Welfare and Sustainability Measures for Portugal, 1992 ' 2004

Welfare and sustainability measures for Portugal, 1992 - 2004

Rui Pedro Mota, Tiago Domingos and Victor Martins Environment and Energy Section, DEM, Instituto Superior Técnico Address: Avenida Rovisco Pais, 1, 1049-001 Lisboa, Portugal. Phone: +351 - 218 419 442, Fax: +351- 218 417 365, E-mail: [email protected].

Abstract

The context of this paper is the measurement of welfare and sustainability dynamic economies, or in others words, green accounting. In this context, sustainability is usually concerned with intergenerational equity and is de…ned informally as non-declining utility. The objectives of this paper are to contribute to the theory of welfare measures in dynamic economies and sustainability by empirically estimating the GNNP and GS for a particular economy, and thereby showing the impact of some assumptions on the measures of welfare and sustainability; to contribute to the discussion of sustainability in Portugal, by estimating the GNNP and GS for the period 1991 - 2004, where economic and environmental data are analyzed in a theoretically coherent framework; and …nally to contribute to the theory of green accounting by testing empirically a theoretical result for Portugal - the mismatch found by Pezzey et al., (2006). This paper hints at the possibility of the mismatch to be explained through empirical assumptions rather than fundamental changes in the theory. Keywords: Welfare measures, green accounting, technological progress, theory mismatch. JEL Classi…cation: Q20, C51, C55

1 1 Introduction

The seminal paper that paved the way for all the subsequent developments allowing the construction of a theory of welfare accounting was Weitzman’s(1976) "On the welfare signi…cance of National Product in a Dynamic Economy". This paper provided a relationship between sustainability and national accounting. More precisely, in the optimal path of a dynamic economy with a stationary technology and perfect competition, where the social objective is to maximize a discounted utilitarian welfare function, Weitzman was able to show that the NNP (measured as the sum of consumption and investment) in the current period is proportional to the maximum welfare attainable along the optimal path. One important aspect of Weitzman’s result is, therefore, the interpretation of NNP as a static equivalent to future utility. Following Asheim (2007) and entailing that dynamic welfare corresponds to a discounted utilitarian welfare function, this result is presented with a clearer relation to welfare accounting as, dynamic welfare is improving if and only if NNP is improving, along the optimal path. Improving NNP means that net investments are positive. The concept of NNP should be interpreted in a broader sense to include, in addition to physical capital, natural resources and stocks of knowledge resulting from learning and research activities (Weitzman, 1976). Net investment interpreted in this manner has been termed genuine savings by Hamilton and Clemens (1999). However, Weitzman (1976) assumes that the utility function is a linear function of a vector of consumption goods and that the objective of the economy is to follow a discounted utilitarian path. Asheim and Weitzman (2001) prove that the welfare interpretation of NNP holds if the utility function is not a linear function of a vector of consumption goods, under the provision that NNP is de‡ated by a consumer price index. The interpretation still holds even if dynamic welfare does not correspond to a discounted utilitarian welfare function (Asheim and Buchholz, 2004). The debate on how to de‡ate green NNP to obtain a measure of welfare in a comprehensive setting is still unresolved (see for instance Sefton and Weale, 2006; Li and Löfgren, 2006; and Asheim, 2007). Concerning the empirical application of the green accounting theory, Repetto et al., (1989) …rst calculated green NNP to include subsoil assets (petroleum) and agricultural soils, in addition to forest resources in a study conducted by the World Resources Insti- tute in Indonesia for the period 1970-84. This paper popularized the net price approach for estimating net investment and valuing the timber stock, found that net investment in timber was substantially smaller than for petroleum and substantially larger than for agricultural soils, and was equivalent to approximately 5 percent of GDP and 25 percent of gross domestic investment. After this study many came. Vincent and Hartwick (1998) obtained and reviewed more than 30 studies for incorporating environmental resources into the national accounts, of more than 20 countries since the late 1980s. Concerning the depletion of natural resources, such as oil and other exhaustible assets, forest and agricultural assets, the adjustment is equal to 0.2 - 4 percent of GDP for all the studies. Measuring sustainability has often been done using just a measure of green net investment, for example by Pearce and Atkinson (1993), Atkinson et al. (1997) or Hamilton and Clemens (1999). Pearce and Atkinson (1993) used data for 18 countries, from the USA to Burkina Faso, in which they relied on savings instead of investment data to calculate the net increase in built capital. The value of changes in natural capital were calculated by using data on net changes in resource stocks valued at current market prices. Rough adjustments also were made for the ‡ow of di¤erent environmental disamenities.

2 Hamilton and Atkinson (1996) devised a simple model treating air emissions as cumula- tive pollutants is used to derive measures of ”green net national product”. They found that genuine savings ranged from [-4, 14] % of GDP in Europe and that, air pollution damage as percent of GDP in Europe is about 1 - 8 % of GDP. Concerning sustainability, the only formal proof available, so far, to test if a development path is sustainable was presented in Pezzey (2004). Pezzey proves that, if an economy with multiple consumption goods (including environmental amenities) uniquely maximizes present value with constant discounting, it is unsustainable at some time if either of two measures— augmented net investment, or the change in augmented green net national product— are zero or negative then. ”Augmented”denotes that time is treated as a productive stock, which includes in each measure the value of future, exogenous changes in technology or terms of trade. Most studies on green accounting ignore technical progress and shifts in the terms of trade. These are considered to be the most important e¤ects that cause exogenous shifts in production possibilities. The most cited papers are Weitzman (1997) and Weitzman and Löfgren (1997) on exogenous technical progress (estimates the technological progress premium) and Vincent et al., (1997) focusing on exogenous shifts in oil export prices facing Indonesia. The empirical results suggest that by neglecting exogenous technological growth, one obtains a downward biased estimate of GNNP. Estimates on Weitzman (1997) and Weitzman and Löfgren (1997) imply that this bias can be as high as 40-50%, that is to say, the ”true”annuity equivalent is obtained by scaling current NNP by 1.4-1.5. Pezzey et al., (2006) estimate and compare two empirical measures of the weak sustainability of an economy: the change in augmented Green Net National Product (gNNP), and the interest on augmented Genuine Savings (GS) thereby providing an emprirical test of the general framework. Yearly calculations are given for each measure for Scotland during 1992–1999. They found that the change in augmented gNNP greatly exceeds the interest on augmented GS even when macroeconomic ‡uctuations are taken into account. This is a mismatch which poses an unresolved problem with the theory. In the next section we present the general theory and the results relevant for welfare measurement and sustainability in section 2. In order to estimate the GNNP and GS for Portugal, we specify a model of a small open dynamic economy in section 3 adapted from Pezzey et al, (2006). In section 4 the data and the estimated welfare and sustainability indicators are presented and some comments on the results are made. Section 5 concludes.

2 The theory of green accounting

Consider a continuous-time, representative agent, competitive, time autonomous, determin- istic, constant population economy. The m-dimensional consumption bundle C(t) contains everything that in‡uences well-being U(C(t)), where U( ) is concave, non-decreasing and as smooth as required1. More speci…cally, component i ofC(t) measures the instantaneous ‡ow of consumption services from consuming at the rate of Ci(t) units of commodity i per unit time at the instant t, for i = 1; 2; :::; m. The consumption vector is conceptualized as a complete list containing everything that in‡uences current well-being, including environmental amenities and other externalities. Consumption here would ideally include all components that determine the true ”standard of living”. As stated by Weitzman (2003), ’notjust goods we buy in stores and the governments services "purchased" with our taxes,

1 The convention throughout the text is that vectors are represented in bold.

3 but all non-market commodities, such as those produced at home, and environmental services, such as those rendered by natural capital like forest and clean air.’ We assume that income accounting is complete in the sense that comprehensive consumption is presumed to be fully observable, along with its associated m-vector of competitive e¢ cient prices. Suppose that there are n capital goods that include natural resources, man-made capital, human capital (education and knowledge accumulated in R&D) and foreign capital, forming a vector K(t). The stock of capital of type i (1 i n) existent at time t is denoted by Ki(t), and its corresponding net (of depreciation) investment ‡ow is Ii(t) = K_ i(t). Hence the n-vector of net investments is I(t) := K_ (t). Thinking of a natural capital asset like a commercial forest, the net investment ‡ow of the resource would be negative whenever the overall harvest rate exceeds its natural regeneration rate. So, net investment of a natural asset is positive (negative) whenever the assets is being built up (depleted). It is required that the attainable possibilities of consumption and investment at any time can be described as a function of the capital stocks existing at that time and time itself. Therefore, a consumption-investment pair (C(t); I(t)) is attainable at time t from the capital stock K(t) if and only if C(t); I(t) S K(t); t , where S is a convex attainable production possibility set with freef disposalg (Weitzman, 2 f g 2003). The time argument is inserted to denote non-autonomous time e¤ects on the production possibilities frontier. For instance, in the model developed for a small open economy, this corresponds to growth in national production not attributable to any production factor. Having this stated, we assume that, seeking to maximize intertemporal welfare with a utility constant discount rate > 0, the representative agent (or central planner, or benevolent dictator) chooses paths of consumption C(t) and net (of depreciation) investment subject to a smooth and convex production possibility set A, with initially given capital stocks K(0) = K0, i.e., the multisector optimal growth model is of the form

1 t max U(C(t))e dt; (1) C;I Z0 subject to the constraints C(t); I(t) S K(t); t ; (2) f g 2 f g or equivalently, the s production possibilities constraints

F^k (C(t); I(t); K(t); t) 0; k = 1; :::; s the di¤erential equations K_ (t) = I(t); (3) and obeying the initial conditions K(0) = K0: De…ne the current-value Hamiltonian, Hc(C; I; ) := U(C) + cI for each t, where c is the vector of current shadow investment prices (co-state variables) in utility numeraire2. Assume that there exists a unique trajectory (C(t); I(t); K(t)) that solves the multisector optimal growth problem for K0 > 0. Hence, by Pontryagin’s Maximum Principle, (C (t); I (t)) maximizes H(C(t); I(t); (t)) at each t, subject to F^k (C(t); I(t); K(t); t) 0. 2 The current value Hamiltonian relates to the present value Hamiltonian as Hc( ) := etHp( ), such that the current and present shadow prices obey c(t) := et p(t). We drop the superscript c in the text, so (t) and H( ) are the vector of current value co-state variables and the hamiltonian respectively.

4 Assume there exists a vector of piecewise continuous functions = (1; :::; s). De…ne the Lagrangean, L(C; I; K; ; t) = H(C; I; ; t) + F^ (C(t); I(t); K(t)) The solution (C(t); I(t); K(t)) maximizes L(C; I; K; ; t) with respect to (w.r.t) the controls C(t) and I(t). This provides the …rst order conditions. Additionally, (t) obeys the Euler equations

_ (t) = KL(C(t); I(t); K(t); (t); t); (4) 5 t 3 and the transversality conditions limt (t)K(t)e = 0 are veri…ed . Also, on the ^ !1 optimal path, k(t) = 0 if Fk (C(t); I(t); K(t)) > 0, otherwise, k(t) 0. This in ^ particular implies that kFk ( ) = 0. As Weitzman (2003) stresses, probably the single most important idea in all of economics is Adam Smith’sfamous insight that ferocious competition in the marketplace, far from being the formula for chaos and decay that it seems at …rst glance to be, actually induces an allocation so orderly that the result is as if guided by an "invisible hand". The rigorous mathematical essence of the modern version of the invisible hand principle is that there exists a fundamental isomorphism between "resource allocation as a constrained optimization problem" and "resource allocation as a competitive equilibrium". Loosely speaking, every allocation of resources that can be described as a solution of a constrained optimization problem can also be described or interpreted as being the outcome of a competitive equilibrium - and vice-versa. The maximum principle of optimal control theory …ts this paradigm exactly. For more on this see Weitzman (2003, p.99) or Asheim (2000, p.28). De…ne the maximized intertemporal welfare at time t as

1 (s t) W (t) := U(C(s))e ds: (5) Zt This quantity is also termed dynamic welfare in Asheim (2007).

Proposition 1 (Hamilton-Jacobi-Bellman Equation) For the multisector optimal growth model, if (C(t); I(t); K(t)) is an optimal solution starting at time t, then

1 (s t) W (t) = U(C(t)) + (t)I(t) + Lt(t)e ds (6) Zt is true for any t.

Proof. Take the total derivative of the maximized Lagrangean

L (C; I; K; ; ; t) = U(C) + I + F^ (C; I; K; t) with respect to (w.r.t.) time,

d @L( ) L ( ) = C_ C L( ) + I_ I L( ) + K_ K L( ) + _ L( ) + _ L( ) + : dt 5 5 5 5 5 @t

Since we are evaluating welfare changes on the optimal path, CL( ) = 0 = IL( ), the 5 5 third and fou rth terms cancel since _ = KL( ) and L ( ) = I = K_ . From the 5 5 3 KL( ) represents a vector of derivatives w.r.t. each component of the vector K. 5

5 ^ …rst order conditions for the controls, CL( ) = 0 CU(C) = CF (C; I; K) ^ 5 , 5 5 since CF (C; I; K) < 0 and CU(C) > 0 then k(t) > 0. This implies that L( ) = ~ 5 5 5 Fk ( ) = 0 and so we obtain dL (t) @L (t) = I . dt @t ^ _ Substituting the Lagrangean L( ), and noting that kFk ( ) = 0, we get L (t) = (L(t) U(C(t))) (s t) (s t) Lt(t). Integrating in [t; [ we obtain L(t)+ t1 Lt(t)e ds = t1 U(C(s))e ds. which is equation 6. 1 R R Equivalently we could have used the time t as a stock, by including the state equation _ t _ t t t = 1 (I = 1) obeying the Euler equation = Lt(t). This allows to write the t t (s t) above result as W (t) = U(C(t)) + (t)I(t) + , where = t1 Lt(t)e ds from integrating the Euler condition for the stock of time. R This result is interpreted in Weitzman (2003) as the Wealth and Income version of the Maximum Principle. Think of a simple model with one composite consumption good _ consumed at rate c(t), and de…ne Y (t) := c(t) + (t)K(t) as NNP as conventionally measured (in monetary units) by the sum of consumption expenditures and net investments. Now, it is possible to rewrite the Hamilton-Jacobi-Bellman (HJB) equation as

1 (s t) 1 (s t) C(s)e ds = Y (t)e ds. (7) Zt Zt This interpretation is the fundamental result of Weitzman (1976) and can be stated as ’the maximum welfare actually attainable from time t on along a competitive trajectory (right hand side (RHS) of 7) is exactly the same as what would be obtained from the hypothetical consumption level Y (t). Hence, in this simpli…ed setting, NNP is what can be called a stationary equivalent of future consumption. Note that proposition 1 means that changes in the stock of forward looking welfare can be picked up by changes in the ‡ow of the value of current net product. More speci…cally, this proposition relates current intertemporal welfare, which needs information from the future to be calculated, to a quantity that only uses information from current time t, namely the stocks’initial conditions Kt, and the initial conditions for the controls that put the economy on the optimal path, Ct and It. So, according to proposition 1 the welfare signi…cance of the utility-NNP is the following:

along the optimal path, changes in real utility-NNP are proportional to changes in dynamic welfare.

Proposition 1 allows to prove the fundamental result about the welfare signi…cance of net investments.

Proposition 2 (Utility-GS) Under the assumptions of proposition 1,

t W_ (t) = (t)I(t) + (8) holds for any t.

_ (s t) Proof. Using the Leibniz rule, W (t) = t1 U(C(s))e ds U(C(t)) = W (t) U(C (t)), which is the di¤erence between interest on the value of total discounted future R

6 utility W (t) and current utility U(C(t)). For the optimal trajectory, the HJB equation can be used on the above expression to obtain expression 8.

The RHS of expression 8 represents the genuine investment with utility as numeraire, and it is this term, but in monetary units, that is called adjusted net savings or genuine savings (GS) (Hamilton, 2000). The welfare signi…cance of the genuine investment is the following: along the optimal path, genuine investment with utility as numeraire measures changes in dynamic welfare, i.e., having instantaneous positive net investment is equivalent to having increasing instantaneous dynamic welfare. Our aim is to infer future welfare from present observations of the current competitive economy. At …rst glance, it seems that proposition 1 provides a way to do just this. There are, however, two fundamental problems. First, all consumption goods are aggregated in the utility function that is not observable by the national income accountant. Second, as stated above, prices of investment goods are expressed in utils (utility as numeraire) and the national accountant does not know how to de‡ate money prices into utils. No quantity can be measured in utility units from a real economy. Propositions 1 and 2 will not be useful in the real competitive economy where only competitive money prices are observable. In the green accounting literature, measurable NNP here Y (t), is frequently de…ned making use of a linear approximation of the maximized hamiltonian using a …rst order approximation of U(C) CU(C)C (Hartwick, 1990; Hamilton, 2000). Dasgupta and Mäller (2000) agree with the 5 welfare interpretation of the Hamiltonian as utility NNP when they state that "the Hamiltonian equals constant-equivalent utility". However, since "both theory and empirics imply that the Hamiltonian is a non-linear function of consumption and leisure", they do not agree that a linearized version of the utility NNP could have any welfare signi…cance. This result has been proved wrong by Asheim and Weitzman (2001), showing that de‡ated by an appropriate Divisia consumer price index (transforms utility metrics into real Divisia prices) growth in real NNP can indicate welfare improvement. In order to obtain welfare measures we de…ne NNP in real Divisia prices as,

t Y (t) := P(t)C(t) + Q(t)I(t) + Q (t) = P(t)C(t) + Qy(t)Iy(t), (9) where P(t) and Q(t) are the vectors of real prices for consumption and net investment. PC represent the consumption expenditures and QyIy the real augmented net investment (genuine savings). What is the welfare signi…cance of a NNP in monetary units (real prices), i.e. in what conditions do the previous results follow to the linear index of national production in 9. The vectors of real Divisia prices for consumption and net investment are de…ned, re- t t spectively, as, P(t) := CU(C(t))=(t), Q(t) := (t)=(t) and Q (t) := (t)=(t) where 5 _ (t) > 0 is an extended price index verifying P(t)C(t) = 0. This is the Divisia property of price indices but in continuous time. For a discussion on (Divisia) price indices in continuous time see the appendix in Asheim (2007). Asheim and Weitzman (2001) use (t) = (t)(t), where (t) > 0 is the not directly- observable marginal utility of current expenditures and (t) > 0 is a Divisia consumer price index satisfying _ (t) _p(t)C (t) = ; (t) p(t)C(t) _ which implies that, P(t)C(t) = 0. For a thorough discussion on the interpretations of (t) and (t) see Weitzman (2003).

7 So, Asheim and Weitzman (2001) de…ne nominal consumption and investment prices as p(t) := CU(C(t))=(t) and q(t) := (t)=(t), and a nominal interest rate at time t, r(t), given by5r(t) := _ (t)=(t). The corresponding real prices are de…ned as P(t) := p(t)=(t) and Q(t) := q(t)=(t). It is then possible to show that,

Proposition 3 Under the given assumptions, R(t) Y_ (t) = R(t) Q(t)I (t) + Qt(t) := R(t)Q (t)I (t) = W_ (t) (10) y y (t) where the real interest rate R(t) := _ = holds for any t. Proof. For simplicity drop the time argument in all the functions. Since PC_ = 0, then Y_ = P C_ + d Q I =dt. Taking the time derivative of the HJB equation, W_ = y y CU(C )C_ + d I =dt. Making use of the de…nitions of real prices we obtain W_ = 5 y y PC_ + d Q I =dt. Proposition 2 in real prices is W_ = Q I . Substituting this in y y y y _ the last expression obtained and rearranging, we have QyIy = PC+d QyIy =dt + _ QyIy. Rearranging and using again proposition 2 in real prices we obtain the desired result.

The second equality comes from rewriting proposition (2) in real prices, and allows to conclude that, provided that R(t) > 0, instantaneous changes in real NNP de‡ated by a consumer price index have the same sign as changes in welfare at that same instant. Asheim (2007) states that "provided that real consumption interest rate is positive, growth in real NNP (de‡ated by a consumer price index) in …xed net investment prices can be used to measure welfare improvement along the optimal path". Note that substituting the de…nition of Y (t) in the …rst equality of proposition 3 and R(s t) integrating we obtain that Y (t) = R t1 PC(s)e ds if the real interest rate is constant. t R t @Y (s) R(s t) Concerning the value of time, Q ,it is straightforward to obtain Q = t1 @s e ds. Following Pezzey (2004) let us de…ne a sustainable economic path. R De…nition 4 A sustainable economic path at time t is one that obeys U(C(t)) U m(t), where U m(t) is the maximum sustainable utility, de…ned as U m(t) := max U subject to U(C(s)) U for all s t. This de…nition is generally implied by the de…nition of sustainability as forever non- declining utility. With this de…nition of a sustainable path, Pezzey (2004) showed the following result, which he called the ’one-sided unsustainability test’:

Proposition 5 (One-sided sustainability test) Under the given assumptions (with a unique non-constant utility path), at t,

m Qy(t)Iy(t) 0 or Y_ (t) 0 U(C(t)) > U (t). ) Proposition 5 is equivalent to stating that measuring non-positive real net investment (genuine savings) or non-rising real NP at instant t means that the optimal economy is in an unsustainable development path. At time t, current utility (or consumption, if U(C) is

8 monotonically increased with C) is higher than the maximum sustainable utility, implying that utility will decrease at some future time. However, positive net investment or genuine savings do not entail that the economy is sustainable. So far no general test for sustainability is known. Incidentally, proposition 3 provides a way to test empirically the underlying theory, by estimating both the change in green NNP (here Y ) and the interest on genuine savings (here RQyIy), on the …rst equality,

Change in green NNP = interest on GS for both changes in real NNP and real genuine savings can be measured (approximately) in real economies.

3 Small open economy

We will consider, then, a model of a small open economy which is adapted from Pezzey et al. (2006). This model is itself a particular case of the multisector optimal growth model of section 2. Concerning the capital stocks of this economy we have the vector K := K;Kf ; S . Let S represent the vector of stocks of commercial renewable natural resources, K be the stock of domestic man-made capital, which grows at the rate of gross investment (Domestic Fixed Capital Formation) I minus depreciation K, as in

K_ = I K, (11) and Kf represent the stock of net foreign capital held privately or by the government, which earns a return at the exogenous, constant world interest rate r. Let Kf grow as a result of interest on the capital plus exports KX minus imports KM according to

K_ f = rKf + KX KM . (12) The stock of commercial renewable natural resources is harvested for domestic use in the production process, Rd, and for export, RX , and regenerates at the natural rate, G(S). Therefore, S changes according to,

S_ = G(S) (Rd + RX ). (13) Production with non-autonomous technological progress uses the stock of man-made capital along with the domestic commercial resources harvested and imported to produce a consumption/investment good, as in F (K; Rd + RM ; t). Part of the natural resources is exported at world market prices QR. The stock of natural assets imported is valued also at world market prices. So, the net value of resource transactions is QR RX RM , and adds to the production of the consumption good and to net imports KM KX , to be used for material consumption, gross investment I, …rms’pollution abatement current expenditure, a and harvesting, with the …rm’sharvesting cost function, f(Rd + RX ; S). Formally,

F (K; Rd + RM ; t) + QR RX RM + KM KX = I + a + C + f(Rd + RX ; S). Rewriting this expression in a more familiar manner, we have,

K_ = F (K; Rd +RM ; t)+KM KX +QR RX RM C f(Rd +RX ; S) a K. (14) 9 Regarding the household’s utility function, we assume that U(C) = U (C; E), where C is material consumption, and E is a vector of emission ‡ows, dependent on resource use and abatement expenditure, E Rd; a . In fact, we could have the vector of emissions dependent on production and abatement that it wouldn’t change the formulas for the genuine saving and green NNP derived below. Each emission level Ei ( ), depends on domestic resource use Rd and abatement expenditure ai for each pollutant i = 1; ::: The marginal cost of abating pollutant i, is denoted by 1 @Ei ( ) ei := . (15) @ai Consider that the vector of marginal costs of abating pollution emission is, e = e1; :::; ei; ::: . In the context of discounted utilitarianism, we assume that the central planner for this economy acts to maximize the PV-utility as in 1 subject to the economic dynamics given by 14, 12 and 13. In order to achieve this objective, the central planner controls C, Rd,RX , RM , a, and KM KX . In accordance with simple national accounts procedures we identify NNP in this setting as NNP := C + K_ + K_ f . (16) All functions are assumed to be as smooth and convex as necessary for the propositions of section 2 to apply. Accordingly, we have

Proposition 6 (GNNP and GS) For the economy described above, green NNP is given by R t gNNP : Y = NNP + (Q fR)S_ eE+Q , (17) and genuine saving by

R t GS : QK_ = NNP C + (Q fR)S_ +Q , (18) where t 1 R(s t) Q = Fs(s)e ds. (19) Zt Proof. According to the maximum principle in 2 the Hamiltonian for this problem is H(C;I; ; t), where the arguments are the vectors of consumption rates C = (C; E), gross investment I = K;_ K_ f ; S_ and investment prices = K ; Kf ; S; t . The …rst order d X M conditions, i.e., Hi ( ) = 0with i representing the control variables C, R ,R , R , a, and M X K K S K R K K , respectively imply that = UC , (FRd fRd ) = , Q fRX = S K R K Kf , FRM Q = 0, UE = eUC and = . Noting that fRX = fRd := fR R C E and F d = F M implies that Q = F d . Using the real Divisia prices P = P ; P R R R K Kf S C K K R S and Q = Q ;Q ; Q , these conditions imply that P = Q , Q Q fR = Q , f QK = QK and P E = eP C . These conditions allow to rewrite equation 9 and real genuine savings QI, respectively as,

C f R t Y = P C + K_ + K_ + Q fR S_ eE + Q , C n f R t o QI = P K_ + K_ + Q fR S_ +Q . n o 10 Now, rewriting the Divisia price index property, PC_ = 0, using PE = eP C , we obtain, P_ C _eE = . (20) P C (C eE) We assume that _e = 0, due to lack of data on the evolution of marginal damage costs. This way, P C can be set to unity, yielding expressions 17 and 18.

Equations 17 and 18 show the adjustments necessary to reach to gNNP from the usual NNP:

deduct the amenity cost of emission eE; R deduct the value of rents from resource stock depletion (Q fR)S_ . Basically, these are the expressions we will estimate for Portugal (1990 - 2004) in chapter 4. As it could be perceived throughout this section there is an endless number of di¤erent ways that one could use to integrate di¤erent concerns about the environment.

4 Green accounting in Portugal

This chapter uses the formal theory of green (or welfare) accounting presented is section 2 and further speci…ed in section 3 to estimate a measure of welfare and a measure of the extent to which Portugal is on a path of sustainable development. Namely, the GNNP and the GS formulas given in 17 and 18. We include the damages from air pollution ‡ows as a disamenity, and the depletion of commercial forests in Portugal for the years 1992 - 2004. The major problem with performing green or welfare accounting is data (un)availability. So, the main purpose of this section is not to specify thoroughly the way to proceed to derive measures of welfare and sustainability from the national accounts, but instead, and as the …rst approximation of these measures for Portugal, to indicate the di¢ culties and drawbacks behind the calculations of a green accounting aggregate. Here, we work with e of 2000.

4.1 Pollution emissions and valuation For each pollutant considered, the term to be included in the calculations of the green NNP and genuine savings is the product of the vector of emission ‡ows multiplied by an estimate of either the marginal bene…t of abatement (also termed the marginal damage cost - MDC) or the marginal costs of abatement. The basic question in valuing air pollution emissions is which of these to choose. Note, however, that this distinction makes sense only away from the optimum, since on the optimal path these costs are equal. In this case, according to Atkinson et al. (1997, p. 87), if we assume that the current state of the economy is one of overpolluting, then the marginal social costs provide an upper bound on the value of optimal pollution emissions. If underpollution is the case, then marginal social costs provide a lower bound on the optimal emission value. Therefore, using MDC should be viewed as an upper limit estimate and interpreted accordingly. This implies, in addition, that the deduction for pollution emissions in the welfare measure will decrease as the optimum is approached, which is a desirable property. On the other hand, using marginal abatement costs to value emissions will not lead to an unequivocal direction of bias in the estimates of the value of pollution (Atkinson et al., 1997). If the economy is overpolluting, then marginal abatement costs will be below the optimal and emissions above.

11 For all pollutants considered, we used data for marginal damage costs (MDC) rather than for marginal abatement costs, because the former were the only available. Using the preceding model, we wish to estimate the value of air pollution in Portugal caused by carbon dioxide (CO2), sulphur dioxide (SO2), nitrogen oxides (NOx), particulate matter (PM10), volatile organic compounds (VOC), methane (CH4), nitrous oxide (N2O) and carbon monoxide (CO). The emission data for the air pollutants considered, except PM10, was taken from the Portuguese Environment Institute’s submissions in the context of the United Nations Framework Convention on Climate Change and from the National Inventory Report (2007) referring to the period 1990 - 2005. The emission data on PM10 was taken from the Environ- ment Institute’ssubmissions in the context of the Convention on Long-range Transboundary Air Pollution (UNECE) relative to the period 1990 - 2005. Overall, most of the pollutant’s emissions do not decrease in the period 1990-2005. For instance, the CO2 emissions have a clear increasing tendency. Also, the CO2 emissions per GDP is practically constant. The marginal damage costs were obtained from a literature review. For most of the pollutants considered, various estimations of marginal damage costs were available in the literature, and a few estimations concerned Portugal. For others, such as the N2O, few or only one value is obtained from the literature. Whenever possible values for Portugal were used. All the prices estimated were considered constant throughout the period of accounting due to lack of data on the evolution of these estimates. The studies used were considered relevant for Europe: COWI (2000), ExternE project for Portugal (Martins et al., 1998), and BeTa database (Holland and Watkiss, 2002). In table 1 we present the values we used to calculate the term eE in the green NNP expression 17.

Table 1: Estimates of MDC by air pollutant in Portugal [e2000/ton].

Best Low High CO2 16 3 52 CH4 108 67 300 N2O 1836 1836 1836 SO2 7898 169 14126 CO 9 2 9 NOx 5985 286 20778 VOC 1201 113 5111 PM10 10005 1056 23620

The best estimation refers to values of the above studies that were calculated speci…cally for Portugal. Averages were taken when more than one value existed for Portugal. The low and high estimations in table 1 were calculated from all the values above (for Portugal or not) to give an idea of the di¤erent values existing in the literature. For the CO2 we have also considered the famous estimation of the marginal global damage per ton of carbon emitted of $204. This value is used by the World Bank to estimate genuine savings (Bolt et al., 2002). To bound the range of values found in the literature we also used bene…t transfer techniques, in particular we have adjusted values estimated from other countries to

4 Since the data is for CO2 and the damage estimate is per ton of carbon the estimated marginal damage for CO2 emissions is 20 12=44 = 5; 4545 $/ton CO2 .

12 Portugal by using purchasing power parities. Figure 1 illustrates the costs of emissions as percentage of the total cost for the best estimation.

45 CO2 CH4 40 N2O SO2 35 CO NOx 30 VOC 25 PM10

15 Cost of Emissions [% Total] of Emissions Cost 10

0 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005

Figure 1: Cost of air emissions per pollutant as percent of total. Best estimate for Portugal.

Note that, surprisingly, comparing to the physical quantities of emissions, SO2 is the pollutant that bears the higher costs on the order of 25 - 40% of the total. Then follows, NOx about 25% and then a group of three pollutants between 10 - 15% of total cost composed of emissions from PM10, VOC, and CO2. The costs corresponding to CO, N2O and CH4 are almost negligible as a percentage of total costs. As mentioned above, and in accordance with the practical convention we have considered an upper and lower bound for the marginal cost of emissions of the pollutants in question. The …gure 2 illustrates the range of MDC estimates encountered in the literature.

25 Best Low High 20

10 Cost of Emissions [% of Cost Emissions GDP]

0 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005

Figure 2: Total cost of emissions [% GDP].

Figure 2 presents the cost of emissions as % of GDP. The costs are considerably high but declining. The lower bound is also decreasing but it is not evident from the …gure. Atkinson et al., (1997) estimated the damages of PM10, SO2, NOx, and CO2. They estimated a value of 8.7% of GDP in 1980 for Portugal, and noted that ’this seems high, with the probable

13 cause lying in the adoption of the estimates of marginal social costs based on UK emissions (weighted for di¤erences in per capita income)’. For the pollutants they consider we have that in 1990 the total cost is about 5.0% of GDP and this value steadily declines until it reaches 3.5% of GDP in 2005. Our results, then, suggest that di¤erences in income do not explain the high value of costs of emissions because we have considered values estimated for Portugal speci…cally. Nonetheless, the values estimated for the ExternE project for Portugal are believed to be high, but in the absence of better estimates, and keeping in mind that the prices obtained should be seen as upper bounds to the true costs of air emissions, those were the adopted prices.

4.2 Depreciation in commercial Portuguese forests R In this section we present the values used to estimate (Q fR)S_ in expressions 17 and 18. Both, data on stocks, prices and especially marginal harvest costs. Concerning commercial forests we have considered two of the most important commercial sources of wood in Portugal, that is, conifers and eucalyptus. Mendes (2005) divides Portuguese forestland into two main functions: in 1995, the main function of 51.8% (24.4% of conifers, 17.7% of broad-leaves and 11.6% of mixed stands) of forestland was wood supply, and the second function, corresponding to 48.2% of the forestland, was for non-wood forest products (NWFPs), mostly cork production in the southern regions. In 1998, the forest sector represented 2.93% of the GDP, which places the country in a top position within the EU 15, in terms of this indicator, being surpassed only by Finland and Sweden (Mendes, 2005). Most of this value added was due to cork products. Corks exports are the most important part of total forest exports. However, since Mendes (2005) argues that ’it is believed that the industrial demand for cork induces harvesting of all sustainable production’but not more, we have considered the net growth of "cork forests" equal to zero, and so we did not consider it in estimating the depreciation of commercial forest use in Portugal. We estimate S_ directly, i.e., we obtained data on the stocks for some years, estimated the gaps, and then used the approximation S_ S(t+1) S(t). The data was obtained from the National Forest Inventory 2005/06 (IFN)' of the DGRF (Direcção-Geral dos Recursos Florestais5) for the years 1990, 1992, 1995 and 2005 in units of area. This is depicted in …gure 3. The data on volumes of standing stock (m3=ha) was also obtained from the IFN 2005/06 and was considered to be 85.5 m3=ha and 55 m3=ha throughout the period 1990 - 2005, for conifers and eucalyptus, respectively. This allowed us to calculate the stocks S(t). The area …gures presented do not include burnt areas. However, since the data is being collected with a 5 year interval this information is di¢ cult to interpret. Also, in order to use these data in our very simpli…ed model of section 3, we have to assume that there is a myriad of decisions concerning the optimal harvest time that overlap each other, so that we approximate the manage of a forest with a continuous harvest rate. This, however, might be an approximation for the portuguese case since most of our forest is privately managed and not subject to aggregate interests concerning the ideal age to cut the trees. Vincent and Hartwick (1998) present some formulas to calculate the depreciation of forest resources when there is a waiting period and a certain optimal age to cut. Information on prices was obtained through the SICOP system (Sistema de Informação

5 www.dgrf.min-agricultura.pt/

14 1400

1200 Conifers 1000 Eucalyptus

800

10^3 ha 10^3 600

400

200

0 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005

Figure 3: Total cost of emissions [% GDP].

de Cotações de Produto Florestais na Produção)6, for the period 2000 - 2005, and directly from DGRF for the period 1990 - 1995 based on roadside prices. The gaps were estimated using a linear approximation.

100

Coniferous 50 Eucalyptus

0 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005

-50 million € million

-100

-150

-200

Figure 4: Forest depreciation by species in Portugal.

The data on marginal cost of harvesting was impossible to obtain. An average value for the marginal cost of harvesting 7 e=m3 was obtained through inquiries with several …rms that provide forest services. As it will become clear in the next section, we believe however that this value may not be that critical. Having said this, …gure 4 presents the forest depreciation by species in Portugal. Adding the species depreciation to get the total depreciation, we conclude that the commercial forests considered here have been depleted from 1990 - 1993 and from 1996 - R 2004. Between this period, the value of net depletion (Q fR)S_ was positive, meaning that the forest appreciated then. Rising the marginal costs of extraction would lower the

6 http://cryptomeria.dgrf.min-agricultura.pt/

15 value of the depreciation of commercial forests throughout. Since the value added of the forest sector is around 3 %, this implies that the value of the change of commercial forests in Portugal is of the order of 10 % of the value added of the forest sector in the years of 1998 an 1999 (the highest depreciation values). This has the interpretation that in 1999, the forest value added should have been 10 % less, to account for the loss of ’potential’ timber in the future due to harvest in the current period.

4.3 The value of time Including the value of non-attributable technological progress requires estimation of equation 19. First of all, GGDC database7 provides data on TFP growth for Portugal (1980- Ft t 2004). We consider this to be the estimate of F in our model. Since Q is forward-looking we need projections of TFP growth and GDP growth. This was obtained from the Portuguese Prospective and Planning Department (DPP)8 until 2015. For this reason we truncated the integral to 2015. This reinforces the ideia put forth in Weitzman (1997) that sustainability appears to depend more critically on future projections of the residual than on the typical corrections now being undertaken in green accounting. Moreover, omiting technological progress likely understates an economy’s indicator of sustainability. We optimistically believe that the key words here are ”typical corrections now being undertaken”. Although it is clear that technological progress contributes considerably to the GNNP and GS, the environmental and welfare corrections made here are fairly standard and lots others stocks (environmental and human) or interactions could be considered that may have a substantial impact on GNNP and GS. For instance, the proximity of environmental thresholds is not included in this framework though most likely will have a big impact on green accounting results. On the other hand, it is not at all clear what is being captured in the TFP measure. As Pezzey et al. (2006) comment, TFP includes both exogenous and endogenous growth whereas the model requires exogenous growth; and TFP estimates depend on the factors of production, that can be more than just capital and labour.

4.4 Green Net National Product and Genuine Savings results We now proceed to the calculation of green NNP and genuine savings according to expressions 17 and 18. We do this in two sections, one presenting the results following the most common calculations, not including the value of technlogical progress, Qt, and one with GNNP and GS including Qt. This is done so, because it is instructive to see the e¤ect of the non-attributable technological progress both on the magnitude of GNNP and GS, and on its dynamics (sustainability message). The main results are shown in table 2 (1990 - 1997) and table 3 (1998 - 2004). The values of GDP and consumption of …xed capital (CFC - UNSTAT’s series no 30227) were taken from UNSTAT for Portugal9. Consumption of …xed capital is subtracted from GDP to obtain net national product (NNP). We then subtracted the total cost of emissions of air pollutants and added the term related to depletion of commercial forests, to obtain an estimation of the green net national product for Portugal.

7 http://www.ggdc.net/ 8 http://www.dpp.pt/ 9 http://unstats.un.org/unsd/snaama/dnllist.asp

16 Table 2: Green NNP, Genuine savings and their components for Portugal 1990 - 1997 [103 e2000].

[Million e2000] 1990 1991 1992 1993 1994 1995 1996 1997 GNP 84972 88215 91649 90582 92854 96652 99321 104472 CFC 12798 12875 12849 12978 13469 15322 15784 16568 NNP 72174 75341 78800 77605 79386 81330 83537 87905 eE 6578 6694 7443 6889 6755 7132 6475 6878 Forest Depletion -368 -394 30 32 196 -115 -115 Value of time 11590 13274 7570 7358 10351 11421 10957 9337 GNNP 81553 78533 78103 83014 85815 87904 90248 GS 20158 14161 11738 14015 15983 14500 12903 Change gNNP -3020 -430 4910 2802 2089 2344 2906 Interest on GS (2%) 403 283 235 280 320 290 258

Table 3: Green NNP, Genuine savings and their components for Portugal 1998 - 2004 [103 e2000].

[Million e2000] 1998 1999 2000 2001 2002 2003 2004 GNP 110263 115426 119192 120493 123141 121740 124026 CFC 17364 18274 20091 20587 20846 20864 21089 NNP 92899 97152 99101 99906 102295 100876 102937 eE 7396 7499 7147 7172 7180 6478 6512 Forest Depletion -117 -311 -159 -143 -137 -133 -131 Value of time 7767 10908 12221 11406 14009 16341 17864 GNNP 93154 100250 104015 103997 108987 110606 114159 GS 12176 14068 12737 11536 14385 15366 14706 Change gNNP 7096 3766 -18 4990 1619 3553 Interest on GS (2%) 244 281 255 231 288 307 294

Green NNP is about 10 – 6% less than NNP, with the gap falling steadily over 1991– 2004, without accounting for the value of time; whereas including Qt, GNNP is around 1 - 10% higher than NNP. Note that we have considered few environmental corrections, and many more can be made in this context, namely, concerning other resources in Portugal like, other types of forests, …sh stocks, minerals, water, soil (erosion), biodiversity or lanscapes. Figure 5 shows GNNP and the terms that compose it. Note that the pollution term is depicted as positive in the …gure but it is subtracted in the calculations. The depreciation of man-made capital has increased, as a percentage of GNP, from 14 % to 17% in 2004. The cost of emissions decreased from around 9% in the beginning of the period to 6% of NNP in 2004. The term corresponding to commercial forest depletion ranges between - 0.5% of NNP in 1992 and 0.3% of NNP in 1995. Throughout the accounting period, the value of technological progress accounts for 8% to 18% of NNP. Overall, the GNNP as a growing trend, but punctuated by decreases following a ten year cycle. Figure 6 compares the growth rates of NNP, GNNP and GNNP when the value of time is ignored. The growth rates are signi…cantly altered after including the value of time. Excluding this term, the growth rates are very proximate as expected, since the commercial forest depreciation is low compared to NNP, and the cost of emissions is practically constant

17 140000

120000

100000

GNP 80000 CFC eE 60000 Forest Depletion

Million € Value of time 40000 GNNP

20000

0 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 -20000

Figure 5: GNNP and its components.

when compared to NNP. We should note that we have assumed a constant price for the marginal cost of emissions and we expect the growth rates to be di¤erent if these prices are not constant. In order to calculate the genuine savings for Portugal we …rst estimated the net saving for Portugal with no environmental terms. Then, and according to the expression 18 we have added the value of depreciation of commercial forests and the value of time. We present the results with and without the value of time in …gure 8. We interpreted NNP C as the measure of net saving for the small open economy model. So, as in Bolt et al. (2002), net savings is equal to gross savings minus consumption of …xed capital, NS = GS CFC. The data was taken from UNSTAT’s series no 30243 and series no 30227, respectively. Without including the value of time, genuine saving for Portugal depicts a decreasing tendency, having negative values after 2002, providing an indication of unsustainable development. This unsustainable pattern arises in the economic data. The net savings for Portugal are negative after 2003. We note that during the period, GDP was increasing (though slowly) almost everywhere. In spite of this, there is no signs of alteration of the decreasing tendency of net savings. When the value of time is included, genuine saving is always positive providing no indication of unsustainability. From the theory presented in section 3, we would expect that changes in green NNP should be roughly equal to interest on genuine savings as in proposition 3. We used the interest rates of 2 and 6% following Pezzey et al. (2006) and the comparison of both aggregates is depicted in …gure 8. In general, the value of changes in green NNP is much higher and ‡uctuates more than the value of genuine savings. From …gure 8, it seems clear that using a higher interest rate reduces the mismatch, indicating that, most likely, a model with variable interest rates will have very di¤erent results. However, we do not pursue this here. _ t With the value of time included, the mismatch (m(t) = Y R Q(t)I(t) + Q (t) ), shows a tendency to increase in the accounting period, averaging 2225 million e with a standart deviation of 2654 million e, whereas excluding the value of time, the mismatch seems to ‡uctuate around the mean (2092 million e) with the standart deviation of 1530

18 10 NNP GNNP 8 GNNP no Qt

% 2

0 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 -2

-4

-6

Figure 6: Growth rates of NNP and GNNP with and without the value of time, Qt.

25000.000

GS 20000.000 GS no Qt

15000.000

10000.000 Million €

5000.000

0.000 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004

-5000.000

Figure 7: Genuine Savings for Portugal, with and without the value of time.

19 million e. This mismatch suggests the rejection of the underlying theory presented in section 2, the rejection of the underlying model developed in section 3 or evidence showing that the data provided by national accountants is not adequate for these models. There are some other ideas to explain the mismatch. Let us see what is the e¤ect of changing the MDC of pollution emission according to the range in table 1. Considering the low (high) estimates of MDC of pollution emissions, the mismatch is slightly increased (decreased), as expected. However, this does not amount to much in explaining the mismatch. Another test, which also increases the interest on GS relative to the change in green NNP, is to follow Hamilton and Clemens (1999, p. 346). They argue that current, ultimately arbitrary conventions in national accounting practice treat the vast majority of educational expenditure as consumption, which is better reclassi…ed as investment in human capital (Pezzey et al., 2006). Reclassifying items from consumption to investment increases GS, but leaves GNNP unchanged which would explain part of the mismatch. Regarding the mismatch problem, we found that the mismatch is slightly reduced to around 2107 million e (with a standart deviation of 2646 million e). Meaning that it increased a slightly the explanation of the mismatch. But looking at this kind of corrections, the expenditures made by consumers to buy a house should also be considered as investment or a form of saving, and reclassi…ed to test the mismatch. For instance, in Portugal this is particularly relevant, since the rental market is very small compared to the buying houses market, and the percentage of people who own more that one house is considerable. There are other explanations of the mismatch proposed by Pezzey et al. (2006) like noting that the theory of section 2 assumes full capacity utilization at all times and thus excludes business cycles and as Geir Asheim commented that potential GDP should be used instead of the actual GDP. Concerning the veri…cation of the equality between the change in GNNP, Y_ (t), and the interest on GS, R(t)GS(t), with a 2% interest rate and with(out) the value of time, the mismatch depicts an increasing (decreasing) trend and averages 2227 (2053) million e with a standart deviation of 2423 (777) million e. Thus, using potential GDP did not reduce the mismatch signi…cantly, in fact, the mismatch is higher than the case of actual GNNP with the value of time. However, it is clear that the ‡uctuations are reduced when using potential GDP. The results for the multisector optimal growth suggest that Y_ (t) should be compared to R(t)GS(t). Another way of taking the e¤ect of short-run cycles using potential GDP is simply to adapt the result of proposition 3 (Y_ (t) = R(t)GS(t)) by using the output gap, OG. De…ning Y a as the actual GNNP, from the de…nition of output gap, Y a = Y + OG is _ a dOG(t) obtained. Taking the time derivative and using proposition 3 we obtain Y (t) dt = R(t)GS(t). This means that the change in time of the output gap must be subtracted from the change in actual GNNP to compare with the interest on real genuine savings. Y a Y Frequently we know the output gap as a percentage of potential output, Y , and Y a have no information on the potential output. Hence, Z := Y is also known. Taking the time derivative of Z, we have Y^ a = Z^ + Y^ .10 Substituting proposition 3 yields Y_ a(t) = Z^(t)Y a(t) + R(t)GS(t)Z(t). However, in this analysis, the GS are suposed to be "potential" GS but instead, no adjustment was made to take the e¤ect of business cycles. So, in reality we are using actual genuine savings, GSa to test the theory. Pezzey et al. (2006) suggest the decomposition

10 ^ X_ X := X

20 8000 Change GNNP Interest on GS (2%) Interest on GS (6%) 6000 Change GNNP no Qt

4000

2000 million € million

0 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003

-2000

-4000

Figure 8: Green NNP and interest on genuine savings.

a GS GS a _ a ^ a a Z(t) GS = GS =Z , where Z := GS =GS. So, Y (t) = Z(t)Y (t) + R(t)GS (t) ZGS (t) . The e¤ects of business cycles in GDP are the same as in GS (see equations 17 and 18), meaning that Z = ZGS. So, R(t)GSa(t) compares to Y_ a(t) Z^(t)Y a(t) to test the theory. The empirical results above show that the change in output gap and ZY^ a are small compared to Y_ a, implying that the business cycles, though relevant for green accounting, have no major in‡uence in explaining the mismatch in proposition 3. For now, we do not have a clear strategy to resolve the mismatch problem, but, besides the interpretations of the aggregates required by the model (is NNP really equal to C + K_ + K_ f ?, or why use potential GDP when no other information is calculated with the full use of resources?), the assumptions used to prepare the data (for instance truncating the integral in the value of time, or de‡ating GNP with the CPI as the theory suggests), it appears that we left out some important environmental corrections, so, the model of section 3 is misspeci…ed; the data obtained is not yet adequate and consistent with the assumptions made, and there may be misspeci…cations of the utility function in section 2. This section suggests that the remarks made in Pezzey et al. (2006) proposing fundamental changes in the utility function (to include relative consumption or status e¤ects) loose some ground11. So, in paralel to theoretical advances and bold proposals for new green accounting terms, we should consistently (across studies) analize the e¤ects of empirically justi…ed assumptions. We suggest, as the most relevant for the mismatch problem here, the interest rate and the projections of future technological progress and GDP growth.

11 Note that, any changes regarding the form of the utility function, will have to deal with the need to de…ne new price de‡ators in order to maintain the welfare signi…cance of GNNP in real terms.

21 5 Conclusions and future work

The terms we included in the calculations of green NNP and GS are, the disamenity of air pollution emissions to households, the depreciation of commercial forests - pine and eucalyptus, and the value of technological progress. The pollution disamenity term is around 6 - 9% of NNP, and the depreciation of commercial forests of the magnitude of - 0.5% in 1992 and 0.3% in 1995. Finally, the value of technological progress accounts for 8% to 18% of NNP. In regard to the depletion of commercial forests, the highest value of depreciation term is estimated to be around 10% of the total value added in the forest sector in the year 1995, which is considered high in the context of the speci…c sector. However, when using average costs, with increasing marginal costs, one is obtaining a measure that is overvaluing commercial forest depreciation. The obtained data for marginal costs of abatement is at best a crude approximation of the true costs (or even the average cost), and this is a subject that deserves further attention in future green accounting studies in Portugal. Also, the cost of extraction need further investigation. Without the value of technological progress, the net savings are decreasing, even when Portugal experienced GDP growth, and eventually becomes negative around year 2003. This is also visible, from the World Bank estimations of the Adjusted Net Savings for Portugal. This is expressing that, clearly, Portugal has economic problems in terms of maintaining its welfare at a non-decreasing level, and that the reason for this is not environmental12. So, as an important demonstration of the power of green accounting in providing a framework that really integrates the three dimensions of sustainability, is that the economic problems in Portugal are seriously pulling towards unsustainable development. Including the value of technological progress changed the sustainability message, once more suggesting that this is an important term to include in future green accounting studies. However, it also means that it can change a lot when di¤erent assumptions are made to estimate it, particularly, the end time of the integral. Regarding the test of the theory, in spite of the sensitivity analysis for high and low estimates of MDC, of changing interest rates, of the reclassi…cation of education expenditures, of estimating GNNP using potential GDP, the mismatch persists. The interest rates, the reclassi…cation of expenditures as investments and the calculation of the value of technological progress are the topics that imply signi…cant changes in the mismatch. This suggests that we should consistently (across studies) analize the e¤ects of empirically justi…ed assumptions on the estimations of GNNP and GS. This work should be seen as a beginning step towards a theoretically sound discussion about sustainability and welfare measures in Portugal and as a continuation of the discussion of the mismatch problem in the relevant literature.

References

Asheim, G. (2000), Green national accounting: Why and how?, Environment and Develop- ment Economics, 5, pp. 25-48.

Asheim G. (2007), Can NNP be used for welfare comparisons?, Environment and De- velopment Economics, 12, pp. 11–31.

12 At least considering air pollution emissions and commercial forests only.

22 Asheim, G. and Buchholz, W. (2004), A general approach to welfare measurement through national income accounting, Scandinavian Journal of Economics, 106, 361–384.

Asheim, G. and Weitzman, M. (2001), Does NNP growth indicate welfare improvement?, Economics Letters, 73, pp. 233–239.

Atkinson, G., Dubourg, R., Hamilton, K., Munasinghe, M., Pearce, D. and Young, C. (1997), Measuring Sustainable Development: Macroeconomics and the Environment. Chel- tenham: Edward Elgar.

Bolt, K., Matete, M. and Clemens, M. (2002) Manual for calculating adjusted net savings, Environment Department, World Bank.

COWI, 2000. A study on the economic valuation of environmental externalities from land…ll disposal and incineration of waste. Report to ECDG Environment. COWI, Den- mark.

Dasgupta, P. and Mäler, K.-G. (2000), Net national product, wealth, and social well- being, Environmental and Development Economics, 5, pp. 69-93.

Hamilton, K. (2000), Genuine saving as a sustainability indicator, The World Bank Environment Department Paper No 77.

Hamilton, K. and Atkinson, G. (1996), Air pollution and green accounts, Energy Policy, 24(7), pp. 675-684.

Hamilton, K. and Clemens, M., (1999), Genuine savings rates in developing countries. World Bank Economic Review, 13(2), pp. 333-56.

Hartwick., J. (1990), Natural resources, national accounting and economic depreciation, Journal of Public Economics, 43, pp. 291-304.

Holland, M.R. and Watkiss, P. (2002) Bene…ts table database: Estimates of the marginal external costs of air pollution in Europe BeTa Version E1.02a.

Li, C.-Z. and Löfgren, K.-G. (2006), Comprehensive NNP, social welfare, and the rate of return, Economics Letters, 90, pp. 254–259.

Martins, A., Fernandes, M., Rodrigues, V. and Ramos T. (1998). Implementation in Portugal of the ExternE accounting framework. Avialable at: http://externe.jrc.es/pt.pdf.

Mendes, A. (2005) Portugal, in: Merlo, M. and Croitoru, L. (eds.), Valuing Mediter- ranean Forests: Towards Total Economic Value, Wallingford:CABI Publishing

Pearce, D. and Atkinson, G. (1993), Capital theory and the measurement of sustainable development: An indicator of ’weak’sustainability. Ecological Economics 8(2), pp.103-108.

Pezzey, J. (2004), One-sided sustainability tests with amenities, and changes in technology, trade and population, Journal of Environment Economics and Management, 48, pp. 613–631.

23 Pezzey, J., Hanley, N., Turner, K., Tinch, D. (2006), Comparing augmented sustainability measures for Scotland: Is there a mismatch?, Ecological Economics, 57, pp. 60-74.

Repetto, R., Magrath, W., Wells, M., Beer, C. and Rossini, F. (1989), Wasting Assets Natural Resources in the National Income Accounts, World Resources Institute.

Vincent, J. and J. Hartwick (1998), Accounting for the bene…ts of forest resources: concepts and experience, Report Commissioned by the FAO Forestry Department, mimeo. Available at: http://www.fao.org/DOCREP/005/AC272E/AC272E00.HTM.

Sefton, J. and Weale, M. (2006), The concept of income in a general equilibrium, Review of Economic Studies, 73, pp. 219–249.

Vincent, J., Panayotou, T. and Hartwick, J. (1997), Resource depletion and sustainability in small open Economies, Journal of Environmental Economics and Management, 33, pp. 274-286.

Weitzman, M. (1976), On the welfare signi…cance of national product in a dynamic economy, Quarterly Journal of Economics, 90, pp. 156–162.

Weitzman, M. (1997), Sustainability and technical progress, Scandinavian Journal of Economics, 99(1), pp.1-13.

Weitzman, M. (2003), Income, Wealth and the Maximum Principle, Massachusetts: Harvard University Press.

Weitzman and Löfgren (1997), On the welfare signi…cance of green accounting as taught by parable, Journal of Environmental Economics and Management, 32, pp. 139-153.