Dynamic macro modelling and materials balance

Economic Modelhn9 1994 11 (3)283-307

Dynamic macro modelling and materials balance Economic-environmental integration for sustainable development Jeroen C.J.M. van den Bergh and Peter Nijkamp

In this paper a model is presented with the aim of studyin9 the long-term relationship between an economy and its natural enviroment. The approach is based on two main elements: reciprocal interactions between on the one hand population 9rowth, investment, allocation of inputs and outputs, technology and productivity, and on the other hand declinin9 environmental quality, pollution and resource exhaustion; and a more realistic and consistent representation of the interdependence between various environmental effects, from extraction to emission, by usin9 a materials balance perspective on economic processes. In order to develop the model attention is devoted to production functions that are consistent with materials balance. The model is multisectoral, includin9 economic processes of extraction, production o f commodities and investment 9oods, waste abatement and recycling. Environmental processes of resource regeneration and waste assimilation are linked throuoh the economic and environmental sphere, and the model allows for endooenous development o f resourceefficient technology. Keywords Sustainable development; Economic growth; Dynamic modelhng

Environmental concern has become a major issue in our modern society. In the past years, there has been an avalanche of literature in the field of environmental-economic analysis and modelling. Much of this was based on a straightforward extension of conventional welfare-theoretic models encapsulating externalities in resource utilization. After the publication of the Brundtland Report (WCED [21]) there has been an increasing need to develop models focusing explicitly on ecologically sustainable economic de-

The authors are with the Faculty of Economics, Free University, De Boelelaan 1105, 108l HV Amsterdam, The Netherlands. This study was supported by the Foundation for Advancement of Economic Research (Ecozoek), which reports under the Dutch Organization for Scientific Research (NWO), project No. 450-230007. We are grateful to an anonymous refereefor comments which have led to a considerable improvement of this paper. Final manuscript received 4 March 1994.

0264-9993/94/030283-25 c~ 1994 Butterworth-Heinemann Ltd

velopment (SD). Up till now comprehensive attempts at building such models in a dynamic setting have been exceptionally rare. Furthermore, the objective of sustainable development also requires that environmental economics is extended to macroeconomic analysis (see Daly [8]), for which adequate models have to be constructed. This paper addresses the design and use of a dynamic macro model which aims to provide an analytical framework for the study of the long-term development of an economy in relation to its natural environment. Particular attention will be devoted to the conceptual structure and specification of such a model. Subsequently, calibration and results of scenario analyses are presented. The model will serve to assist decision makers in distinguishing between various policy strategies (or scenarios) that give rise to sustainable and unsustainable developments. In order to provide a sufficient background for a discussion of the model, its presentation is preceded by a discussion of economic-environmental modelling

283

D~,umuc macro modelhnq and materiah bahmce' J.C.J M. tan den Ber,qh and P ,Vtlkamp

in the next section, which focuses on materials balance production functions which have received little attention in the literature. The fifth section includes a discussion of the specification and calibration of the model. The results of scenario analysis with the model are presented and conclusions are drawn in a final section.

Economy-environment interactions and materials balance production functions The approach behind the model proposed in the next section uses the insight that a long-run economicenvironmental analysis, which is needed for issues of sustainable development, should be based on two main elements. First, the long-run relationship between the economy and the natural environment is characterized by twoway interactions between on the one hand population growth, investment, technology and productivity, and on the other hand declining environmental quality and resource exhaustion. Second, a more realistic representation of the interdependence between various environmental effects, from extraction to emission, can be realized by adopting a materials balance perspective on economic processes. The result of including these two elements means that direct mutual impacts between the economy and the environment, as well as indirect economic-environmental influences are taken into account, by separating effects from and on production, consumption and welfare. Wilkinson [20] uses the idea of ecological disequilibrium to link economic change to environment economy relationships. Inclusion of such environmentally influenced economic change in models has been performed by Faber and Proops [9] and Van den Bergh [6]. Related models stem from applied systems theory, notably in the fields of biophysical "macroscopic mini-models' derived from energy language diagrams (Odum [16]), and global modelling (Meadows et al [15]). The main shortcomings of these models in comparison with the one proposed here are, first the lack of substitution between productive inputs or components of welfare, and secondly the lack of economic feedback mechanisms, as will be discussed later. For an investigation of economic-ecological integration at both a theoretical and operational level of modelling we may - as indicated above also include materials balance conditions to account in a consistent way for material flows that lead to various interlinked effects. Although the use of materials balance models was propagated more than two decades ago (see Ayres and Kneese [3]; Kneese et al [14]), they have seen unfortunately few applications. Furthermore, the combination of non-linear models and materials balance

284

conditions is rare, in both theory and applications. The main reason is that materials balance or materials accounting can be done much more easdy with linear production functions. Exceptions are Faber et ul [10], Van den Bergh [4] and Ruth [17]. The concept of materials balance applies to all natural and economic processes. It means that materials in a physical system are not lost, and that material inputs in processes end up in either stock accumulation or material output flows. In addition a derived result has to be mentioned here, namely that the materials input is larger than the useful goods output, especially in view of spillage and auxiliary materials (like water and fertilizer in agriculture)(see Ayres and Kneese [3]). In formalizing the materials balance principle in environmental economic models, the following steps are required: (i~ relevant variables should be in material units; (ii) where necessary, transformations must be modelled between (variables in) material units and other units; and (hi) materials balance conditions should be specified for economic variables in the economic system, for ecological/physical variables in the environmental system~ or as a supplement to a description of economic~environmental interactions (which include both economic and environment variables). Production functaons can be formulated in various ways to satisfy the materials balance principle. Apphcation of materials balance to the production process expresses that all material input must end up somewhere; in final or capital goods or in waste. The link between production theory and materials balance is rarely touched upon in the literature. Some theoretical and conceptual steps taken in this direction were set out by Anderson [1] and Smith and Weber [18]. Some properties for a Cobb-Douglas production function that satisfies materials balance are derived by Gross and Veendorp [12]. They show with a standard economic growth analysis that such a function sets a limit to growth for the case of an economy that obtains its material inputs from a non-renewable resource. In what follows we will devote more detailed attention to characteristics of non-linear production functions that are consistent with the law of materials balance. This will lead to several possible formulations, out of which two will turn out to be useful for the model in the next section, namely those given in Equations (4) and (6). The production process may be envisioned as a transformation of resource inputs into goods and waste outputs by actors (funds/agents; see GeorgescuRoegen [11]). We may expect considerable potential for substitution between subcategories of actors

Economw Modelhng 1994 I'olume 11 Number 3

Dynamic macro modellin9 and materials balance" J.C.J.M. van den Bergh and P. Nijkamp

labour and capital - since they serve a similar role in the production process, therefore, they are aggregated into the variable 'actors' (A))An increase in the use of agents may reduce the amount of waste output. Substitution is possible within the category of resource inputs to production (R). Substitution between the categories of actors and resources is limited. This is not assumed a priori; it follows from the application of the materials balance condition to the production function. 2 A materials balance can be expressed as follows: (i) the inequality R > Q (R and Q denote the levels of material input and goods output from production, respectively) as a minimal consistency condition; or a more strict condition, such as R > Q + x (x is a lower bound for waste residuals from production), based on knowledge of technical and physical constraints; (ii) the equality R = Q + W (W is waste residuals from production) if material accounting is strived for (and possible); clearly, (ii) encompasses (i) since W is always positive. The equations in (1) show a general relationship between the output of goods Q on the one hand, and all factors involved in its production on the other hand. These factors include A, R and W. The materials balance principle is explicitly stated in terms of an equality or inequality condition that relates the total resource input to the output of produced goods and waste. The parameter t in this (and the subsequent) production functions denotes the change resulting from technical progress. In the formal representation of (1) A, R and W are treated identically, ie their conceptual difference is not made explicit in F(-), but becomes clear only after the material constraint is added.

process, namely only in material terms. Specific characteristics of the final product are not considered, so that a simple waste production function can be derived, as W = R - F(A, R, W, t). Therefore, an ex post relationship can be established between the production functions for useful output and waste, ie after the application of the materials balance condition. The second type of formulation of production subject to a materials balance shown in (2) starts with two separate (ex ante) independent production function for goods and for waste. Q=F~(A,t)

and

W=Fz(A,t)

(2) R=Q+W

or

Q+W<<,Rc

The formulation in (2) with the equality constraint can be interpreted as follows: a given actor (and activity) level A determines the levels of useful and waste outputs; the sum of these gives the resource requirement. The interpretation based on the inequality constraint is that for a given amount of resources Re, the inequality constraint should be satisfied, namely by choosing an actor level A such that the sum of the resulting values of Q and W is feasible. As a special case of such a constrained process we may distinguish between actors allocated to production and to an activity (denoted by the function F3(.)) which reduces the amount of waste resulting from the (regular or main) production process (denoted by FI(') and F2(.)). It is assumed that the available levels of capital, labour and resources are given. This is formalized in (3). Q=FI(AO W = F 2 ( A 1) - F I ( A 2 )

Q=F(A,R, W,t) (1)

AI + A2 <~Ac

R=Q+W Q+ W<~R c All partial derivatives of F(.) are positive. 3 We have here a very aggregate description of the production

1 In a dynamic analysis the distinction between these two types of actors is relevant m order to deal with distinct process of capital accumulauon and labour/population dynamics, and for accounting of locked up resource matenal in capital stocks. 2 Substitution between actors and resources is conceptually different from substitution within each category; the latter can be referred to as "replacement'. The first is only substitution ex post ie after more efficiency in resource use is realized by an increased (intensity of) use of 'actors' as inputs in production. 3 Notice that the negative effect of waste or pollution on production ~s not dealt with here. The fact that the parual derivative of F with respect to W is posltwe must be interpreted as follows" for a given combination of actors and resources, and In the absence of materials balance conditions, production can increase by working faster and leaving more waste per unit of actor.

Economw Modellin9 1994 Volume 11 Number 3

(3)

The conditions that apply to these functions are that all derivatives be positive, and that F2 always has a higher value than F3. In contrast to the formulation in (2), one may add the objective of maximizing Q or minimizing w to the formulation in (3).4 *These two optimization problems have the same solutions in (A 1, A2). In that case all available resource materials will be used, le for optimal values of A t and A 2 we will have F 1+ F , - F 3 = R,. Then, choosing values for AI and A 2 to maximize F~ is the same as choosing them to maximize the expression ( R , - F 2 + F3). The latter can be rewritten as R , + m a x l m u m ( - W ) , so that this formulation implies the same solution values for A t and A 2 (and consequently for Q and W) as minimizing W. We can see an analogy between the relationship between these physical optLmlzation problems and the duality in microeconomics (eg profit maximization and cost minimization).

285

D~mmuc macro modellhtq and matertals hahmce J C.J.M ~'an den Ber~lh a m / P Ntlkamp

A third type of formulation of materials balance production functions uses a production function F that (automatically) satisfies the consistency restriction of a materials balance ie F(A, R) <~R for all values of R > 0. This can be accomplished in two ways. The first is shown in (4), and is characterized by taking the minimum of any general production function and some share of the resource input: F(A, R, t)= min{F(A, R), a(t)'R}

(4)

The parameter a(') describes technological efficiency in resource use; it falls between zero and one, and has a positive derivative. It can be defined as: W

a(t) = 1 - - -

R

= 1

(5)

F2(A.R,t)

R where we regard waste in terms of a production process as formalized in (2). From (5) it is clear that a(.) is to be interpreted as the efficiency of resource use in production at time t (ie with the technology available at t), which has a lower bound of zero. The second way, shown in (6), uses a function that is based on a resource efficiency coefficient r(.) which can be regarded as a variable coefficient that relates useful output to resource input. This coefficient is increasing in all its arguments: Q=r(A,R,t)'R

0~
(6)

Resource efficiency in production is thus assumed to be improved either by increasing the intensity of the production activity factors relative to the resource input (indicated by an activity-resource ratio A/R), or by technological progress (indicated by t). Since the materials balance condition implies a linear (in)equality, it complies easily with linear types of models well, such as fixed proportions and linear production functions (see Van den Bergh [4], Appendix 4). From the above distinction between the three types of representations of production processes satisfying materials balance, it is clear that we can choose between various specifications of materials balance production functions. In the next section we will see applications of such functions.

A dynamic macro model based on materials balance In this section we will analyse the implications of production combined with materials balance for

286

long-term development, by presenting a macro model with capital ('actor') accumulation, technical progress, and production with renewable and non-renewable resources and emission of waste residuals. The model describes two phenomena: the material flows tand processes based upon these flows) in the economy, the natural environment and their interdependencies: and the feedback mechanisms from economy, environment and value systems to economic actions and policies. The latter occurs over a long-term horizon. A link therefore exists between the present model and economic growth models with ecological variables (see Kamlen and Schwartz [13]; for a critical overview from the perspective of sustainable development see Van den Bergh and Nijkamp [5]). The material flow is shown in Figure I. It describes an economy with six sectors. The model has a supply orientation reflecting a long-term horizon. The model includes economic and materials balance equations, economic activity, and production functions. These production functions satisfy materials balance conditions, as discussed in the previous section. Economic activities include resource extraction, production, waste treatment (abatement), recycling, research and development of environmental technology, and environmental cleaning. Some of these activities are taken to be competitive for economic (financial) means, and can to some extent be stimulated by government policies. In Figure 2 the economic environmental relationships represented in the model are displayed. They include flows as well as impacts upon processes. An environmental quality indicator related to stocks of resources and pollution is used as a state variable for codetermination of the level of natural processes of regeneration and assimilation. Environmental quahty is also assumed to have an impact upon the efficiency of final goods production (eg agriculture) and the quality of extracted renewable resources (eg the stock of fish). It is important to note that changes in non-economic variables, viz. technology and population, are also included. The description of the economic activities module is based upon production and activity functions for six sectors: final goods production; investment goods production; waste treatment: recycling activity: renewable resource extraction; and non-renewable resource extraction. The functions satisfy, where necessary, materials balance conditions, and may include a mix of environmental and economic production factors, available resource materials (in inventory), environmental quality and the technological progress indicator. The capacities of each sector are influenced by feedback mechanisms related to investment allocation, that become operational when sustainable development

Economw Modelhng 1994 Volume 11 Number 3

Dynamic macro modelling and materials balance." J.C.J.M. van den Bergh and P. Nijkamp

LEGEND: MATERIALS FU~N'8 IN 1"HE ECONO~IY ~, TIME DELAy INVOLVED FLOW FROM/TO ENVIRONMENT I i A MA'III~RIAL8 STOCK

g; NON-RENEWABLE RESOURCE EXTRACTION

RENEWABLE REEOURCE EXTRACTION

I

I

SUFFERING

FINAL GOODS PRODUCTION

I

PRIVATE AND PUBUC CONSUMPTION

INVESTMENT GOOD8 PRODUCTION

WASTE PRODUCTION

PRODUCTIVE CAPITAL

RECOVERED AND TREATED PROD. WASTE

CAPITAL DEPRECIATION

f.

' RECYCLABLE WASTE

t

]

UNUSED STORED WASTE

EMITTED WASTE

RECYCLED MATERIALS

g;

Figure 1. Material flow diagram of the economy.

I,

RENEWABLE

NON-RENEWABLE RESOURCES

NATURAL ENVIRONMENT

RESOURCES

+

+

+ "

RENEWABLE

:E EXTRACTION ~SPRODUCTION

ENVIRONMENTAL QUAUTY

', EMISSION .~.

L

~

÷

4I, POLLU~ON

TECHNOLOGY

POPULATION I I POPULATION

+

LEGEND: __~

IMPACT UPON ENV1RONM QUAU'F~

--

--~- . . . .

SLOWLY RENEWABLE

IMPACT UPON A PROCESS

RESOURCE t

MATERIAL FLOW A MATERIALS STOCK

+

Figure 2. Material and non-material economic-environmental relationships.

Economic Modellm# 1994 Volume 11 Number 3

287

Dvnamtc macro model/htg and materials halance." J.C.J.M. t'an den Bergh and P. Nqkamp

conditions with respect to resource use and/or waste emission are violated (see the fourth section). The precise choices of investment allocation mechanism will be formalized in the context of specific development scenarios. The first economic sector is an aggregate of all final goods producing sectors (including relevant types of agriculture). 5 Output (Q) is produced with capital (Ke). It requires resource inputs ce(T~d) per unit of output. A higher overall environmental quality (E) affects positively the productive efficiency. The availability of resources (R~,p) in inventory (ie supply of resource materials) imposes an upper limit on the output level of production. Therefore, we have the output function as in (7). It is in agreement with the third type of materials balance production function formulation as given in (4):

RsuP

Q = min{Fq(KQ, E), %(T~d)J

(7)

It is clear that output Q cannot exceed resource input and that some material loss in production is inevitable. This means that ce(T~e)> 1. Technological change is assumed to generate more efficiency in terms of a lower ratio of resource input to Q, so that dco(x)/dx < O. A second activity is capital goods formation (I). This may be interpreted as the production of machines and new technology. The level of output is directly related to the amount of capital in this sector (Kt). An upper limit to the output level is set by taking the ratio of the supply (inventory) of resource materials (R~,p) less the amount required for the first (Q) production process to the per unit of output required input in this sector; thereby it is assumed that Q production is more important than I production for general welfare, and is therefore given priority for resource use; c t ( T J is like ce(T,d) made dependent on the state of technology T~d. Again, (8) is of the general form as given in (4):

I = min~Ft(K,), Rs"p-- cO(TJ* Q~ (

c~(T~)

)

(8)

Next, we consider two other economic sectors that are related to environmentally beneficial activities. Both sectors use capital. One process represented in (9) treats production waste in such a way that not all of it is directly carried to the natural environment. The amount of waste treated (Rw,) is determined by the level of waste arising directly from the two 'real' production processes (WQd). the amount of capital 5 For an explanation of symbols, the reader ts referred to Appendix 1.

288

used (Kwa), and the state of technology (T,d). The latter two affect the effectiveness coefficient [f,.o) of abatement positively:

Rw~= f,,,(T,d, Kw~)* WQ~

(9)

A second process represented in (10)is concerned with recycling of materials. Its output R ~ is determined by the waste flow suitable for recycling (W,~) and the state of technology, which positively affect the effectiveness coefficient (,fr~¢)of recycling: Rr~=Le~(T~d, Kre~)*W~ec

(lO)

The functions f,.a and f~e~ have values between 0 and 1, so that abated (recycled) waste does not exceed production waste (waste amenable for recycling): Rw, < We (Rre~< W,e~); all first partial derivatives are positive. Both (9) and (10) are special cases of the general materials balance production function formulation as given in (6). Finally, two resource based economic activities remain to be described: renewable and non-renewable resource extraction (R~, and R s, respectively), both using capital (Ku and Ks, respectively). The production functions, given in (11) and (12), are based upon respective stocks or resources; in the case of renewable exploitation, the environmental quality is also significant since it determines the part of the stock that is of sufficient quality (eg clean water, or healthy, non-toxic resources, normal size fish): R N= min{ FN(KN, N, E), RN,perc}

(11)

R s = min{Fs(Ks, S), Rs.p~,~ ]

(12)

All production functions (FQ, F r, FN, Fs) have positive partial derivatives. Extraction rates are limited from above by the perceived or acceptable levels of extraction (Ru,pe,c and Rs.p~,c), which are based on a combination of ethical and ecological considerations. Although somewhat similar to the formulation in (4) the production functions in (11) and (12) should not be confused with materials balance production functions per se. Rs.ver~ will in general be beneath a level of material availability as represented by actual physical stocks in the ground, since they represent perceived or acceptable levels from an ethical/value point of view. This will be discussed further below. The economic dynamics incorporate changes in capital stocks, population, technology/knowledge, stored waste, and the inventory of resource materials. The changes in capital stocks depend on the allocation of investment (I,, i~K, K = {Q, I, wa, rec, N, S}) and the rates of depreciation (D(K)). The stock of capital

Economic Modellin9 1994 Volume 11 Number 3

Dynamic macro modellin9 and materials balance J.C.J.M. van den Beroh and P. Nijkamp

depreciates at a rate given by monotonically increasing: dKi

dt

=li-D,~Ki)

D(K) which

is strictly

i~K

(13)

The equation to describe technological progress is based on sustainable development feedback (e~), total investment (I), governmental support for R&D (O,d), and the Kaldor-Verdoorn effect (dZ/dt); 6 falls in between 0 and 1 and where the two remaining coefficients are positive and increasing in ee: d Tra = ~X(ee).I + e(e.)* ~O,a + 6 * dZ-] dt L dt ]

(14)

The population change is determined by the population level (Pop)and the level of material consumption (C) per capita (used as a welfare indicator):

dPOPdt=B(p~p)*Pop

(15)

This may require an additional assumption that extraction also involves some processing into a sufficient quality or concentration of required materials. Finally, Z is an indicator for that part of total production output in which a change has a strong impact on materials saving progress in production technology (see the equation for T,d): dZ --

dt

= Q + I- z

Q=C +Ord

dt

I,

-RN+ Rs + Rrec-(co(T,a)*Q+ct(T,d)*I)

(17)

The choice for aggregation of renewable and nonrenewable resources is to see how the use of one type develops over time relative to the use of the other. It is implicitly assumed then that the units of measurement of both R N and Rs are such that they can be aggregated via simply adding the respective variables.

Economic Modellm# 1994 Volume 11 Number 3

(19) /2o) /21)

IEK

(16)

Two state variables are introduced to represent time delays. The inventory (buffer) of resource materials R~up is introduced to allow for a time delay between the processes of recycling and resource extraction on the one hand, and the reuse of materials in production of final goods and investment goods on the other. This inventory can be regarded as the total supply of resources (then its initial condition has to be in accordance with this interpretation). This inventory originates from four sources: renewable and nonrenewable resource extraction, recycling and buffering (inventory). The latter will occur when the amount of materials needed for production is smaller than that in the stockpile:

dRsup

=

K = E K,

d---~-= s, * R..a + s 2 * (W.ec-- Rrec)

(18)

The initial conditions are K~(0)= K~o, (ieK), T.d(0)= 0, Pop(O)=Popo, Sw(0)=0, Rsup(O)=Rs.~,o, Z(0)=Q(0) + I(0), with all parameters non-negative. Next, three economic balance conditions are required: Equation (19) reflects the fact that production output of the final goods sector equals consumption (C) plus social R&D outlays (O~d);(20) reflects the idea that production of capital goods equals the sum of sectoral investments (Ii); and in (21) its is stated that total capital is the sum of sectoral capital stocks:

A stock of stored waste that cannot be reused (Swa) is filled from regained production waste (a part sl) and waste left after recycling (a part s2; 0 < Sl, s2 < 1): dSwa

z ( 0 ) = Q(0) + I(0)

As far as the description of the ecological system is concerned, an aggregate ecological model should be consistent with a macroeconomic or regional system in terms of geographical coverage. Therefore, it should describe the essential features of a collection of various (possibly interacting) homogeneous ecological systems. Such a general model would have to be able to deal with the several functions and characteristics of ecological systems: (i) (ii) (iii) (iv) (v) (vi)

regenerative capacity; assimilation of pollution; resource supply; storage of waste materials; non-material services for consumption; decreasing performance of all functions for increasing levels of pollution and/or decreasing resource stocks, and for an increasing level of other disturbances.

The equations in (22) show a model that describes three types of environmental processes: slow and regular regeneration of resource stocks (B and N, respectively), and assimilation of pollution (P). B can be regarded as semirenewable, ie falling in between a renewable and non-renewable resource (see Swallow 289

Dvnatm~ macro modelhng and matertals h a & m e J . C J.M. van den Bergh and P. Ntjkamp

[19]), one may think of such categories as soil, land and water or even rain forests and similar slowly regenerating and sensitive natural systems. N may, for instance, denote biotic resources or ecosystems. The respective stocks and the overall environmental quality (E) have a non-negative relationship with the rates at which each process occurs. E is a function of N, P and B. This means that all environmental processes depend indirectly upon all three environmental stocks. A fourth environmental stock is that of non-renewable resources (S), which is assumed to have no natural environmental linkages with the other stocks or their natural processes. The exogenous impacts upon N and P are resource extraction (RN) and waste emission (We,,) respectively. B is influenced by the pressure of the scale of the economy (indicated by economic capital K), the size of the population (Pop), and the intensity of extractive activities (indicated by the rates of renewable and non-renewable resource exploitation R~, and Rs). S decreases by extraction (Rs): E = H(N, B, P) d N / d t = G(N, E) - RN

amenable for recycling, or emitted waste, as reflected by Equations (16), (25) and (26), respectively. The indicator of the demand for new resources is based on the amounts needed as inputs to production of Q and I less the recycled amounts from the present period: R,e~, = cq(T~d)* FQ(KQ, E) + ct(T~a)* Ft(Kt) - R,~ (24)

Waste amenable for recycling purposes is the sum of private and public consumption, discarded capital and a part of treated production waste: VV,~c= Q + ~ DI(K,)+(1 - s l ) * R w a

(25)

t~K

The result W,ec goes into the recycling process (Equation (10)). As is made clear in Equations (16) and (26), the expression 'amenable for recycling purposes' indicates that only part of ~ec will be recycled (ie recycling is strictly less than 100%), and the remaining part ends up as waste that is being stored or emitted. Emission of waste to natural media (W~m) thus equals the sum of non-treated production waste and the part of waste remaining after recycling that is not stored into Swa:

dP/dt = - A(P, E) + Wem

W~m= (WQ.,- Rw,) +(1 -s2)*(VV~ec-Rrec)

(26)

dB/dt = [b x(E ) - b 2 ( d K / d t ) - b3(dPop/dt) -

b4(RN)- bs(Rs) ] * B

dS/dt = - R s

(22)

The initial conditions are N ( 0 ) = N 0, P ( 0 ) = P o , B(0)=Bo, S(0)=So. All functions and variables are non-negative. H() is increasing in N and B and decreasing in P. The natural growth function satisfies GINmi., E)= G(N~x, E)=0, and for some (N, E), with 0 < Nmin < N* < N . . . . E > 0: G(N*, E) > 0, where Nmi. is the minimum viable level of the regenerative resource and Nmax denotes its maximum level (also referred to as carrying capacity). The natural assimilation function A is increasing in P. G and A are increasing in E. All b,(i= 1,2,3,4,5) and their first derivatives are positive. Finally, the following material balance conditions apply to the flows within the economy and to the natural environment. Total waste output (WQa) from 'real' production is equal to the inputs less the outputs: WQ,, = [Co(T~d) -- 1] * Q + [ct(T~a) - 1] * I

(23)

This 'dirty' waste is treated first (producing Rw~ in Equation (9)) before it goes to one of three categories (see Figure 1), namely unused stored waste, waste 290

All material flows in the system have now been modelled. The feedback from environment and the value system, which was mentioned at several stages, still remains to be formalized. All variables necessary to perform this exercise are available now.

Economic feedback using sustainable development conditions Sustainable development feedback can be regarded as a process of adjustment to meet or approximate sustainable development conditions (see van den Bergh [4] Chapter 2). Such conditions reflect goals associated with intergenerational equity and the maintenance of natural environmental qualities and quantities. We make a distinction between two types of conditions. First, constraints may be set on the level of welfare (for a whole generation or per capita), where the choice is to require that welfare exceeds a given subsistence level, and follows a non-decreasing time path. A second type is formed by constraints on stocks or flows (interchangeable) in and between economic and environmental systems. The notion of stock constancy may serve as an illustration of sustainable development conditions of the latter type. The completed model allows for feedback from environmental quality, overall resource scarcity,

Economw Modelhng 1994 Volume 11 Number 3

Dynamic macro modelling and materials balance: J.C.J.M. van den Bergh and P. Nijkamp

unsustainable renewable resource exploitation, and unsustainable waste emission pollution to decisions regarding investment activities and technology. Conditions based on regeneration and assimilation on the one hand, and concern for future generations and natural environment on the other, are central in the feedback mechanism. They determine the acceptable or aspired to extraction and emission levels. In the model this proceeds as follows. At the core are sustainable development (flow) conditions that apply to the flows of resources and waste of the type mentioned above. These are transformed, via behavioural or social control parameters, into variables that indicate the perceived levels. This involves an ethical choice by society or decision makers with regard to the degree of concern for the well-being of future generations. Market mechanisms (prices) and social controls (regulations and price corrections) are implicitly taken into account. They provide incentives that have an effect on the model outcome via the reaction of investment allocation and technological progress. For instance, a strong incentive may result from scarcity of resources through increasing prices. Low regeneration or assimilation rates, or increasing (decreasing) stocks of pollution (renewable resources), may induce social actions. These may take the form of controlling investment through land-use policies, subsidies on environmentally beneficial investment, or artificially higher prices for resource materials. They may also stimulate certain technological changes by subsidies or time paths for required levels of resource use or waste generation. On the basis of social value considerations with respect to future generations and the relationship with nature, as well as ecological considerations with regard to regeneration and assimilation, we can devise the following three indicators: acceptable renewable (R~.pe~c), non-renewable (Rs.p~J , and total (RpeJ resource extraction:

RN.pe,c=max{O,d*pN* N +(1-d)*G(N,E)}

(27)

The dummy variable d may reflect an objective of sustainable use (d=0) or a less strict objective (d= 1), which requires an additional parameter for intergenerational concern, PN (falling between 0 and 1); the latter shows high degrees of moral concern for future generations by way of taking low values. A second interpretation of this parameter is that it shows variable degrees of caution (prudence or risk aversion) in the face of much uncertainty:

Rs.p~rc = ps*S

(28)

The parameter Ps is similar to PN for non-renewable

Economic Modell,ng 1994 Volume 11 Number 3

resources. Therefore d, PN and Ps reflect value stances: Rperc=RN,perc+Rs,perc

(29)

Thus, total perceived resource availability is simply the sum over the two sources. Notice that this is not simply a sum of two types of resource, but of perceived relevant amounts. A variable R~ho,t indicates the scarcity of resources by taking the ratio of Rperc and the required extraction of resources (R . . . . see Equation (24)). A value higher than one means that there is no reason for an sudden strong economic reaction:

R,ho,, = min{ 1, Rp¢rc/R,¢w}

(30)

Other specifications may serve the same purpose, but (30) has the advantage of generating a dimensionless number. Similar to the approach for resource feedbacks, one can also take a ratio of waste assimilation A(P, E) and waste emission to obtain an indication of the degree of unsustainability of waste emission (too much waste emission, indicated by Wtoo):6 W,oo = min{ 1, A(P, E)/Wem }

(31)

Since the variables Rshor, and W,oo have values ranging from zero to one, the following functional structure ensures a range similar to that of E for the ecological effect variable ee that appears in the model of endogenous technological progress in (14) and later in the investment (feedback) decision process (equations in (52)): ee= Rshor,* Wtoo* E

(32)

On the basis of the indicator ee we can include a feedback from the environmental state and the ethical stance to economic actions or decisions. This means that, in addition to feedback to production technology (Equation (14)), investment rules can be stated that incorporate the relevant indicator. This will be done in the context of specific scenarios later in the paper.

6Sustainable waste emission is used analogously to sustainable resource use in a strict sense (applied to renewable resources): the controlled flow of waste emission is such that the stock of pollution remains at the same level, or, in other words, such that the assimilative capacity is not exceeded. Alternatively, we may define it as avoiding a decrease in the stock of renewable resources, since it is linked to the assimilative capacity. In fact, sustainable management could be defined as a choice of combinations of resource extraction (use) and residuals emission, such that the resource size - and thus the assimilative capacity - is not reduced.

291

Dt'namtc macro modelhng atut matertaLs hahm¢e J.C.J M. tan den Bercth and P ,Vi/kamp

Specification and calibration This section gives information on the calibrated model that was used for numerical simulations. Functional specifications, calibrated initial conditions and parameter values are discussed. The calibration was performed in order to satisfy conditions on initial values that reflect several aspects of supply-demand balance and environmental sustainability, so that a stationary or stable pattern is accomplished over a certain period of time. These conditions are presented in Appendix 2. The calibration also aimed at producing a base case model that represents a rather pessimistic opinion about the ultimate state of the economic system far in the future, namely one that collapses. This is done for the sake of comparative analysis of scenarios ie tracing the differential effects of certain additional developments or policies as compared to the base case. Such a choice certainly does not mean to imply that a base case will give rise to a collapsing system in the very long tun. Such a prediction cannot be provided with any appropriate degree of accuracy. Accordingly, the present model is not aiming to solve predictive issues. The aggregation level of the model makes it difficult to base functional forms and parameter values on empirical data with straightforward interpretations. Estimated values for parameters are partly chosen in a realistic range. Some of these represent fractions, which are logically constrained. Others are based on, for instance, notions of maximum efficiency (such as in the case of recycling). The motivation for such choices are mentioned hereafter. Other variables have a long-run physical interpretation, so that their units of measurement are to be interpreted accordingly. Some values are set fixed over all scenarios, after calibrating to meet the above mentioned goals. Variations were allowed in other variables (controls) on the basis of their interpretation, policy relevance, strategic value, or because of the model sensitivity. It is hoped that the model base case and the various scenarios thus represent a realistic setting, which may be a country with an economy that is to a large extent based on natural resources and environmental conditions within its national boundaries. The specifications and parameter choices that resulted are as follows. First, consistency requirements and functional characteristics are given. Then, the choices for specific functional structures and parameter values (in the basic scenario) are motivated. Finally, the realistic ranges are given for some important, uncertain, policy or behavioural parameters (the latter two types may change over time). All functions and variables are non-negative. The following set of consistency conditions applies to the

292

functions in the model: col "), cA') > 1 Ji,,a(', '), f~,a(', ") ~ 1

sl,szE[O, 1]

(33)

The functions in the model are specified as follows:

Fe(KQ, E)=min~ . E +-aQ ,1}*ko*K Q ( E~r. + aQ cQ(T~a)-

T~d+ bQ T,~ + cQ

(34)

To establish physical capital coefficients (capital divided by total production), the Dutch data given in Table 1 are illustrative (based on CBS Yearbook, data 1988). The capital size was derived by assuming an average price of capital equal to 2 guilders per kilogram. In physical terms a value for kQ can be compared with that for food in the table; we choose kQ=5. It is assumed that cQ(T~d(0))= 1.4, so that with T~d(0) set at 100 (index) a possible choice for (bQ, c e) is (600,400). Estimates are that as a result of environmental deterioration (pollution, soil erosion, water extraction) in agriculture, 5 to 10% damage is caused to crops in some developed countries and 10 to 20% in developing countries; damage caused to recreation, housing etc is not as simple to quantify. Based mainly on agricultural data we take for E = 0 . 5 (E+aQ)/ (Ecr,t+aQ)=0.9; then for Ecr,,=0.8, aQ=2.2:

F~(KI) = k I * K I Cl[Trd}--

T~d+ bt T,d + ct

135)

It is assumed that the capital sector is more capital

Table 1. Crude estimates of physical capital coefficients (thousand

million). Production

Food. clothing O11 Chemicals Construction Metal Total

Capital

(kg)

(kg)

(D

(2)

Physical capital coefficient:

(2)/(1)

I0 70 16 20 20

45 10 35 3 11

4.50 0.14 2 19 0.15 055

136

104

1.31

Economic Modelliny 1994 Volume 11 Number 3

Dynamic macro modellin 9 and materials balance: J.C.J.M. van den Bergh and P. Nijkamp

intensive (physically) than the final goods sector (eg electronics, chemical, metal, construction materials), so that 1/kt > 1/kQ. The efficiency of resource used is assumed to be somewhat higher in the capital sectors than in others: ce(T,d(O))<~ 1.4, sO that a possible choice for (bl, cx) is (550,400):

f~.(T,d, K~,) = aw.*

T,~ "Era-b bwa

*

Kwa

=

(36)

T~d * K"~c 7",n + b,~ K ~ + C,e~

(37)

We choose ar~=0.8 (maximum recycling is 80% of waste subject to recycling); K~c=5. Initially 15% recycling; also here, the contributions of the technology and capital terms are assumed to be equal initially, so that (0.8 * lO0)/(brec + 100) = 0.150. 5 = 5/(c,~ + 5), or br~c= 107 and cr~=8:

FN(KN, N,E) =aN * Ev~N*(N* )/~"aN

(38)

We assume ~tN=0.8, fiN=0.2 and aN= 1.8:

Fs( K s, S) = as* K~s* S Bs

(39)

We assume % = 0.7 (non-renewable resource extraction more capital intensive than renewable resource extraction), and fls = 0.3 (stronger negative effect of decreasing stocks in comparison with renewables) and as = 0.9. In both extraction sectors we thus assume constant returns to scale:

Di(K,)=6i* Ki

C aB----

100

Kwa q- Cwa

We choose awa=0.95 (maximum abatement is 95% of waste subject to abatement); Kw,=5. Initially 65% abatement; the contribution of the technology and capital terms in the multiplicative specification are assumed to be equal initially, so that (0.95"100)/ (b~. + 100) = 0.65 o.5 = 5/(c,,~ + 5), or b~, = 18 and c,,,, = 1.2:

f~(T~a, K,ec) = a,~c*

functions ~() and e() are obtained, which we choose equal to 0.002 and 0,004 respectively. This leads to parameter values ~ = 0.098 and e = 0.096. We assume 6=0.5:

ieK

(40)

Because of new trends capital depreciation is assumed to take place at a faster pace in the final goods (Q) sector, where we assumed 6e=0.04 or an average lifetime of 20 years. In all other sectors we assume a rate of 0.025: ~(ee) = 1 --~*e e(ee) = 1 - - e * e

ee ~- R~ho,,* Wtoo* E

(43)

This simple multiplicative form restricts ee to the same range as each of the three parts, namely in between zero and one:

H(N, B, P) = max{0.2, min{ 1, N/Nc, i,} * min{ 1, B/Bcm } * min { 1, P,,,/(P +

1)} }

(44)

The following values are assumed: E.,i. = 0.2, Nor. = N . (where G(N, E) has a maximum), based upon the initial levels of B and P, the expected Bc,,t=lO0 and P~,i, = 450. Initially the E level is approximately 0.5:

G(N, E) = min{E/Ec,,,, 1} * r* N

(

N

* 1-min{E/Ec,,,1}.CN

)

(45)

N(t) is initially assumed at 10000, a third of its maximum value CN = 30 000. r is 0.05, SO that regeneration at a maximum environmental quality (E = 1 and N = N . = 15 000: M(P, E( = rain {E/Ec,i,, 1)} * ap* pbp

(46)

ae=0.5 and be=0.9, in order to include 'decreasing returns to scale' in waste assimilation. Initially P is equal to 100 in the base scenario:

bl(E)=a*E bE

dt /

b*,~K dt

(41)

In (42), for e = 1 (maximum) the minimum levels of

Economic Modelling 1994 Volume 1! Number 3

In (43) it is assumed that population increases at a rate depending on the difference between C/Pop (estimated initially at around 5) and a level %. The initial growth is assumed 0% so that aB=5. The functional structure applies especially to medium developed contries:

b3(dP°P~= c* dPop \dt ./ dt 293

Dymmm

m a c r o mode[hn~! a n d matertal.~ h a & m e

b4(Rx)=d*

J.C J M

can &'n B e r g h a m t P

R,~

(47)

bs(R s) = e* R s

a=0.005, b=0.00005, c = d = 0 . 0 0 0 1 , e=0.00004, in order to obtain terms of similar size. Finally, the critical damage level for natural regeneration, assimilation, and slow regeneration is equal to that for economic production (see above), namely 0.8. The distribution of Q and I is as follows:

.Vtlkamp

chosen such that E(0)=0.5: N(0)= 10000, B(0)= 100, P(0) = 200, S(0) = 3000. In order to find the initial condiuons of the economic stocks, the following set of equations has to be solved (see Appendix 2): first, the balance between resource matertals supply and demand: T,d + 6 0 0 , 5 * K o + min{(E + 2.2)/(E + Err,). ! } T~e+ 400 + T'd+bt *k~*K, T,d + 400

(50)

= Rre c + R N + R s

C=ac*Q+b c

(48)

O,d = Q - C

The consumption propensity is set equal to 0.5, and the fixed consumption level is 30. Investment allocation equals all sectoral relative growth rates of capital:

with R .... R N and R s given as above; second, the balance between investment goods supply and demand for a stationary path: 0.04" K o + 6 K * (K,,~ +

Kre c +

K N + Ks)

(51)

= ( k t - a K ) * Kt I~=6 , K , + ( I _ j ~ K a j , K j ) , "

K~

(49)

E Ks 3EK

The initial economic capital stock values are such that supply and demand for both new capital and for resources are in balance for the basic scenario (see Appendix 2): Kq(O) = 30, K,(0) ---4, K ~.(0) = K,~d0) = 5, KN(0)=I5 , K s = 3 0 . The other stocks are at the beginning as follows: X(0)= Y(0)= Z ( 0 ) = 0 since the structure of their equations is such that they are set to zero each time; immediately after the beginning they will attain their 'right' values. T,a(0)= 100, S~(0)=0, Pop(O)= 100. The initial values of N, P and B are

For an initial choice of T,d=100, N = 1 5 0 0 0 , P = 100, B = I00 - so that E(0)= 1 (maximal environmental quality) - the choice (KQ, Kz, Kw,, K .... KN, Ks) = (43, 3.6, 5, 5, 30, 30) satisfies these conditions. Initial values for R,,p and S may be chosen so that the initial conditions mentioned in Appendix 2 are satisfied. In Table 2 we show the values of parameters in the basic scenario.

Scenario and sensitivity analysis In this section the results of scenario and sensitivity analyses will be shown, based on the model formulated

Table 2. Parameter values in the simulation model. Parameter

Variable

Crmcal environmental quahty level: below which negatwe impact upon regeneratmn, ass~m,lanon and productmn CaDtal product,vity in investment sector Parameters in technology effect on resource use m mvestment sector Scale factor abatement funetmn Scale factor recycl,ng funct,on Rate of capital depreciation Sustainable development feedback to mvestment in R & D Populatmn growth parameter Fraction of treated waste going into unused stored waste Fraetton of recycled waste go,ng into unused stored waste SustainaNhty d u m m y Fraction of renewables" stock regarded avmlable Fractmn of non-renewables" stock regarded available Cnt,cal renewables' level for environmental quality determmation Crmcal slow renewables" level for env,ronmental quality determination Crmcal pollutmn level for environmental quahty d e t e r m m a u o n Intr,nsm growth of renewables Carrying capacity of renewables Assimdauon function scale parameter Population growth funct,on parameter

E ....

08

kt h~ a,, a,,,, 6,

1 550 0.95 0.8 0.025 0 098 5 0.5 05 0

294

an .st s2 d p ?~

Ps N ,,,t B , ,,, p,,,, r C~ ae an

In base scenario

- -

1 15 000 I00 450 0.05 30 000 0.5 0.005

In equation Q, N, B. P, R.¢, 1, R.e ~ 1, R .... 14'~2.t R~o R,ec V~;e,, dK, 'dt, leK'. [Q } d T,d'dt Pop dSw/dt, 14;~¢ dS~/'dt, W~,, Rv.p,.,¢ R N.perc

Rs.pe,~ E E E dN/dt, Rsho, , dN/dt, Rs,ort dP,"dt, H'~oo dB/dt

Economic Modelling 1994 Volume 11 Number 3

Dynamic macro modellin9 and materials balance: J.C.J.M. van den Bergh and P. Nijkamp

Table 3. Scenarios for analysis; empty cells denote the same value as in the base case scenario,a Scenarios

0. Base case 1. No ethical concern 2. Low environmental quality 3. Low non-renewables 4. Low quality and ethical concern 5. Moderate growth 6. Strong growth 7. Extreme growth 8. Sustainability and ethical concern 9. Extreme growth, sustainability and ethical concern 10. Extreme growth and sustainability

KI 3.6

N

P

S

d

inv

15 000

100 599 599

3000

1 0 0 0

0

10000

1000 10000 5 7 10

0 0 0

10 10

0

l l 1

K t, N, P, S, d and int, stand for initial stocks of capital in the investment sector, initial stocks of natural resources, pollution and non-renewable resources, and two dummy variables for thepresence or absence of ethical concern and the feedback to investment allocation, respectively.

above. First we will outline the scenarios and discuss an investment correction scheme that deals with the sustainable development feedback to capital investment in the economy for some scenarios. Next, results of simulations are presented and discussed. The scenario analyses serve two purposes. First, they will show the type of patterns that can be generated by the model. Second, certain types of (policy) strategies and exogenous scenarios can be illustrated by it. The sensitivity analysis is restricted here to changes in certain initial environmental stocks, as these may have a large impact upon the dynamic behaviour of the system. Table 3 lists 11 scenarios under which model simulations were performed. The results of these in terms of generated time patterns for certain indicators are shown in Figures 3 to 10. Table 3 indicates which control variables in scenarios 1-10 differ from the base case scenario. These variables were chosen in order to take the value system, environmental quality, nonrenewable resources, and the pace of growth into account. The base case scenario 0 represents a stationary economy (no capital stock changes) with a balance of the demand for a supply of investment goods, maximum environmental quality, a balance of demand for a supply of resource materials, and maximum ethical concerns for future generations. Each of the other scenarios deviates from this base case scenario in at least one of these respects. Scenario l, no ethical concern, differs from the base case by including a minimum of ethical concern, as reflected by the dummy d (see Equation (27)). In the scenarios 2, low environment quality, and 4, low quality and ethical concern, the environmental quality variable E is initially equal to 0.5 as a result of the chosen initial lower than in the base c a s e - stock values for renewable resources and pollution. The scenarios 5, 6 and 7, moderate growth, strong growth and extreme growth, represent moderate, strong and very strong ex ante Economic Modelling 1994 Volume 11 Number 3

growth schemes, based on a choice of the initial capacity for growth, given by the stock of capital in the investment sector. Scenarios 8 to 10, sustainability and ethical concern, extreme growth, sustainability and ethical concern, and extreme growth and sustainability, try to differentiate the effects of extreme growth, and ethical concern, given the active sustainability feedback to investment decisions. This means that investment is reallocated from final output to abatement and recycling when the indicator ee (taking values between or equal to 0 and 1) is below its maximum. The correction terms that are applied respectively to investment in final goods production, waste abatement, and recycling are given in (52). The parameter values chosen are as follows: partQ = p a r t w a = 0 . 5 ; the pattern of Q was similar when partwa was changed in 0 or 1. The dummy inv denotes whether or not the feedback to the investment allocation is working (1 and 0, respectively). In scenario sustainability and ethical concern the initial allocation and level of investment are based on the assumption of a stationary state. In scenario 9 strong growth is combined with endogenous investment allocation. Scenario 10 differs from 9 by suppressing strong ethical concern, so that reactions in both investment allocation and technological progress will be less than under scenario 9. correction IQ = corse = - inv* partQ* (1 -- ee)* IQ correction Iwa = partwa * corle correction Irec = partre c * cor lQ partwa + partre c = l

(52)

Since environmental quality is higher for scenarios 0, 1 and 3 than for scenarios 2 and 4, the initial production output is also higher (see Figure 3). For 295

Dt'namtc macro mode/l#tg and materta/s balance J C.J. ,l,I. ran den Ber.qh and P A,'okam p 23O 220 210 200 190 180 170 (D

160 150 140 130 120 110 100 90 1

3

5 0

7 0

+

9 1

11 t ime 0

2

13

15 z~

3

17 X

19

21

23

25

4

Figure 3. Development of final goods production over time for scenarios 0-4. scenarios 2 and 3, environmental quality is the single cause of decreases in output. For the other three scenarios resource scarcity is an additional cause, as it leads to under-investment and decreasing stocks of capital over time (see Figure 4). However, the curve for scenarios 4 in Figure 3 shows that more concern for future generations and natural environment gives rise to a slowing down of the decline in output. Notice that the difference between scenarios 0 and 1 is negligible, due to the fact that a stronger ethical concern (as in the base case scenario 0) does not give rise to impacts on (tempered) growth as long as the system behaves in a sustainable pattern over the time period considered. However, when a non-stable pattern is followed, the differential outcomes of scenarios 2 and 4, which is due to the same difference in control settings, is not negligible. The pace of technological progress is apparently influenced by three factors: investment, environmental effects and ethical concerns. With specific attention (or ethical concern) for future and environment, and with a non-optimal environmental quality, technological progress is seen to be highest in scenario 4 (see Figure 5). In scenario 4 two out of three factors are active. Scenario 2 shows also high technological progress, because the system described by it suffers from very 296

low environmental quality (one factor). Scenarios 0 and ! have an equal pace of technological progress as a result of equal capital investment (both initially stationary state paths). Scenario 3 shows the slowest technological progress, partly since the environmental effects are missing. To observe this completely, one should compare the environmental quality for each scenario in Figure 6. This may be interpreted as few non-renewable resources (eg fossil energy resources) giving rise to output decline and neutral or propitious environmental effects. Supply patterns of resource materials (Figure 7) differ widely because of the following factors: renewable resource stock, nonrenewable resource stock, extraction and recycling capital, technological progress affecting extraction and recycling efficiency of capital. Concern for future generations allows the supply of materials for the present choice of initial natural resource stocks to keep increasing (scenarios l and 4). A low environmental quality causes materials supply to be initially lower for scenario 2 than for 3, but at a later stage this relationship inverts. This change results from a favourable turn in the development of the capital stock and technology. In Figure 8 different growth patterns are shown. Here, we can compare long-term effects of variation

Economw Modellinq 1994 Volume 11 Number 3

Dynamic macro modellin# and materials balance." J.C.J.M. van den Bergh and P. Nijkamp

46 44 42 40 38 36 34 O

I

32 30 28 26 24 22 20

6 1I ~ 3I z 5I & 7I ~ 9I1'o 1111'2 13I1~ 15I1'~ 1711'8 19I 2'o 21I ~'~ 2 312~ 2 I5 time

Figure 4. Development of capital in the final production sector over time for scenarios 0-4. 34o 320 300 280 260 240 k_ F-

220 200 180 160 140 120 100

I ~ 3I ~ 5I ~ 7I ~ 9I1'0 1111'2 13I I~ 15I1'~ 1711'8 1912'o 2112'2 2 312', 25I

1

t_ Ime

[]

0

+

1

O

2

A

:3

X

4

Figure 5. Technological progress for scenarios 0-4.

Economic Modelling 1994 Volume 1l Number 3

297

D v n w m c macro modelling wul materials balance." 7.C.J.J,1. vwl den Beryh atul P. Ntjkamp q 1 1

0

9

0

8

0

7

o

6

0

5

i

0 4

0

3

0

2

0

1

h ~ \ h ~

0

Q

\

0

0

0

0

0

0

0

0

0

0

0

0

b

0

. . . .v . . ,~

X

)-'.

X

,~,

X

X

X

X

)-"

X

I ~ 3I 4 5I ~ 7I ~ 9I~'o 11I I'. 13I I~ 15I1'~ 17I I'~ 19IJo 21I.'. 23I.~

1

I

25

t irne

[]

0

+

1

o

2

z~

3

x

4

F i g u r e 6. E n v i r o n m e n t a l q u a h t y o v e r t i m e for s c e n a r i o s 0-4. 1

ogL

0 8

0

9

~c

?

0 6

(0

~o

0 5

w

0 4

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1

3

5

[]

7

0

+

9

1

11 t ~me

<>

2

13

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3

17

X

lg

21

23

25

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F i g u r e 7. Total supply of natural resource materials o v e r t i m e for scenarios 0-4.

298

Economic Modelhny 1994 Volume 11 Number 3

Dynamic macro modelling and materials balance J.C.J.M. van den Bergh and P. Nijkamp 330 320 310 3OO 290 280 270 260 250 24O o

220 220 210 200 190 180 170 160 150 140 1

l

3

lZl5

I

7

11'0 1111'2 13I

9

11'6 1711'8 1912'o 2112'2

15

23

I

25

TIME 0

Stationary

+

moderate

o

stron~

~

very

strong

~rowth

Figure 8. Final goods production over time for scenarios 0, 5, 6 and 7.

in the initial capacity for growth on output. Only moderate growth seems sustainable over the time period shown. Strong growth leads to a quickly decreasing environmental quality, and a collapse in output. The size of the fall in output levels is comparable for strong growth and extreme growth. As a consequence, it seems not to matter (relatively) how fast the growth, since the collapse will be relatively hard. However, the output level under strong growth is catching up with that under extreme growth at the end of the period shown (the environmental quality levels are also equal). Figures 9 and 10 show the results in terms of final goods output of various scenarios. We have taken a time horizon of 100 years since we wanted to investigate the very long-term effects of a completely different development of the sectoral structure. Here the investment allocation is endogenously influenced by the state of the environment and ethical concern, which we referred to in Section 4 as sustainable development feedback (according to Equations (52)). From Figure 9 it is clear that this reaction (called 'adjustment') has a positive effect on output in the long run, as compared without such a reaction. Collapses followed by growth are evaded ie patterns are smoothed out. Initially the output

Economic Modelhng 1994 Volume 11 Number 3

decreases faster under the investment allocation reaction, but from time 40 on output is higher. The collapse followed by recovery and a second, catastrophic collapse are explained by the fact that a collapse of the economy allows for decreasing environmental pressure and new economic opportunities for growth. However, the growth path is so steep, because of the relatively large supply of investment goods, that environmental pressure increases along with it. This causes the final collapse. In Figure 10 patterns can be compared between extreme growth (without adjustment of investment allocation) extreme growth, sustainability and ethical concern (with investment reaction and ethical concern) and extreme growth and sustainability (minimum ethical concern for future generations and/or natural environment). It is clear that without much ethical concern the reaction is too weak for output to stay on a growth pattern. When adjustment of investment allocation is based on the strong notion of ethical concern, the growth pattern can be maintained for a very long period of time. Finally, a sharp fall in output results, caused by both the negative impact on the environment of maintained growth and the investment reaction diverting investment from final goods production to waste abatement

299

Dymtmt~ macro modelhnq and matertal,s hahmce J.C.J.M. can den Berqh and P. ,Vukamp

24o 220

200

-

180

-

160

0

140

-

120

-

100

-

BO

-

60

40

20

0 TIME []

no

adjustment

0

adJustment

Figure 9. Development of final goods production over time for scenarios 0 (no adjustment) and 8 (adjustment). 900

800

700

600

500

400

300

200

100

t

00 TIME +

no

adJustment

A

adJustment

x

I ~ttle

concern

Figure 10. Final goods production over time for scenarios 7 (no adjustment) and 10 (little ethical concern).

300

Economw Modelhng 1994 Volume 11 Number 3

Dynamic macro modellin# and materials balance. J.C.J.M. van den Bergh and P. Nijkamp

and recycling sectors. The pattern finally seems to stabilize on a positive lower level. The conclusion may be that the development of sectoral structure has a large impact in the long run on the level of output of final goods. Finally, sensitivity analysis was also performed to investigate the model reactions to changes in certain initial conditions. Especially the natural renewable resources N and pollution P are open to different interpretations, and therefore their levels were varied. The results are shown in Figures 11 to 14, for various combinations of renewable resource and pollution stocks, all under the base case scenario. The results show that patterns depend strongly on initial values of these variables, and that patterns of collapse are usually followed by recovery, though at a lower level than the initial one. This can be explained by the fact that a collapse of output may go along with a decrease of environmental pressure from both less resource use and less waste residuals being generated. This depends first of all on the magnitude of a fall in environmental quality and resource scarcity that causes an economic breakdown. Furthermore, whether recovery can occur, especially at a fast speed, depends also on certain characteristics of the economic system that determine

its recovery capacity, such as technological progress, and capacities of abatement and recycling activities relative to production capacities. In Figure 11 one can find patterns that have a short recovery followed by a second collapse (or a phase-wise collapse). Here, the environmental breakdown causes an economic collapse, which allows environmental pressure to be weakened. The stationary path up to time 19, however, did not stimulate technological progress very much, so that the economic recovery capacity was weak, giving rise to the second collapse after time 22. A general conclusion is that the two-way economic-environmental interactions cause interesting feedback loops. One cannot simply make the general statement that a better initial environmental state will lead to better economic performance over a certain period of time. One has to realize that a better environment may give incentives for high growth and (ex post) undesirable or wrong directions of technological progress.

Conclusions At the end of this study some retrospective remarks are in order. Economic modelling for the purpose of obtaining insight into the long-term behaviour of an

220 210

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Figure it. Development of final goods production over time for an initial renewable resource stock N(O)= tO000 and four different initial pollution stock levels.

Economic Modelhng 1994 Volume 11 Number 3

301

Dvmmtic macro modellm,q and matcrtal~ hulam'e J ('.J.M. ran den Beryh and P ,\"tlkamp 230 220 210 2OO 190 180

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Figure 12. Development of final goods production over rime for an inmal renewable resource stock N(0)= 15000 and four different initial pollution stock levels. 230 220 210 2OO 190 180 170 160 O

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Figure 13. Development of final goods production over time for an initial renewable resource stock N(0)=20000 and four different initial pollution stock levels.

302

Economw Modelhny 1994 Volume 11 Number 3

Dynamic macro modelling and materials balance: J.C.J.M. van den Bergh and P. Nijkamp

230 220 210

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Figure 14. Development of final goods production over time for an initial renewable resource stock N(0)= 25 000 and four different initial pollution stock levels.

economic system faced by environmental and resource constraints requires an approach that combines dynamic models of growth and technology with environmental processes. Not only the adverse effects of economic sectors on environmental quality and resource availability can then be dealt with, but also the impact of environmental degradation and resource scarcity on economic performance. This may take the direction of physical effects, such as on health and productivity, and in addition, as was also pursued here, a focus on feedback mechanisms to economic decisions on technology and investment allocation. Such feedbacks were based on sustainable development conditions and the intensity of ethical concern about the environment and the future. More concern was interpreted here to imply a more cautious approach to designating resource availability and environmental quality as sufficient. This was one important characteristic of the model presented. The other important element is inclusion of the materials balance principle, via specification of production functions and materials' accounting between phases of extraction, production, consumption, emission and recycling. The advantage of this approach is that it provides Economic Modelling 1994 Volume 11 Number 3

a consistent and general framework for dealing with complex dynamic intereactions between an economy and its environment, especially taking account of the particularly relevant economic reaction mechanisms that are available and may become operative in such a context. The approach extends growth theory, materials balance accounting, and integrated modelling by combining complex interactions within both the economy and the environment. As a result, the model that was developed here is not analytically solvable. Therefore, it was calibrated to fulfill certain conditions in a base case scenario, linked to equilibrium and sustainability. Logical and realistic or plausible values were used for choosing parameter values. Subsequently, simulation experiments were carried out, focusing on initial economic and environmental stocks, feedback mechanisms, sustainability conditions and ethical concerns. It is clear from the simulation and sensitivity analysis results that interesting and non-trivial insights can be obtained. The model can be regarded as helpful in our understanding (ie deduction) of how economy and environment interact in the long run, when material and physical relationships, and behavioural 303

Dvnamw macro modelling and materuds halance J.C.J.M. van den Bergh and P. Ni/kamp

feedbacks are regarded. However, the important interpretations of the results should not be that within a known period of time the system will break down. More important are the types of patterns, economic reactions and intermediate dynamics of collapse and recovery. The results lead to an important observation: permanent reductions in environmental quality of environmental stocks seem to make it very difficult to sustain a positive trend or even a constant level of economic performance. We may even draw the conclusion that cautious behaviour does not necessarily lead to worse performance in the long run, but may certainly protect against adverse long-term developments. Furthermore, the model is very sensitive to changes in initial environmental and economic stocks, while patterns often tend to return to stable levels, even though possibly preceded by strong growth and collapse patterns. This is a clear non-linear characteristic of the model, which is tempered mostly by internal consistency provided by materials balance. The inclusion of a materials flow and materials balance in dynamic models with non-linear processes has been shown to be able to provide a realistic and helpful tool for investigating long-term relationships between economy and natural environment. Application of this approach is limited by on the one hand data limitations, and on the other hand the problem of aggregation of physical information. One should either choose experimental models like the present one, or adopt a more specific disaggregated and often partial approach. The resulting model system provides a direction for further model oriented research for long-term environmental policy and scenario analysis.

References 1 C.L. Anderson, 'The production process: inputs and wastes', Journal o f Environmental Economics and Management, Vol 14, 1987, pp. 1-12. 2 R.U. Ayres and A.V. Kneese,'Production, consumption and externalities', American Economic Review, Vol 59, 1969, pp 282-297. 3 R.U.Ayres and A.V. Kneese, 'Externalities, economics and thermodynamics', in F. Archibugi and P. Nijkamp, eds, 4

Economy and Ecology" Towards Sustainable Development, Kluwer, Dordrecht, 1989. J.C.J.M. van den Bergh, Dynamic Models for Sustainable Development, PhD dissertation, Thesis Publishers/

Tinbergen Institute, Amsterdam, 1991. 5 J.C.J.M. van den Bergh and P. Nijkamp, "Aggregate dynamic economic-ecological models for sustainable

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6

7 8

9 10 11

development', Environment and Planning ,4, Vol 23, 199l, pp 1409-1428. J.C.J.M van den Bergh, ~A framework for modelling economy-environment-development relationships based on dynamic carrying capacity and sustainable development feedback', Environmental and Resource Economics, Vol 3, 1993, pp 395-412. CBS, CBS Yearbook, Central Statistical Office (CBS), SDU, The Hague, 199l. H.E. Daly,'Elements ofenvlronmentalmacroeconomics', in R. Costanza, Ecological Economics: The Science and Management o f Sustainability, Columbia University Press, New York, 1991. M. Faber and J.L.R. Proops, Evolution, Time, Production and the Environment, Springer-Verlag, Heidelberg, 1990. M. Faber, H. Niemes and G. Stephan, Entropy, Environment and Resources. An Essay in PhysicoEconomies, Springer-Verlag, Heidelberg, 1987. N. Georgescu-Roegen, The Entropy Law and the Economic Process, Harvard University Press, Cambridge

MA, 1971. 12 L.S. Gross and E.C.H. Veendorp, ~Growth with exhaustible resources and a materials-balance production function', Natural Resource Modeling, Vol 4, 1990. pp 77-94. 13 M.I. Kamien and N i . Schwartz, 'The role ofcommon property resources in optimal planning models with exhaustible resources', in V.K. Smith and J.V. Krutilla, eds, Explorations in Natural Resource Economics, Johns Hopkins University Press, Baltimore, MD. 14 A.V. Kneese, R.U. Ayres and R.C. D'Arge, Economics and the Environment. A Materials Balance Approach,

Johns Hopkins Press, Baltimore, MD, 1970. 15 D.H. Meadows, J. Richardson and G. Bruckmann, Groping in the Dark. The First Decade of Global Modeling, Wiley, New York, 1982.

16 H.T. Odum, ~Models for national, international and global systems policy', in L.C. Braat and W.F.J. van Lierop, eds, Economic-Ecological Modelling, NorthHolland, Amsterdam, 1987. 17 M. Ruth, Integrating Economics, Ecology and Thermodynamics, Kluwer Adadem,c Publishers, Dordrecht, Netherlands, 1993. 18 J.B. Smith and S. Weber, "Contemporaneous externalities: rational expectations, and equilibrium production functions m natural resource models', Journal of Environmental Economies and Management, Vol 17, 1989, pp 155-170. 19 S.K. Swallow, ~Depletion of the environmental basis for renewable resources: the economtcs of interdependent renewable and non-renewable resources', Journal o f Environmental Economics and Management, Vol 19, 1990, pp 281-296. 20 R Wilkinson, Pover O' and Prooress An Ecological Model of Economic Development, Methuen, London, 1973. 21 WCED, Our Common Future, World Commission on Environment and Development, Oxford University Press, Oxford/New York, 1987.

Economw Modelhny 1994 Volume 11 Number 3

Dynamw macro modelling and materials balance." J.C.J.M. van den Beroh and P. Nijkamp

Appendix 1 Model notation The set K = {Q, 1, wa, rec, N, S} denotes the six sectors.

WQ,I

Stock variables

W,ec Wtoo

B K Ke K~ Kwa K,~ Ks

Ks N P

Pop R~ S S~ Tr~ Z

= a slowly renewable resource (soil, land, water) = total e c o n o m i c capital = productive sector capital = investment sector capital = waste a b a t e m e n t / t r e a t m e n t capital = recycling capital = renewable resource extraction capital = non-renewable resource extraction capital = the stock of renewable resources = stock of pollution in natural media or organisms = h u m a n p o p u l a t i o n level = inventory (supply) of natural resource materials = the stock of non-renewable resources = the stock of useless, stored waste = progress indicator of e n v i r o n m e n t a l technology = artificial variable (total 'real' o u t p u t delayed)

Flow variables C E I

l,(i~K) O,d Q Rde,~ RN RN,perc

Rnew Rp~c

Rs Rs.pe,c R~ho,, Rrec Rshor t

R~,,~ e

W~m

= consumption = indicator for overall environmental quality = total investment in replacement a n d new capital = investment in sector i = social investment in research a n d development = o u t p u t of final goods sector = total productive a n d consumptive d e m a n d for resources -~ renewable resource extraction ----- subjective/perceived availability (rate) of renewable resources = required extraction of resources -- subjective/perceived availability (rate) of all resources = non-renewable resource extraction = subjective/perceived availability (rate) of non-renewable resources = indicator for insufficiency of perceived resource supply = recycled resource materials = perceived shortage of resource supply to demand = a b a t e d / t r e a t e d waste = ecological effect indicator for technical progress = emitted waste

Economic Modelling 1994 Volume 11 Number 3

= gross waste from final a n d investment goods sectors = waste a m e n a b l e for recycling = indicator for unsustainability of waste emission

Fractions A

= assimilation function = p o p u l a t i o n growth rate b,(i= l ..... 5) = regeneration a n d d a m a g e functions of slowly renewable recourses = ratio of resource input to material o u t p u t Co in final goods sector = ratio of resource input to material o u t p u t Cl in investment goods sector = discarded capital Di(ieK) = unrestricted p r o d u c t i o n function final FQ goods sector = unrestricted p r o d u c t i o n function FI investment goods sector = unrestricted p r o d u c t i o n function Fs renewable resource extraction sector = unrestricted p r o d u c t i o n function Fs non-renewable resource extraction sector = part of p r o d u c t i o n waste t h a t is fwo abated/treated = part of waste a m e n a b l e for recycling that f, ec is recycled = regeneration function of renewable G resource capacity H = e n v i r o n m e n t a l quality function ~t = general investment effect on technology = effect of social R & D a n d p r o d u c t i o n 8 growth on technology B

Parameters d PN Ps Sl S2 Ecrlt

aQ bo, c O

bt, cl kQ, k~

= d u m m y for basing resource availability on stock or sustainable flow = fraction of stock of renewables regarded as available for use now = fraction of stock of non-renewables regarded as available for use now = fraction of treated waste ending up in unused stored waste = fraction of recycled waste ending up in unused stored waste = below this value of e n v i r o n m e n t a l quality negative impacts on regeneration, assimilation, a n d p r o d u c t i o n = e n v i r o n m e n t a l effect p a r a m e t e r in commodity production = parameters of function co() = parameters of function c d ) = capital p a r a m e t e r in functions Fo( ) a n d Fd )

305

Dl'namw macro modelhng and matertala balance. J.C.J.M. t'an den Bergh and P Nijkamp a,,,,, b,a, c,~,a a~e~.b,~.~,,, a.~,, :¢,,j,fl~,

as, ~s, fls 6,(i~k) 6

= parameters of the waste abatement,' treatment process function = parameters of the recycling process function = parameters of function F~,~ = parameters of function Fs( ) = depreciation of capital = production increase parameter in technology formation equation

,,, e,

= parameters in functions ~( ) and el I

N ,~,,, B,r,,, Pcr,t = parameters of environmental quality r, CN

ae, hp aB

function H() = intrinsic growth and carrying capacity parameters in regeneration function G() = parameters in assimilation function M() = parameter in population growth function

B( )

Appendix 2 Requirements for initial values Here we will state conditions for initial values of capital stocks. We have to solve a set of equations reflecting a balance of demand and supply initially on markets for investment goods and resource materials. Furthermore, we give conditions on economic stocks of capital as having initially sustainable resource extraction and sustainable waste emission. Finally, we list the conditions for stationary growth paths (proportional growth of all sectors). The balance between the supply of and the demand for investment goods requires a certain sectoral distribution of capital such that: F ( K , I = ~ I,

(53)

holds, and, if we require at least stationary development of all sectors, the following inequality is satisfied:

F(K,)>- ~ D,(K,)

(54)

A second important balance is that between the demand and supply for resource materials. For a stationary path it is formulated as R , ~ , + R , ~ = R N + R s . It implies that Q = FQ(Kq, E) and I = FI(KI), and leads to

- ( 1 -s~l* J',,~(Tr~, K~,a)* J;~(T,a , K,~¢) * (Co("Ira) - 1)] * Fo(Ko., E~

+ [ct(T~a)-(l --.sl)*fwalTrd, K,.a)*Jr~(T~a, Kre¢) *(c,(T,d)-- l)]* F,(K,)--L~(T,a, K,e~)* ~ D,(K,)

- Fu(K~, N, E ) - Fs(K s, S) = 0

156)

When the extraction capacities exceed (ethical-ecological) acceptable resource extraction levels, the equation to be solved becomes (57) instead of (56t: [cQ( Tra) - J'~ec(Trd" K rec) --(1 --sO* f~a(T,d, K~,a)* f~ec{T,d, K,e c) *(cQ( T~al- 1)] * Fo(K O, E)

*(ct(T~a)- I)]* FI(Kt)-J,e,.(T, a, K,e,.)* ~ D,(K,)

= R,ec + min{F~(K v, N, E), R,v,per~l"

t~K

(55)

For a stationary path, where for all positwe t and all x<~t 14~e~(t- x) = W,ec(t), R,e~(t -- X) = R,ec(t), T~a(t- x) = T~a(t)etc we can solve it as follows. In the case where the perceived renewable and non-renewable resource amounts exceed the extracuon capacities (based on FN( ) and Fs()), we can derwe that a balance between supply and demand occurs for sectoral capital stock sizes satisfying, for gwen state of technology, environmental quality, and resource stocks, the equality in (56). We will use this to make our choice of initial values of the sectoral stock variables, so that initially a

306

(co(T,d) --.f~e¢(T,a, K,ec)

+ [c/(Tra) - I l --~1 )* f,.a( "/;a, K,,.)*J~,[ T,a. Kr~c)

co.{T,d)* FQ(K e, E) + ci(T,d) * FI(K I )

+ rain{ Fs(K s, S), Rs.v~,~}

balanced economy is represented. Because of non-linear relationships between capital and activity levels, proportional sectoral capital growth may lead to an unbalanced development of activity levels, and a gap between supply and demand for resources:

-d*p~.* N - ( l - d ) * G ( N , E ) - p s * S = O

(57}

Trying to estabhsh a dynamic path which satisfies (56) or (57) may be impossible; it is at least very hard to do. It requires that the equations have multiple solutions so that new values of K, on a development path are in the solution space. Sustainable use of renewable resources requires a stock of renewable resource extraction capital that satisfies R~ <~G(N, E) or:

F~.(KN, N, E) <~G(N, E)

(58)

Economw Modelhn9 1994 Vohtme 11 Number 3

Dynamic macro modelling and materials balance. J.C.J.M. van den Bergh and P. Nijkamp This can be written as:

*(1 - f, ec(T,a, Krec))] * (cq(T,d)- 1) +(1 -- S2)*(l --frec(Trd,K,ec))} * FQ(KQ, E)

[co(T,a) - f,~(T,a, K,e~)

+ [1 -fwa(Tra, Kwa) + (1 - sl)*(l -s2)*fwa(Tra, Kwa)

- ( 1 - s l ) * fw.(T,a, K~.)* f,~(T, a, K,~)

*(1 - f, ectT,a, K,ec))'] *(c1(T,a)- 1)* Ft(Kt)

* (CQ(T~a)- 1)] * FQ(KQ, E)

+(1 -s2)*(l -- f, ec(T,d, r,ec))* ~ D,(K,)~ A(P, E)

+ [ct(Tra ) - ( 1 -st)*f~,(T~ a, Kwa)*frec(Trd,K,,~) *(c,(T,a)- 1)] * F t ( K t ) - f,~(T,a, K,e~)* ~ D,(K,) - Fs(K s, S) <~G(N, E)

(59)

Sustainable waste emission, defined as We,.~
Econom,c Modelling 1994 Volume 11 Number 3

(60)

t¢K

Finally, in order that a stationary path be generated, at least the following conditions must be satisfied: I,=D,(K,) (iEK), B(C/Pop)=O, RN=G(N,E) and We,.=M(P,E ) and b I(E) = b2(dK/dt) + b3(dPop/dt) + b4(Rs) + bs(Rs). The first of these can be solved by choosing, for a given total capital stock K, K~ such that Ft(K~)- D~(Kt)+ Kj = K, subsequently allocating K - K t to the remaining sectors (such that other conditions are satisfied).

307