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The theory of Green Accounting Rui Mota [email protected] Tel. 21 841 9442. Ext. 3442 Tiago Domingos May 2009 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? Welfare in the Ramsey Model • Assumptions: – – – – – Discounted utilitarianism Closed economy with no government No technological progress No population growth Competitive economy max U (C (t ))e t dt s.t. c 0 dK (t ) F ( K (t )) C(t ), K (0) K0 0 dt • What is the SNA’s conventional net product (or income) measuring? – NNI = consumption + investment in capital stocks, i.e., Y C I . – Supply of goods, Y, equals demand of goods, C + I. Or resources equal uses. Welfare in the Ramsey Model max U (C )e t dt c 0 • Current-value Hamiltonian s.t. H (C , K , ) U (C ) dK dt HC 0 • First Order Conditions • Euler Equation dK F(K ) C dt d H K dt H H (C , K , ) dH dC dK d HC HK H dt dt dt dt dH dK dt dt dH H U dt National Product and Welfare, Weitzman (1976) QJE • Define Welfare at time t: W (t ) U (C ( s ))e t s t ds dH H U H (t ) W (t ) Hamilton-Jacobi-Bellman equation dt Useful Expressions: - Leibniz Integral Rule: b ( z ) f b( z ) b a f ( x , z ) dx dx f ( b ( z ), z ) f ( a ( z ), z ) a( z ) z z a( z ) z z s - ( z ) dz dx(t ) (t ) x(t ) a(t ) x(t ) a( s )e t ds t dt - Integration by parts: • Noting that t df (t ) g (t ) f ' g fg ' dt e ( s t ) ds 1 f ' g fg fg ' the HJB equation rewrites as National Product and Welfare, Weitzman (1976) QJE H (t ) W (t ) t H ( t )e s t ds U (C ( s ))e t s t ds • The Hamiltonian is the stationary equivalent of the optimal path of utility • Consider that U (C ) C , hence, the Hamiltonian is exactly the conventional net product measured in a closed economy with consumption as numeraire, i.e., H (t ) C I , where net investment I dK . dt • 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. 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., dK dt . • From the definition of welfare and using the HJB equation dW dW dK W U (C ) dt dt dt • Moreover, from the HJB equation and the above expression, dH dK dt dt • With consumption as numeraire, dW Net Investments dt • 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). 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 y pC qI , with nominal prices being p MU , q where (t ) 0 is the marginal utility of money. • Do changes in nominal net product indicate welfare changes? Nominal interest rate r y pC qI W • 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 and Real Economy • Define real net product Y PC QI , with real prices being P p , Q q (t ) 0 is the price index that deflates nominal into where real prices. • Do changes in real net product indicate welfare changes? Y PC PC Real interest rate QI R W d p p C pC pC 0 dt 2 pC • This is the definition of a Divisia price index. Hence, Y RQI R W • Growth in real net product means that welfare is increasing, if R 0 . • 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 Chained CPI, Asheim (2007) EDE • Real and nominal prices P p • A Divisia price index can be approximated in discrete time by a chain index, which is re-based every year. t 1 p C pt 1 pt Ct 1 CPI t 1 1 t p C pt Ct This implies that pt 1 Ct CPIt 1 pt Ct t t 1 CPIt 1 t CPI t 1 • The usual CPI has a fixed base year, e.g., year 0. pt C0 CPI t p0 C0 • Chained CPI may be approximated by CPIt 1 p C p C CPIt 1 t 1 0 t 1 t CPIt pt C0 pt Ct CPI t Which implies that t The usual way to deflate CPI 0 is a good proxy Multisector Optimal Growth • m-dimensional consumption bundle, including everything that influences well-being. – Includes all non-market commodities, e.g, produced at home, environmental services, … • n-dimensional capital vector (variables in bold are vectors): – 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 C(t ),I(t ) S (K(t ), t ) • The model max U (C (t ))e t dt s.t. c 0 dK I dt C(t ),I(t ) S (K(t ), t ) K(0) K 0 Criteria for Sustainability, Pezzey (2004) EDE • An economy is sustainable at time t if and only if the representative agent’s current utility does not exceed the maximum level of utility which can be sustained forever from t onwards. • This is implied by sustainability as forever non-declining utility. • One-sided sustainability test: QI 0 or Y 0 un-sustainable development. • Multisector results in real terms. – Real Net Product, Y P C Q I – Genuine Saving, Q I – Y RQ I R W Small Open Economy • Include – – – – stocks of commercial forests, stocks of minerals, welfare costs of air emissions, value of technological progress. • The capital stocks are K : ( K , K f ,S) : – Domestic man-made capital, K I CFC – Net foreign capital held privately or by the government, K f rK f X M Q R (R X R M ) – Stock of commercial natural resources S G(S) R d R X • Production K F ( K ,R d R M , t ) M X C a f (R d R X ,S) CFC Time as a capital in the production function represents technological progress Small Open Economy • Households’ utility function U (C) : U (C ,E) depends on material consumption rate and (negatively) on the flow of emissions • The vector of emissions E( F ( ),a) depends on production and abatement expenditure. • Maximize welfare subject to the above relations, and having as controls, consumption, C (t ) , all forms of extraction, Rd (t ), R X (t ), RM (t ), abatement expenditure a(t ) and M (t ) X (t ) . • Conventional (SNA) NNI: NNI : C K K f Y NNI (Q f R ) S e E Qt • Green Net National Income: R • Genuine Saving (Adjusted Net Saving): Q K Q NNI C (Q fR ) S Qt • The value of time Q (t ) Fs e R( s t )ds t t t R Small Open Economy – Human Capital • The model of the small open economy can be extended to include human capital as a form of capital, K H , i.e. assuming K : ( K , K H , K f ,S) . • Following the world bank model, human capital changes according to dK H q( m ) dt Education expenditures m are transformed in human capital by q(.) • In our expressions for GNNI and GS, – The GNNI is not altered because education expenditures are already included in the conventional NNI, as government spending. In the above model, this expenditures are considered an investment and not a form of consumption. This implies a reallocation of education expenditures that does not alter the value of NNI. – In GS just add the value of education expenditures since they are a form of investment. Small Open Economy – Table of symbols C (t ) K Consumption rate at time t Man-made capital, Kf U () Utility E() Rate of emissions of air pollutants e F () a Ri , i d , X , M MX Marginal cost of abatement = Marginal damage cost Production function Abatement expenditure Extraction of natural resources for domestic use, exports and from imports. Imports - Exports r Constant nominal interest rate S Stock of resources R Constant real interest rate QR Resource price f (R d R X ,S) fR Net foreign capital Cost of extraction of resource Marginal cost of abatement For more information check Small Open Economy • Starting from conventional SNA aggregates: – Deduct the damage from flow pollution emissions, e E – Deduct (add) the value of rents from resource depletion (or not), (Q R fR ) S – Add the value of technological progress Q t . 140000 120000 100000 GNI CFC Million € 80000 Air emissions Forest Depl. 60000 Tech. Progress GNNI 40000 Pot GNNI GNNI, T=100 20000 0 1990 -20000 1995 2000 2005 GNNI and GS in Portugal – Air Emissions • How to value a unit of emissions? – Marginal benefit of avoided emission, – Marginal cost of emission (MDC), or – Marginal abatement costs? • Marginal cost of emission per emitted pollutant [€2000/ton]: [€2000/t] SO2 NH3 NOx VOC PM2,5 Best 6872 7399 2040 1150 44000 Low High 3472 9972 3699 10999 1140 3040 450 1550 22000 64000 GNNI and GS in Portugal – Air Emissions 70 60 SO2 % of total cost 50 NH3 40 NOx VOC 30 PM 2,5 20 10 0 1990 1995 2000 2005 GNNI and GS in Portugal – Forests • National Forest Inventory 2005/06 1400 1200 Conifers Eucalyptus 10^3 ha 1000 800 600 400 200 0 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 • Average Volumes: [m3/ha] 95/98 05/06 Coniferous 88.5 82.5 Eucalyptus 55 55 GNNI and GS in Portugal – Forests 100 Coniferous Eucalyptus 50 million € 0 1990 1995 2000 2005 -50 -100 -150 -200 The depreciation of commercial forests in Portugal is on average 10% of the contribution of forestry to national product (around 4%). GNNI and GS in Portugal – Technological progress • The integral may be approximated by, 45000 40000 35000 Million € 30000 25000 20000 15000 T=17 T=20 T=40 10000 T=60 T=80 T=100 5000 T=120 Potential Qt, T=17 0 1990 1995 2000 2005 GS in Portugal 40000 35000 30000 GS, no Qt 25000 Million € GS 20000 GS, T=100 15000 Potential GS 10000 5000 0 -5000 1990 1995 2000 2005 -10000 • 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.