or income) measuring? NNI = consumption + investment in capital stocks, i.e., . Supply of goods, Y, equals demand of goods, C + I. Or resources equal uses. s.t.

4. Welfare in the Ramsey Model Current-value Hamiltonian First Order Conditions Euler Equation s.t.

5. National Product and Welfare, Weitzman (1976) QJE Define Welfare at time t: Noting that the HJB equation rewrites as • Useful Expressions: • Leibniz Integral Rule: • Integration by parts: Hamilton-Jacobi-Bellman equation

6. National Product and Welfare, Weitzman (1976) QJE The Hamiltonian is the stationary equivalent of the optimal path of utility Consider that , hence, the Hamiltonian is exactly the conventional net product measured in a closed economy with consumption as numeraire, i.e., , where net investment . Welfare significance of net product or income: The maximum welfare attainable is what would be obtained if one could consume all the net product in each period. From the HJB equation changes in net product measure changes in welfare.

7. Genuine Saving in the Ramsey Model What is the welfare significance of net saving/investment? Net saving/investment – Value of the portion of net product not used in consumption, i.e., . From the definition of welfare and using the HJB equation Moreover, from the HJB equation and the above expression, With consumption as numeraire, Net investment indicates changes in welfare (Negative net investment indicates decreasing welfare). Measuring negative net saving at a point in time implies that future utility will be less than current utility over some period of time (Hamilton, 2000 WB).

8. Nominal and Real Economy, Asheim and Weitzman (2001) EL Problems: Utility is not observable. Hamiltonian is in Utils as numeraire. The national accountant has to convert observable market prices in money units to utils. Define nominal net product , with nominal prices being where is the marginal utility of money. Do changes in nominal net product indicate welfare changes? Positive nominal net product does not measure welfare improvements. Net product should be measured in constant consumption prices. Only consumption goods should be used as quantity weights in the price index. Nominal interest rate

9. Nominal and Real Economy Define real net product , with real prices being where is the price index that deflates nominal into real prices. Do changes in real net product indicate welfare changes? This is the definition of a Divisia price index. Hence, Growth in real net product means that welfare is increasing, if . Net saving measures the instantaneous change in welfare. Both nominal and real net saving have the same welfare significance. Change in Net Product is equal to interest on Net Saving. Check theory Real interest rate