CHAPTER 2 – Background

This chapter is a presentation of the background knowledge relevant to the application of dynamic environmental life-cycle assessment in a structural economics context. The discussion begins with an introduction to static and dynamic economic models, then more specifically a discussion of static and dynamic I–O models. Central to the discussion of I–O modeling is the concept of equilibrium. I–O modeling is an empirical model based on Walrasian General Equilibrium constructs, thus, a brief discussion of its importance is included. The basis of dynamic I–O modeling is structural change. An introduction to this topic as it relates to the model as well as changing technologies and prices. The bridge between LCA and I–O is then discussed in an historical account of previous studies utilizing I–O for environmental analyses. Finally a discussion of how dynamic I–O will be used as the basis of dynamic environmental LCA. Dynamic LCA will be defined and described within this context.

Section 2.1 – Static versus Dynamic Economic Models General

Economists model how society meets its needs with given resources and technologies. There are essentially four general categories of temporal distinctions to the models that economists use: static, comparative static, dynamic and comparative dynamic.

The first temporal distinction, static models, represents phenomena at a single interval of time. A static model would be able answer the question: what was the level of employment in the United States on January 1 1998? In this context, static models are not precursors to dynamic models, they have an independent status of their own. There exist applied problems, which, by their nature, are purely static. This type of problem is one that involves the state of the economy and not process of change. Questions such as this are static questions and they can be readily solved within the realm of static modeling theory (Hicks 1985) (Ruth and Hannon 1997).

The second temporal distinction, comparative static models, compare phenomena at several instances in time, that is, they are comprised of a sequence of static models. Hence, comparative static models are often confused with dynamic models (Ruth and Hannon 1997). For example, a comparative static model is appropriate to answer the question: what was the annual trend of employment in the computer industry from 1975 to 1995? In this example, the comparative static model is a collection of similar static in this case, two models to compare employment in 1975 to employment in 1995.

Typically, static models are assumed to be in equilibrium. Hence, a comparative static analysis can be thought of as examining a system in equilibrium, before and after a change (Fisher 1983) (Baumol 1970). Although, comparative static models are ‘static’ in nature, there is still an important element of time involved with their formulation. “If the predictions of comparative statics are to be interesting in a world in which conditions change, convergence to equilibrium must be sufficiently rapid that the system, reacting to a given parameter shift, gets close to the predicted new equilibrium before parameters shift once more” (Fisher 1983, 3). Hence, in order for comparative static models to be useful, the parameters that remain static in the model within the period of study, must also remain relatively static in the real world.

The third temporal distinction, dynamic models, are models that try to reflect changes in time and take into account model components that are constantly changing as a result of previous actions or future expectations (Ruth and Hannon 1997). Here, a dynamic model would be appropriate to answer the question, what are the impacts of employment in the computer industry now and into the next century? It is important to note the distinction of comparative-statics to dynamic models. Although comparative static model may appear dynamic, they are not sufficient to answer issues concerning planning and are limited to historical accounts (Hicks 1985).

Therefore, a primary distinction of a dynamic model versus a static model is the scope of examining intra-period relationships. Within a period we define a sequence of intervals. Static models do not consider intra-period relationships of the intervals and dynamic models do. Dynamic economic modeling involves an understanding of how phenomena within an interval are related to activities outside the interval yet within the period of study.

Hicks (1985) eloquently points out the distinction of the inter-period study within static and dynamic models:

“Proper dynamic theory, even at its single-period stage, must take account of the fact that many activities that go on within the period are oriented outside the period; so that what goes on, even within the period, is not only a matter of tastes and resources, but also of plans and expectations. In statics there is no planning: mere repetition of what has been done before does not need to be planned. It is accordingly possible, in static theory, to treat the single period as a closed system, the working of which can be examined without reference to anything that goes on outside it (in the temporal sense). But this is not possible in dynamics. Even at the single-period stage the links which relate the single period to the rest of the dynamic process cannot be neglected” (Hicks 1985, 25).

Both static and dynamic models are concerned fundamentally with the structure of the interrelationships or interdependencies among variables and data of models (Kuenne 1963)(Kuznets 1953). However, a fundamental difference between models is that a specific solution to a static system yields a single solution vector, whereas a specific solution to a dynamic system is “a set of such vectors linked in a path through time” (Kuenne 1963, 14). A dynamic model may have more than one path converging to the same or different positions of rest (Kuenne 1963).

Incorporating the notion of inter-period relationships, “a dynamic model contains the potential for the derivation of theorems concerning the values of the variables, or changes in those values, before the position of rest, or equilibrium has been attained” (Kuenne 1963, 14). In contrast, a static system can yield theorems about “the values of the variables only in a state of rest, or theorems about changes in the values of the variables only between two states of rest” (Kuenne 1963, 14). Further, the distinction between static and dynamic models is not simply the existence of time in a dynamic system and its absence in a static model. The use of a static model must involve the interpretation of its solution “against time as a backdrop” (Kuenne 1963, 15). The difference between the models is more accurately reflected in the distinction between potentially derivable relationships (Kuenne 1963).

An intuitive presentation of the difference is presented by Kuenne (1963):

“A static model is one whose structural relationships do not contain time in any analytically meaningful way. By contrast, dynamic systems are those which do contain time-relationships among the relations of the variables in meaningful ways, i.e., in ways which could not be eliminated without affecting the solution to the system or eliminating the possibility of the solution” (Kuenne 1963, 457).

Essentially, a dynamic model is one where the incorporation of temporal information makes a difference in the ultimate solution of the system modeled.

The fourth distinction, comparative dynamics, is similar in concept to comparative statics. In the method of comparative static analysis, solutions to two sets of simultaneous equations are compared, while in comparative dynamics two sets of mutually exclusive differential equations are compared. For example, a dynamic system to determine quantity, q, consumed for the present time period is given by the differential equation of a consumption function F(x):

(2-1)

and by a second set of differential equations for the next time period:

(2-2)

The effective quantities for the first period are given by the values which solutions to (2-1) take on at t = ¥. Similarly, the values for effective quantities for the second period are given by the solutions described by (2-2) at t = ¥. By creating an imaginary system (2-2)´ (where (2-2) is the actual system in the next period but (2-2)´ is an imaginary one in the present), the analysis is then reduced from the comparison of effective quantities in two consecutive time periods to a comparison of two mutually exclusive dynamic systems (Morishima 1996, Ch. 5).

Baumol (1970) presents the following analogy: Here, an analogy to the study of a photograph can be made. A “still” photograph of a system in motion can be used to examine the position of various parts and the way they fit together. The “still” must include a reference to time, but the analysis of the still can be static (Baumol 1970, 5). One can expand the analogy that a motion picture is a succession of “still” photographs representative of comparative statics. And further, that the rules governing “continuity” such as in the art of cinematography, i.e., the relationship of a single frame to its preceding frame and its succeeding frame, is analogous to a dynamic study. It then follows that a comparative dynamic analysis would then be the comparison of the continuity of two segments of a motion picture.

In summary, both static and dynamic models involve some element of time. Static models are confined to a point in time or a single interval of time, and in general are concerned with changes in social behavior, such as price, wages, and demand. Further, the general assumption is that static models are at rest, or in a state of equilibrium. In contrast, dynamic models are expanded to include several intervals of time. They include inter-period relationships that go beyond social phenomena, such as the accumulation of capital and technological changes. In general, dynamic models describe time-based relationships that ultimately are reflected in the solutions obtained. Comparative static models are examinations of specific equilibrium points in time and comparative dynamic models are examinations of one system of inter-period relationships to another.

Section 2.2 – Static and Dynamic I-O Models

The distinction between static and dynamic I-O models is a complex topic that is interwoven with the mathematics of dynamic linear programming. The following discussion will introduce static I-O economics and the introduction of dynamic I–O in the mid–20^th century.

What is an input-output model? Economic I–O analysis is a method to systematically quantify the interrelationships among various sectors of an economic system. The economic system may be as large as a nation or even the entire world economy, or as small as the economy of a metropolitan area (Leontief 1985a). The I-O model is a formalization of the basic concepts published in 1758, by French economist, François Quesnay, in his "Tableau Economique." More than 100 years after Quesnay's work, León Walras developed a theory of general equilibrium that utilizes a set of production coefficients that related the quantities of factors required to produce a unit of particular product to levels of total production of that product. Wassily Leontief's model is a linear approximation of the Walrasian model, constructed in a similar fashion as the Tableau Economique, that allows the general theory of equilibrium to be applied (Miller and Blair 1985).

The approach to economic I–O analysis is as follows. The structure of each industry’s production process is represented by an appropriately defined vector of structural coefficients that describes in quantitative terms the relationship between the inputs it absorbs and the output it produces. The interdependence among the sectors of the given economy is described by "a set of linear equations expressing the balances between the total input and the aggregate output of each commodity and service produced and used in the course of one or several periods of time" (Leontief 1985a).

Thus if the economy is divided into n sectors, and if we denote X_i the total output (production) of sector i and by Y_i the final demand for sector i's product, we have:

(2-3)

for , and, .

The z terms on the right-hand side represent the interindustry sales by sector i to sector j. Thus, the entire right-hand side represents all of the interindustry sales, z_ij to final demand of sector i, Y_i, hence the total output of sector i. We then construct the system of equations for n sectors and we have:

(2-4)

If we then look at the jth column of z's we then have the following column vector:

(2-5)

These elements are the sales or inputs to sector j representing the intermediate input components necessary for the production of output by sector j. In addition to material inputs, there are labor activities (value added) that are also associated with production. We now have the basis of the Leontief table illustrated below:

Table 2–1. Input–Output Table of Interindustry Flows (Miller and Blair 1985).

				Purchasing Sector
		1	2		…	j	…	n
	1	z₁₁	z₁₂		…	z_1j	…	z_1n
	2	z₂₁	z₂₂			z_2j		z_2n
Selling Sector
	i	z_i₁	z_i₂			z_ij		z_in

	n	z_n₁	z_n₂		…	z_nj	…	z_nn

In input-output work, a fundamental assumption is that the interindustry flows from i to j depend entirely on the total output of sector j. That is, if sector j represents vacuum cleaners, we assume that if there is an increase in the sales of vacuum cleaners, there will be a corresponding increase in the sales of electric motors that are used in vacuum cleaners. From this concept we then formulate a ratio of input to output termed a technical coefficient. That is for a z_ij, the flow of input from i to j, and X_j, the total output of j, forms the technical coefficient denoted a_ij:

(2-6)

The a_ij's are fixed relationships between a sector's output and its inputs. Thus, there is an explicit definition of a linear relationship between input and output and there are no economies of scale, rather the Leontief model represents constant returns to scale. Thus, doubling inputs will double outputs, reducing inputs by half will reduce outputs by half. In essence, the coefficients represent the trade from industry i to industry j. By accepting the notion of fixed coefficients we can rewrite equations (2-4), replacing each z_ij, by a_ijX_j.

(2-7)

For input-output analysis, a common question to be asked is: given a forecasted demand (the Y_i's), how much output from each of the sectors would be necessary to supply these final demands? The Y_i's and the technical coefficients, a_ij are known and we solve simply solve for the outputs of each sector, the X_i's. Therefore, for a given set of Y's, we solve for n unknowns, X₁, X₂, …, X_n.

In matrix terms, we define:

, , (2-8)

Thus in matrix form the complete n × n system is:

(2-9)

The matrix A is known as the matrix of technical, input-output, or direct input coefficients. If , then can be found and a unique solution is given by:

(2-10)

where is commonly referred to as the Leontief Inverse. For a more detailed derivation of the input-output methodology, please refer to Miller and Blair (1985) and Leontief (1985a).

The following is a simple example using the input-output methodology. We are given data regarding two industrial sectors as shown in Table 2-2. This table quantifies the transactions between the two sectors, their final demand, and the row element of payments, representing the value added.

Table 2–2. Flows from two hypothetical sectors (Miller and Blair 1985).

		To Processing Sectors		Final Demand	Total Output
		1	2	(Y_i)	(X_i)
From Processing	1	150	500	350	1000
Sectors	2	200	100	1700	2000
Payments (value added)		650	1400
Total Outlays	(X_i)	1000	2000

The corresponding table of technical coefficients is found by dividing each flow in a particular column of the processing sectors in Table 2–2 by the total output. Thus a₁₁ = 150/1000 = 0.15. The resulting technical coefficient matrix, commonly referred to as the "A" matrix is shown in Table 2–3.

Table 2–3. Example technical coefficient matrix (Miller and Blair 1985).

		To Sectors
From		1	2
Sectors	1	0.15	0.25
	2	0.20	0.05

For this example, the technical coefficient matrix of Table 2–3, can be used to construct the recipe of commodities in each of our sectors. For sector 1, we need a interdependency of 15 cents of sector 1 and 20 cents of sector 2 to produce a dollars worth of commodity for sector 1. A typical question for this input-output analysis table is to find the resulting production as a result of increased demand, or output. For our example the initial output was $350 for sector 1 and $1700 for sector 2. It is important to note that for the year of observed data , and , thus the interindustry demands were greater than the final output.

For our analysis example we increase final demand to $400 for sector 1 and decrease demand for sector 2 to $1600, thus and . We then use equation (2-9) to find the new production levels.

, and .

The needed output are then found from equation (2-10):

The values of DX₁ and DX₂ then represent the impact to the economy as a result of changes in demand. For this case, DY₁ = $50 and DY₂ = -$100. This change in demand resulted in an increase of sector 1 activity of $29.7 and a decrease in sector 2 activity of $99.0 (Miller and Blair 1985).

Referring to the simple 2 × 2 model presented in Table 2-3, conceptually the simple model can be thought of as a nested feedback. The feedback is a relationship of the demand for two commodities (Y₁ and Y₂), and the two production activities that supply two commodities as shown in the digraph of Figure 2-1.

Figure 2–1. Simple Two-Sector Digraph.

In our example, the demand vector is , and we use the technical coefficient matrix presented in Table 2–3. For the first round, the amount of sector 1 and sector 2 production will be respectively, $400 and $1600 to meet, as a minimum, final demand. However, we know that from Table 2–3, that an additional (0.15)($400) = $60 sector 1 and (0.20)($400) = $80 from sector 2 will be necessary to produce $400 worth of sector 1 commodity. Also, for sector 2, we will need to produce an additional (0.25)($1600) = $400 from sector 1 and (0.05)($1600) = $80 from itself to produce the $1600 worth of sector 2 commodity. Therefore, for this "round", the total economic activity will be $60+$400 = $460 for sector 1, and $80 + $80 = $160 for sector 2. The next "Round-By-Round" impacts are then calculated for an intermediate demand of Y₁' = $460 and Y₂' = $160. The total "Round-By-Round" are summarized in Table 2–4:

Table 2-4: Round-By-Round Impacts (in Dollars) of (Miller and Blair 1985).

Round	1	2	3	4	5	6	7	³ 8
Sector
1	400	460	109	41.4	12.9	4.34	1.42	0.64
2	1600	160	100	26.8	9.61	3.06	1.02	0.51

Thus, the right hand side of equation (2–10) can be thought of the algebraic equivalent of:

(2–11)

Or removing the parentheses,

. (2–12)

Thus, the direct impacts can be considered:

(2-13)

and the indirect impacts:

(2–14)

As seen by this example, the second and third orders of effect can be significant, which if excluded from an analysis may influence the qualitative outcome of an LCA study to an incorrect conclusion (Lave, Cobes-Flores, et al. 1995). By using an I–O framework approach, the interdependent relationships are inherently captured.

General assumptions of the static Leontief model are as follows:

· The interindustry flows from i to j depend entirely and exclusively on the total output of sector j for that same time period (Miller and Blair 1985). This is important. This means that all activity, both direct and indirect economic activities occur within an interval. In the Leontief model this interval is generally accepted to be annual. For example, the direct requirements that it takes to produce automobiles over 1 year, and all indirect requirements that it takes to produce that car are captured within that same year – all of the energy, raw materials, finished goods, anything directly or indirectly associated with the production of the automobile.

· There is a fixed relationship between a sector’s output and its inputs. Economies of scale in production are ignored in the short-run; production operates under constant returns to scale. Hence, technical coefficients of production are fixed (Dorfman et al. 1958) (Miller and Blair 1985). In the case where technical coefficients (a_ij’s) of the “A” matrix, are described in value terms versus physical terms, this assumes that the price ratio is fixed. Here a_ij is the “economic” production function of input from sector i for sector j, which equates to the ratio of intermediate input z_ij to total output x_j in value terms. This is equivalent to the quotient of price ratio, P_i/P_j (price of commodity i / price of commodity j), and the corresponding technical coefficient in physical terms, s_ij/Q_j (physical quantity of input from sector i / total physical quantity output from sector j). Thus, the latter is fixed under engineering production constraints, and it follows that the price ratio, P_i/P_j, is then constrained to remain fixed as well (Miller and Blair 1985).

(2-15)

· Hawkins-Simon conditions are observed. In general this means that in order for the technical matrix to be meaningful, that is, to ensure all goods are producible, the sum of all the direct and indirect inputs of a commodity itself should not exceed the output of that commodity (Hawkins and Simon 1949) (Dorfman et al. 1958).

· Inputs are not substitutable. This means that within a given technology there is one preferred set of input ratios that will continue to be preferred regardless of final demand quantities (Dorfman et al. 1958).

The Dynamic I-O model

In Leontief (1953) Professor Leontief defines a static theory as one that derives the changes in the variables of a given system from the observed changes in the underlying structural relationships. A dynamic theory goes further, and shows how certain changes in the variables can be described “on the basis of fixed, that is, invariant, structural characteristics of the system” (Leontief 1953, 53). “Dynamic theory thus enables us to derive the empirical law of change of a particular economy from information obtained through the observation of its structural characteristics at one single point of time”[2] (Leontief 1953, 53). From the basis of Leontief’s theories, “static input-output analysis describes the economic system in terms of mutually interrelated and structurally conditioned, simultaneous flows of commodities and services” (Leontief 1953, 53). In contrast, dynamic theory is described by “the study of dependence of the future on the past states of the system through the introduction of structural time lags, of structural stock-flow relationships, or of a combination of both (Leontief 1953, 53).

The main purpose of the input-output methodology, both static and dynamic, is to facilitate empirical study.

“… The empirical approach designed to derive the operational properties of a national economy through direct and detailed observation of its structural characteristics at one particular point, or at least a relatively short interval, of time seems to commend itself for the purposes of dynamic as well as of static analysis” (Leontief 1953, 53).

The methodological emphasis on ‘structural’ is deliberate for the following reason.

“The accumulation and decumulation of stocks can, in some instances, be shown to result directly from the operation of primary structural lags. The fluctuation in the amount of ‘work in progress’ (which is a stock of intermediate products) observed in the shipbuilding industry, for example, can be successfully explained on the basis of the structural lag measured by the time which elapses between the laying of the keel of a vessel and its final completion. Conversely an observed lag between the variation in the stream of inputs absorbed by an industry and the corresponding changes in the level of its output can often be traced back to its changing capital requirements based on the technologically determined stock-flow ratio between the amounts, i.e. the stock of equipment, building, and inventory of materials, on the one hand, and the corresponding capacity to turn out the actually observed stream of finished products, on the other”(Leontief 1953, 54).

The assumptions of the dynamic Leontief model include the same restrictions of the static model within a time period: fixed proportions, Hawkins and Simon conditions and restrictions on substitutions (Dorfman et al. 1958). The addition of incorporating capital accumulation activities in the dynamic model, creates an additional restriction in the model. This restriction involves the reversibility of capital stock to prevent negative flows. Typically, transfer of stock occurs when output production decreases. To prevent negative flows, the dynamic Leontief model only increases capital stock when output grows, otherwise the existing stock remains the same (Duchin and Szyld 1985).

In summary, a dynamic model must allow for the “structural relations between stocks (capital) and flows (output) and take explicit account of the fact that substantial increases in output will create additional capacity requirements so that projected changes in final demand will not only require more intermediate goods, but also investment goods from all appropriate sectors in the economy” (Richardson 1972, 184).

Section 2.3 – Equilibrium and Economic Input-Output Analysis

In the Walrasian system of equilibrium, quantity demanded equals quantity supplied. “The static economy (in which wants are unchanging, and resources unchanging) is in a state of equilibrium when all the ‘individuals’ in it are choosing those quantities, which, out of the alternatives available to them, they prefer to produce and to consume” (Hicks 1985, 11). Thus, the quantities produced and consumed are arrived at under the conditions of consumer preference (Hicks 1985). The basic assumptions for Walrasian equilibrium therefore are:

1) the technical coefficients, a_ij, are given and constant, and,

2) inputs = output for each sector.

For a given system, there are always a set of prices and a set of quantities, each of which “separately and simultaneously satisfies the technical structure of production” (Goodwin 1953, 78). That is, there is an infinite set of solutions that can be determined by a factor of proportion. For example, for a given price and quantity that solves a system, multiples of that price and quantity such as 200 times or 1/10 will also satisfy the equations. Thus, if one quantity is specified, then all other quantities are uniquely determined. And, it follows that if one quantity and one price are set equal to unity, then all others are fixed, and these two become the “numéraires” (Goodwin 1953, 78).

In the static I-O open model, or as mathematicians refer to as the non-homogenous system, the general principles of equilibrium are exploited to arrive at quantities produced based on the exogenously determined quantities of final demand. Under the basic assumption that technical coefficients are less than one under the Hawkins-Simon condition, the indirect input requirements converge to zero (Hawkins and Simon 1949). Thus for the static I-O open model, as intermediate production converges, the system is expected to reach a new equilibrium. At this new equilibrium the static Leontief model intrinsically represents the market clearing mechanisms of the Walrasian model. Equilibrium is achieved as total production activities are based on a final demand vector (Yan 1969).

A major assumption in the static I-O open model is that the speed of adjustment is relatively fast in pace with respect to meeting final demand. That is, the model assumes supply will meet demand (equilibrium will be reached) before demand changes again. (Yan 1969) (Fisher 1983). If the adjustments are too slow in pace relative to the changes in demand, elements of time are crucial to the analysis, hence the need for a dynamic interpretation.

What then is the relationship of a dynamic I-O model to the notion of equilibrium? As one moves from a static modeling approach to a dynamic modeling approach it becomes apparent that general equilibrium theory is not readily applied. “Traditional equilibrium theory usually deals only with the correspondence between a data complex at a certain point in time and economic phenomena at that same time, but not with the way in which a change in data at a point in time will subsequently affect them” (Morishima 1996, 2). Further, Hicks (1985) suggests an even more dramatic shift of conceptualizing a dynamic equilibrium: “The static equilibrium, entirely based upon current parameters, is in strictness irrelevant to the dynamic process” the “picture of actual values chasing a ‘moving equilibrium’ (the equilibrium values of which are determined statically) has to be abandoned” (Hicks 1985, 19). The formulation of a dynamic model is not limited to current parameters, they must also include decision parameters of the past, (e.g. choices of capital investment) and ‘individuals’ expectation parameters of the present (Hicks 1985). Therefore, under the conditions that the basic assumptions of a static equilibrium do not hold (convergence and relative speed of convergence is slow), and that there exists inter-temporal relationships based on past decisions and future expectations, dynamic models are more appropriately framed within a disequilibrium context. The focus of the dynamic model is then on the transition states of the model.

The irrelevance of general equilibrium as it applies to dynamics described by Hicks (1985) and Goodwin (1947) is consistent with Leontief’s lack of emphasis on equilibrium in the dynamic I-O model. In the opening sentence of the classic work on I‑O economics, Leontief (1941), Leontief describes I‑O as “An attempt to apply the economic theory of general equilibrium – or better, general interdependence – to an empirical study of interrelations among the different parts of a national economy as revealed through covariations of prices, outputs, investments, and incomes” (Leontief 1941, 3) in (Rose 1995, 295-6).

The careful wording of this statement by Leontief is essential to understanding the Leontief Dynamic I-O approach. In this excerpt and later writings by Leontief,[3] there is emphasis to the distinction between Leontief’s work and the Walrasian system of general equilibrium. Leontief’s model does not require optimization or equilibrium in the traditional sense and he emphasizes that economic interactions are more general than those of the Walrasian model, for which in the former case, interactions are transmitted primarily through the price system (Rose 1995). In Leontief (1949), I-O Analysis is referred to as “empirical general equilibrium” or more appropriately “general disequilibrium analysis” (Leontief 1949, 218). And further, the dynamic I-O model is more comprehensive than conventional general equilibrium theory, for it attempts to explain not only the dynamic properties of stock flow relationships, but also technical changes in the structure of productive processes as well as changes in consumers’ tastes (Leontief 1953, 13).

The irrelevance of general equilibrium to dynamic I-O does not preclude the balancing of final demand and production quantities through price and quantity variations. Within the “empirical equilibrium model” of I-O analysis, one can calculate ‘market clearing prices’ where production is equivalent to consumers’ preferences. In the static I-O analysis, the inverse of the structural matrix of a particular economy post multiplied by a given column vector of final demand yields the vector of corresponding total sectoral outputs. The transpose of the same inverse when post multiplied by a given vector of value added yields the corresponding vector of equilibrium prices. In dynamic I-O, the transpose of the dynamic inverse determines the relationship between the time-phased vectors of value added in each of the producing sectors and the set of equilibrium prices that would balance the total outlays and the total receipts of each producing sector over time (Leontief 1970a). Applying methods of optimization such as in Chenery and Clark (1959), Carter (1970) and in Leontief (1985b) one can vary prices and quantities to achieve equilibrium prices.

Other implementations of the dynamic model such as Miernyk and Sears (1974) and Miernyk (1965), do not include elements of equilibrium analysis as part of forecasting technological change. The Miernyk model is an open model that varies future technical coefficients based on a distribution of current practices. Future technical coefficients are generated by reformulating the distribution of current practices to favor ‘best practices’. In this model prices are not varied to create ‘market clearing’ conditions (Miernyk 1965).

Similar to the Miernyk model, the Interindustry Forecasting Model at the University of Maryland (INFORUM) model also does not consider the constructs of general equilibrium to develop forecasted models (Almon et al. 1974). Instead, production efficiency is balanced against levels of employment to arrive at plausible final demand vectors. The models are developed in three steps (Almon et al. 1974, 4):

1. Specification of structural relationships in the economy,

2. projection of outside factors of population, labor force, employment, number of households, government spending, and projections of interest rates and depreciation rates, and,

3. calculation of the forecasts by combining the overall controls provided by the outside factors with the structure. The basic logic is to determine the course of after-tax consumer income, together with the specified government demand, yields the specified level of employment.

The basic premise is built upon the components of the I-O table, where:

Intermediate Consumption flows + Final Demand = Total Output, and,

Total Output = Intermediate Consumption flows + Value Added

Hence, by equating these two expressions:

Total Final Demand = Total Value Added

(Grassini 1998, 4).

In the case of the Sequential Interindustry Model (SIM) production is emphasized, representing supply and demand is present in the form of orders. Because the timing of demand differs between production modes, “the system’s demand and supply need not be reconciled at each interval during a transition in technology” (Romanoff and Levine 1990b, 10). Supply and demand are reconcilable in the steady-state. That is, “reconciliation is achieved over a period of time as the system tends to converge to new equilibrium toward the end of an episode” (Romanoff and Levine 1990b, 10).

There is one case where a “dynamic” I-O model was found to include the constructs of general equilibrium. In the Temporal Leontief Inverse method:

“new methods of analysis, focusing on price- and quantity-clearing computable general equilibrium (CGE) models have directed attention once again to the issue of structural change. In the case of a quantity-adjustment general equilibrium model developed for Chicago (Israilevich et al. (1997)), it has proven possible to extract forecasted input-output tables from the economy-wide model and to use the same methodology to back cast the input-output tables for earlier years. The result is a set of input-output tables in which coefficients have been adjusted (in lieu of prices) to ensure market clearing” (Sonis and Hewings 1998, 90).

“The procedure [the Temporal Leontief Inverse] includes consideration only of the sequence A₀, A₁, ..., A_t, A_t+1, ...” of Leontief’s dynamic approach (Leontief 1970a). In the Temporal Leontief Inverse method, time-series of input-output matrices have been derived from “a comprehensive general equilibrium system that operates to change the input-output coefficients as part of the market-clearing process” (Sonis and Hewings 1998, 91).

In summary, the I-O method is closely associated with the Walrasian theory of general equilibrium, especially in the static case, as a method to represent the clearing of markets. That is, the I-O model represents the total production required to meet a given vector of final demand. However, the intent by Professor Leontief was not to justify a strict equilibrium model. His intent was to provide an empirical model of interdependence related equilibrium that is less restrictive and has much broader application than its theoretical predecessor. This can be seen in his model Leontief (1970a) and others Miernyk and Sears (1974) and Almon et al. (1974). Recent advances in econometrics have led to new techniques, specifically, dynamic computable general equilibrium. Dynamic computable general equilibrium models are currently being used to assist in the formulation of market clearing prices that are the basis for the generation of technical coefficients in such models as the Temporal Leontief Inverse.

Section 2.4 – Structural Change and Technological Change

The dynamic I-O modeling raison d’être is to gain better insight regarding interindustry relationships, their structure and tendencies of change. Based on this, definitions of structural change, and technological change within this context are presented.

In the following excerpt, Pasinetti (1993) presents a broad definition of structural change, one that describes the dynamics of structural change as being exhibited by changes in the levels of macro-economic indicators and as being permanent and irreversible.

“The evolution of modern economic systems, especially since the inception of the industrial revolution, shows that, as time goes by, the permanent changes in the absolute levels of basic macro-economic magnitudes (such as gross national product, total consumption, total investment, overall employment, etc.) are invariably associated with changes in their composition, that is, with the dynamics of their structure. … In the short run it is not always easy to see clearly a distinction between those changes that are purely transitory and reversible (as they reflect adjustments to temporary scarcities or to various accidental external shocks) and the genuine structural changes – the latter being defined as those changes in the composition that are permanent and irreversible. But in the long run, temporary deviations, in one direction or the other, cancel each other out, while the major basic trends emerge more and more distinctly as time goes on. It becomes therefore reasonable to try and discover the inter-relationships of the cumulative movements of the macro-economic magnitudes and the changes that take place within their structure“ (Pasinetti 1993, 1).

Economic structure is a description of the proportions of economic activity within an economy. Structural change further quantifies structure through "proportions and relationships that characterize … an economic set in space and time" ((Perroux 1939) in Pasinetti 1993, 9).

Structural change in an I-O context is based on the definitions of the technical coefficients. The technical input-output coefficients are obtained by dividing the entries in a column of the transactions table, which are an industry’s inputs by that industry’s output. Input-output coefficients determine the amounts an industry purchased from all other industries and from value added, per unit of its own output. A column of coefficients, then, “gives a detailed quantitative description of the technique of production used by a sector, a sort of recipe for its output, with specifically enumerated inputs as ingredients” (Carter 1970, 7). A dynamic I-O model provides further detail regarding the recipe analogy, where detail of when the ingredients are added is described by the model.

The input-output coefficient table includes a column of input-output coefficients for every sector, thus illuminating a comprehensive structural description of an entire economy for a particular time period, typically a year (Carter 1970). Thus, the structure of each sector of the economy is represented by a column sector of input coefficients and in some cases a corresponding column vector of capital coefficients. Structural change can then be described as “a change in the magnitudes of the elements of these vectors” (Leontief 1985a, 34).

Structural change has two main aspects, a production or technical aspect, and a demand or non-technical aspect. For the strictly technological aspect there are three characteristics: First, the tendency to improve existing technical operations, and introduce new techniques and new goods and services, through the discovery and/or development of new technical production processes, new materials, and new sources of energy. Second, the widespread specialization or division of labor. And third, the external effects of technological change on labor productivity (Pasinetti 1993).

The non-technical aspect of technological change occurs as a result of increased productivity (i.e. changes in prices, in this case lower prices) that allows single individuals with the possibility of obtaining larger amounts, or a larger number, of goods and services, or entirely new goods and services altogether. This leads to increased possibilities of consumption. Further, in order for technological improvements to be realized, it is necessary that the corresponding demand for specific goods and services be present (Pasinetti 1993).

For this research, a restricted and precise definition of technological change is given by Rose (1984). In Rose (1984) technological change is defined as a subset of coefficient changes in an I-O model. Coefficient changes can be due to several reasons: new innovations, changes in relative prices, shifts in preferences, alterations in trading pattern all representing changes in structure. Here, technological changes are limited to changes in physical input combinations in production (Rose 1984). This restricted definition will be used in reference to technological change within this context.

Section 2.5 – Changing Prices in the I-O model.

Although changing prices of commodities and changes in utility will not be part of this investigation of dynamic I-O models, the ramifications of not including these parameters are worth noting. Structural relationships between sectors in an economy would be best measured most accurately in physical units. However, publicly available I-O data-sets are typically based on prices.

Price changes have a direct effect on technical coefficients and vectors of final demand. The influence of prices on the calculation of technical coefficients is illustrated by equation (2-15). As prices change in a manner that is not proportional for all sectors, technical coefficients will change relative to their representation of physical inputs to production. Vectors of final demand are also affected by price if a study involves changes in demand over time. Price deflators are necessary to minimize the effects of changing prices. By using price deflators one can formulate a constant-period pricing scheme such as a constant-year base price, that allows for the use of data obtained from multiple data sets (Blair and Wyckoff 1989).

Price changes in the I-O model are also an issue regarding substitution. Standard neoclassical theory states that an increase in the price of one good, holding other prices constant, will decrease the demand for that good as an input to production. However, the “underlying theory of I-O is portrayed in terms of perfect complements (i.e. right-angled isoquants) that preclude substitution” (Rose 1984, 308). Contrary to the I-O model, empirical research supports that substitutability between inputs does in fact exist and is responsive to changes in relative prices even in the short-run (Miller and Blair 1985). A careful reading of Leontief does indicate a willingness to consider at least some form of strict technical substitution in spite of the zero elasticity of substitution implied by the Leontief production function (Rose 1984, 309).

In summary, price changes affect the technical coefficients, vectors of final demand and responses resulting in substitution. Utilizing constant year base pricing, coefficients can be estimated by changes in quantities in dollar values to estimate changes in quantities in physical unites. Responses to substitution are not present in the I-O model, however, simulations can be done by creating various scenarios that endogenously change input quantities.

Section 2.6 – Environmental I-O Models

The first to suggest an extension of the I-O model to examine environmental issues was Cumberland (1966). Prior to Cumberland, Herfindahl and Kneese (1965) described the resource/environment interface from and economic perspective and Ayres and Kneese (1969) proposed a general materials balance model linking economic activities to residuals generation and waste management (Ayres 1978). There have been several contributions to the extension of I-O to incorporate environmental parameters. A list, although not comprehensive, of known environmental I-O references can be found in Appendix A. Miller and Blair (1985) present three categories of environmental I–O models:

1. Generalized Input-Output Models. These are formed by augmenting the technical coefficients matrix with additional rows and columns to reflect pollution generation and abatement activities.

2. Economic – Ecological Models. These models result from extending the interindustry framework to include “ecosystem” sectors, where flows will be recorded between economic and ecosystem sectors along the lines of an interregional input-output model.

3. Commodity-by-Industry Models. Such models express environmental factors as “commodities” in a commodity-by-industry table. In a commodity-by-industry table, data is compiled for commodities regardless if the commodity is a primary or secondary good or service.

The following paragraphs will introduce and discuss the Cumberland, Isard-Daly, Leontief, Ayres and Knees, Victor, and EIO-LCA environmental models within the context of the above model descriptions.

The Cumberland model

Cumberland was the first economist to include environmental effects in an extended interindustry model (Cumberland 1966)(Richardson 1972). In Cumberland (1966) the approach was to add rows and columns to the traditional input-output table to identify environmental benefits and costs associated with economic activity and to distribute these by sector. The general model is illustrated in Figure 2-2 below:

Figure 2-2. The Cumberland Model (Richardson 1972).

Row R measures the environmental effects of any development project or program, and consists of monetary estimates of any environmental benefits by sector, as shown in row Q, minus estimates of environmental costs by sector, Row C. The entries in Column B represent the costs that would have to be incurred by the public and private sectors of the regional economy in order to neutralize adverse environmental effects and to restore the environment to its base period quality levels. This formulation attempts to place monetary values on environmental effects rather than measuring them in purely physical terms. However, this method was difficult to implement based on the qualitative nature of environmental impacts as well as the need to convert measurable pollutants such as discharge per unit air, water and soil to monetary values (Richardson 1972).

An important characteristic of this model is that it does not incorporate the flows into the economy from the environment and vice versa. Thus, the environmental rows and columns do not measure environment-industry coefficients. Rather they refer to the environmental effects of a specified regional development project or program. Cumberland intended that his extended input-output model to be used as an aid to an empirical regional policy or development tool. This model is much closer to a “cost-benefit” analysis of environmental effects than to an analysis of the inputs and outputs of ecological commodities (Richardson 1972).

Isard (1972)/Daly (1968) models

Isard and Daly developed similar approaches to the extension of environmental issues into the input-output framework. Both models are comprehensive in their approach. Each model shows the interactions both within and between the economic and environmental systems. A general flows matrix that incorporates both economic and environmental activities was developed as shown in Figure 2-3 below:

Figure 2–3. The Daly Model (Daly 1968) (Miller and Blair 1985).

Daly created a highly aggregated industry-by-industry economic sub-matrix and a classification of processes: ecosystem processes such as plants and animals; non-life processes such as chemical reactions in the atmosphere; and, the sun as the primary source of energy. Isard refined the Daly model through the distinction that the production of one-product is not consistent with the multiple of pollution indices created within one industry. Hence, Isard employs the commodity-by-industry scheme first introduced by Stone (1961, 1966). The commodity-by-industry scheme permits an accounting of multiple commodities, economic and ecologic, produced by a single industry (Daly 1968) (Miller and Blair 1985) (Richardson 1972).

In the Isard model shown in Figure 2-4, below, commodity flows are measured along the rows starting from basic trading commodities such as wheat and cloth at the top of the table and transitioning to more boundary commodities such as crude oil down to ecologic commodities such as plankton and fish. Activities are measured in the columns ranging from industries such as agriculture and textiles at the left of the table through petroleum refining and sport fishing to ecological processes such as plankton and fish production (Isard 1972).

Figure 2–4. The Isard Model (Isard 1972) (Miller and Blair 1985).

There are three major issues regarding the Isard table:

1) There is very little information available regarding the A_EE matrix, the interrelationships within the environment.

2) There is an assumption of linear relationships within the ecological system. Ecological processes are often non-linear and exponential in nature.

3) There is an assumption that ‘free’ environmental resources remain stable over time. Changes in resource quality could greatly affect the invariant nature of the production functions (Kapp 1970) (Richardson 1972).

The Leontief Model

The Leontief Model, presented in Leontief (1970b), for environmental analysis is integrated into a standard type of input-output table, as shown in Figure 2-5 below. The distinctive features of this model are that the row represents the physical output of pollutants and the column represents the pollution abatement industry. Since the physical outputs of the pollutants are in physical units, and the rest of the matrix is in monetary units, the pollutant output must be exempt from vertical summations. The pollution abatement industry column is in monetary units and can be treated as other industry sectors. There is no input row for the pollution abatement industry. This is due to the fact that its output is used to offset pollution generation in the economy as a whole irrespective of its source and is not sold as inputs to other industries. It is assumed that the costs for pollution abatement are paid for directly by households. Modification to the matrix can be made so that industry is responsible for abatement costs directly. In this case, households will pay for the costs indirectly (Richardson 1972).

Figure 2–5. Leontief Environmental Model (Richardson 1972).

Another issue regarding the Leontief table is that the pollution abatement output is recorded twice – in physical terms (i.e. amount of pollutants eliminated = negative output of pollutants) in the pollutant output row and in monetary values in the usual fashion at the bottom of the industry’s column (i.e. in terms of the cost of inputs from other industries and value added). The double valuation of the output of the pollution abatement industry enables the monetary cost of eliminating each unit of pollutant to be estimated directly (Richardson 1972).

The simple accounting identities of the Leontief model are as follows:

(2-16)

thus,

(2-17)

This is contrary to the traditional I-O identity of value-added equal to final demand, (V=Y). Sales to final demand are reduced below the level of value added by an amount equal to the expenditure of resources on pollution abatement. Also, the final pollution calculation is based on the final demand pollutants or net output of pollutants, Y_P, not the total production pollutants.

(2-18)

Thus the pollutants are obtained by summing the positive and negative outputs of pollutants generated by each industry including the pollution abatement. The gross output of pollution, X_P, indicates the maximum amount of pollutants that would be created without pollution abatement (Richardson 1972).

Ayres-Kneese Model

Ayres and Kneese (1969) presents a similar Leontief extension to the I-O model, one that incorporates residual flows and pollution abatement. The major difference in the Ayres-Kneese model is that it includes a further elaboration to deal explicitly with raw materials extracted from the environment as well as waste materials returned to the environment (Ayres 1978). The fundamental idea of the model is that of materials balance.

As shown in Figure 2-6, the coefficients in the ‘extraction’ column (I) are part of the conventional I-O matrix. These coefficients represent the fractional inputs (in dollars) per unit output (in dollars) of each sector. The coefficients in the abatement column simply represent the costs of abatement to whatever level is actually achieved. In this respect, the scheme differs from that of Leontief model, which defines the coefficients in terms of dollar inputs per physical unit of pollutant removed.

Figure 2-6. The Ayres-Kneese Model (Ayres 1978).

Ayres and Kneese (1969) then defines a resource input matrix R and a residuals output matrix W. Both matrices R and W, are linked together by the capital I-O matrix as shown in Figure 2-7, below.

Figure 2-7. The Ayres-Kneese Model – Detailed (Ayres 1978).

The Resource input matrix (IV, V, and VI) would have one row for each raw material or other resources and one column for each sector in the central I-O matrix. The R matrix elements would give the resource input (in physical units) per dollar output of the sector. Most of the resources would be collected by the extraction sectors so the majority of the non-zero elements would be in the upper right-hand corner (IV). In the other submatrices (V and VI), there may be entries for other resources such as water for dilution, air for combustion and wastes that are reused or recycled into other sectors. Each entry is in physical units per dollar of output of the sector (Ayres 1978).

The residuals output matrix, W, has one row for each pollutant that is separately accounted for in the system and one column for each industry sector (or commodity) of the main I-O table. Each coefficient of the W matrix represents residuals output, in physical units per dollar value of the product. For the extraction matrix, VII, the columns indicate the gross residuals by extraction in physical units per dollar of output of the sector. For the production matrix, VIII, the columns represent gross production of wastes. And the abatement sectors in matrix XI, represent the net amount of residuals. Typically this number should be negative (Ayres 1978).

In summary the Ayres-Kneese model is an extension of the Leontief pollution/abatement model. The Ayres-Kneese model adds two non-production matrices to account for the resources and wastes in physical units. This model has the distinct advantage to close the loop of environmental impact by including both resource use and residual emissions. It inherently tracks the flows in and out of the production industries. One further insight is the ability to track abatement processes that transfer a waste from one medium to another.

The Victor Model

Victor (1972) presents a model that limits the Isard model described above for reasons of practicability. The Victor model accounts only for flows of ecological commodities from the environment into the economy and of the waste products from the economy into the environment. Victor eliminates the subsystem showing the interrelationships within the environment itself (subsection A_EE of Figure 2-4). The basis of the model limitations are due to reduce data requirements. Victor takes advantage of the commodity-by-industry implementation approach of Stone (1961) and Stone (1966) that allows for multiple outputs, the ability to express economic data in monetary units and ecological data in physical units (Victor 1972) (Miller and Blair 1985).

We begin with a discussion of definitions presented in Victor (1972). The main purpose of an environmental I-O model is to describe the economy as a "manipulation of material by man that is directed towards the satisfaction of human wants" (Victor 1972,54). The economy is a set of activities, where the environment provides the energy and materials for those activities. The main purpose of the model is then to link economic behavior with an associated flow of materials. Thus, the model is represented by commodities, industries and their associated activities (Victor 1972).

All economic activity requires input of raw materials. These input may come from privately owned parts of the environment, such as coal from the land, or from publicly or non-owned parts, such as oxygen from the air. A material input introduced into the economy is referred to as an ecological commodity. However, once a material is processed for further use or is satisfying the demand of a final consumer, it is referred to as an economic commodity. When it is discarded by an economic agent, such as a producer or a consumer, and leaves the economy, it becomes once again an ecological commodity. Factories, machines and consumer goods are all economic commodities. Emissions discharged into the air water and soil are all considered ecological commodities. Some issues arise for materials as they enter the economy. Materials that are not owned by anyone or any institution such as air are ecological commodities. Materials that are owned such as unmined coal, although it has economic value is considered an ecological commodity until mined from the ground. Ownership of the physical environment is insufficient as a classification of economic commodity (Victor 1972).

The term industry is used in its broadest sense to include all economic activity from primary industries such as agriculture and forestry to those concerned with the rendering of services. An industry is composed of establishments engaged in the same or a similar kind of economic activity, e.g. logging camps, coal mines, clothing factories, department stores, laundries. An establishment is defined as the smallest unit, which is a separate operating entity capable of reporting all elements of basic industrial statistics. Thus industries are made up of establishments that undertake similar types of economic activity. These activities may be viewed in terms of the input and output of economic and ecologic commodities.

The Victor model is a conventional commodity-by-industry table augmented with additional rows of ecological inputs P and T, and columns of ecological outputs R and S, as shown in Figure 2-8. Here the ecological outputs are equal to the ecological inputs consistent with the materials balance assumption. This assumes that the model is a closed economy and there is no accumulation of mass in the economy itself (Victor 1972).

Economic Subsystem

Household

Output

Ecosystem

Commodities

Industries

Household

Consumption

Total

Output

Ecological

Commodities

Industries

Value Added

GNP

Total Inputs

Ecological Commodities

Figure 2-8. The Victor Model (Miller and Blair 1985).

The submatrices are defined as follows:

Economic Sectors

U = Inputs of economic commodities by industries, and is referred to as the ‘use’ matrix,

V= Outputs of economic commodities by industries, and is referred to as the ‘make’ matrix,

E = The vector of final demand,

Q = The vector of economic commodity gross outputs,

X = The vector of industry total outputs,

W = The vector of industry value-added inputs,

GNP = The gross national product which is the expenditures on primary inputs by categories of final demand,

Q’ = The sums of columns of matrix V showing total output by economic commodities,

X’ = The sums of columns of matrices U and W showing total economic inputs of industries.

Ecological Sectors

R = outputs of ecological commodities discharged as a result of final demand for economic commodities,

S = discharges of ecological commodities by industries,

P = inputs of ecological commodities used in conjunction with the final demand for economic commodities,

M = inputs of ecological commodities used by industries.

The structure of Victor model approach incorporates those industries that produce secondary commodities (that is, a commodity that is considered primary by another industry), by-products (commodities produced that are closely related to a primary commodity), as well as joint products (commodities that have no primary industry producer). To do this, the Victor model utilizes two distinct data structures to formulate the direct requirement matrix: the make matrix and the use matrix. The make matrix summarizes production output where the rows describe the commodities produced by industries in the economy and the columns describe industry sources of commodity production. Typically, the on-diagonal elements of this matrix are the primary products of an industry, while the off-diagonal elements are the secondary products. The use matrix, also known as the absorption matrix, describes the commodity input to an industrial production process and captures the destination of commodities (Miller and Blair 1985).

The commodity-by-industry models can then be used in several configurations to develop total requirements matrices. For example, data may be available regarding final demand for commodities, however total impacts are to be analyzed as total industry output, therefore an industry-by-commodity total requirements matrix configuration would be desired. Alternatively, if impacts were to be analyzed as a function of total commodities a commodity-by-commodity or a commodity-by-industry total requirement matrix would be used.

Victor’s model achieves the objective of compromising between the theoretical model and an empirical application by (Victor 1972):

· eliminating the internal matrix of the ecological system, and retaining the commodity-by-industry table of the Isard model,

· conforming to the principles of consistent I‑O accounting by adopting the materials balance concept,

· not attempting to integrate the economic and the ecological sectors in the I‑O table into a framework thus permitting summation over sectors by expressing all inputs and outputs in monetary values.

Environmental Input-Output – Life-Cycle Assessment model (EIO-LCA)

The EIO-LCA is a combination of three tools: input-output models, the generation of toxic release inventories and energy consumption by commodity sectors. The basic formulation of the EIO-LCA is the Victor ecological model described above. The EIO‑LCA model uses the Commodity-by-Industry framework introduced by Stone (1961, 1966) and refined by Victor (1972) (Cobas-Flores 1996). Total production activities, X, are calculated using the Bureau of Economic Analysis (BEA) Benchmark Input-Output Accounts based on scenarios of final demand, Y (USDOC 1994a). An environmental matrix, R, is expanded to include elements such as energy inputs, occupational health and safety outcomes, and emissions to the environment. The R matrix, representing residuals is normalized to discharges/energy use per dollar of output from each sectors. An environmental effects vector, E is calculated based on pre-multiplying total outputs by the R, the environmental matrix (Cobas-Flores 1996):

(2-19)

(2–20)

where,

(2-21)

is the factor content matrix expressing the direct and indirect requirements (releases) for the residuals matrix, R, per dollar worth of final demand (Romanoff 1973).

The EIO-LCA model captures LCA inventory components in the following way:

Table 2-5. EIO-LCA Inventory Components (Cobas-Floras 1996).

Life-cycle inventory component	EIO model
Raw materials	Column vectors of the ‘use’ matrix
Process materials	Column vectors of the ‘use’ matrix
Manufacturing process	Column vectors of the ‘use’ matrix
Consumer products	Exogenous variable represented by the final demand vector
Reuse, recycle and remanufacture	Row vector of scrap and second goods in the ‘use’ matrix.
Disposal	Not captured in the EIO model.

Thus, as shown in Table 2-5, the EIO-LCA inventory data does not endogenously capture the full life-cycle of a product or process. The model does capture the industrial complex and the exogenous consumption of finished goods. However, it does not capture the scrap and recovery industries to an extent to fully analyze production sequences. Efforts to improve the full-cycle analysis are in progress.

The EIO-LCA model makes several assumptions;

· One input cannot be substituted for another,

· There are no economies of scale,

· Both the economic I-O matrix and the environmental matrix R use averages for the entire sector,

Section 2.7 – Static and Dynamic LCA

The conventional LCA framework has four components as depicted in Figure 2‑9. The obvious starting point of LCA framework is the Goal and Scope Definition. However, LCA is an iterative process in the formulation of each component. For example, the Goal and Scope Definition component leads to the development of the inventory analysis. However, this does not preclude modifications to the goal and scope based on the data collected in the inventory analysis.

Figure 2-9. Life cycle assessment framework (ISO 1997).

Goal and Scope Definition:

The goal definition and scope stage of LCA defines the purpose of the study, the expected product of the study, the boundary conditions, and the assumptions. The boundary of LCA is illustrated below in Figure 2-10. All operations that contribute to the life cycle of the product, process, or activity of interest fall within the system boundaries. The environment is the surrounding boundary for the system. Inputs to the system are natural resources, including energy resources. Outputs of the system are ultimately a collection of releases to the environment (air, water, or land). If the system represents the manufacture and use of a product, then outputs include the post consumer or discarded product (Boguski et al. 1996). Typically LCA studies are performed in response to specific questions. The nature of the questions determines the goals and scope of the study (Boguski et al. 1996).

Figure 2-10. Illustration of life-cycle system concept (Boguski et al. 1996).

Life-Cycle Inventory (LCI):

The LCI quantifies the resource use, energy use, and environmental releases associated with the system being evaluated. The LCI centers on material and energy balances for each operation within the system and for the whole life-cycle system itself. The inventory of an LCA study is separated into the general materials flow for the life cycle stages of a product. We define the stages as: raw materials acquisitions, materials manufacture, product manufacture, product use or consumption, and final disposition.

Life-Cycle Impact Assessment:

Life-cycle Impact Assessment (LCIA) uses the results of the LCI to quantify potential environmental harm (Boguski et al. 1996). There are three components to impact assessment:

1) Classification - The grouping of inputs and outputs of LCI;

2) Characterization - Translating the LCI data to impact descriptors such as global warming potential; and,

3) Valuation - The assignment of relative values or weights to different impacts, allowing integration across all impact categories.

Within LCA, impacts to the environment are quantified through the classification of various impact categories (a class representing environmental issues of concern into which LCI results may be assigned) (Udo de Haes et al. 1999b). At the present time those categories are outlined as follows:

Table 2-6: Environmental LCA Impact Categories (Udo de Haes et al. 1999b).

Input related categories

Category 1: Extraction of abiotic resources

Subcategory 1: Extraction of deposits: e.g., fossil fuels and mineral ores.

Subcategory 2: Extraction of funds: e.g. groundwater, sand and clay.

Subcategory 3: Extraction of flow resources: e.g. solar energy, wind and surface water.

Category 2: Extraction of biotic resources: Extraction of specific types of bio-mass from the environment.

Category 3: Land Use, with the following subcategories

Subcategory 1: Increase of land competition: physical interventions that lead to changes in land occupation.

Subcategory 2: Degradation of life support functions: e.g. the cycling of nutrients in an ecosystem, the stability of soil and the generation of soil fertility, the generation of a suitable and stable microclimate.

Subcategory 3: Bio-diversity degradation due to land use.

Output related categories

Category 1: Climate Change: All impacts related to climate change caused by changes in radiative forcing.

Category 2: Stratospheric Ozone depletion: All impacts due to stratospheric ozone depletion.

Category 3: Human Toxicity: All impacts on human health caused by the direct emission of toxic substances both outdoor and indoor, and impacts caused by fine particles and by radiation.

Category 4: Eco-toxicity: All impacts on natural species and ecosystems caused by direct emission of toxic substances, including degradation products.

Category 5: Photo-oxidant formation: all impacts related to tropospheric oxidant formation, including impacts from NO_x emissions.

Subcategory 1: The short term and local impacts contributing to smog in the close vicinity of the source, primarily affecting human health and mainly caused by the more reactive VOCs.

Subcategory 2: The medium term and more regional impacts primarily affecting crops and possibly natural vegetation, due to the more long-lived VOCs.

Category 6: Acidification: All impacts due to acidification, including direct impacts on leaves, cat-ion exchange in leaves, and oil through ammonium, and mobilization of aluminum and other toxic metals.

Category 7: Nutrification: All impacts of macro-nutrients on the vegetation, both natural as well as crops, both terrestrial as well as aquatic.

Interpretation of Results:

Interpretation is the phase of LCA in which the findings from the inventory analysis and the impact assessment are used to form conclusions and recommendations consistent with the goal and scope of the study (ISO 1997).

State of the Art of Dynamic LCA

LCA tools under development today develop a static description of the impacts of an existing product or process - a "snapshot" of environmental impact. The reason is primarily limitations of available data. Although by definition, the Goal and Scope phase of an LCA study determines the boundary of analysis, in practice it is the Life-cycle Inventory (LCI) that ultimately determines the actually extent of the research. Contemporary LCA studies are typically bounded by limitations of available data. Although there may be temporal information available in some data, it is not true for all data. Historically, the immense task of collecting data to conduct a comprehensive LCA at best, defaults to a static analysis. The implications of this critical shortcoming make it impossible to perform an evaluation in advance of implementation (Field III et al. 1994). Thus, the construction of a detailed LCA for a new product or process is very difficult (Lave et al. 1995b)(White 1993).

Dynamic LCA to assess long-term environmental impacts was first introduced by Moll (1993). In Moll (1993) static LCA approaches were found to be appropriate to compare and evaluate products under three conditions. First, the products should have relatively short lifecycles, in the order of period of less than 5 years. In this case, the context that surrounds the product can be assumed as non-changing. Second, products should have stabilized consumption levels. Here, average values can be used to accurately describe input and output requirements. And third, products should remain static with regard to technologic or social changes in the lifecycles considered. Essentially, the static life-cycle is relevant as a method of analysis for a context where the system is in steady-state (Moll 1993).

Conversely, Moll (1993) concluded that the dynamic LCA approach is appropriate to compare and evaluate policy options opposite the criteria of the static LCA. That is, dynamic LCA is appropriate to assess products with long lifecycles (greater than 5 years), that involve substantial changes of consumption levels, and undergo changes in the applied technologies. Here the system context is not in steady-state and is possibly far out of equilibrium. The timing and changes in the use of materials and energy and their subsequent environmental repercussions are significant. The significance of the timing and rate of changes are important for assessing long-term results that ultimately influence policy options (Moll 1993).

Moreover, Moll (1993) concluded that the static LCA methodology and the dynamic methodology did not change the rank order of design criteria of the products analyzed. However, additional insights gained by conducting dynamic LCAs of product alternatives that lead to policy options include (Moll 1993):

· The relevant choice of the integration period, that is, the rate the new technology be phased in and an old technology be retired.

· The period required for environmental improvements. For example, the amount of time the policy option is to be implement to achieve its objectives.

· The calibration of the trends in the absolute magnitude of relevant parameters to the environmental policy. That is, a context is established with outside forces, such as trends in national economic conditions or trends in larger sources that affect the dynamics of the policy examined.

· The duration of the period to reach steady-state - how long will the policy option induce change, and what will the final state of that change.

Despite the seminal contribution to the science of LCA by Moll (1993), little work has been published or recognized by the established LCA literature regarding dynamic LCAs. The current “state of the art” of LCA regarding impacts and temporal aspects was summarized recently by Udo de Haes et al. (1999a) in the peer reviewed International Journal of Life Cycle Assessment:

“LCA essentially integrates over time. This implies that all impacts, irrespective of the moment that they occur, are equally included. There are also other options, however. Thus we may approximate infinite time by a given period, say for instance of 500 years. The assumption then is that most of the impacts will have taken place and that the difference with infinite time can be neglected; an assumption which has to be verified. A quite different option is that we want to attach a type of discounting. This can be done because future impacts are less certain and can perhaps be avoided; or just because we value the present higher than the past or the future. Discounting can be accomplished in two-ways: either by a simple cut-off, as is done in climate change modeling by choosing for a 20, 30, 100 or 500 year period. Or it can be done by real continuous discounting of say 1 or 2% per year, ( or 5 or 10% as is usual in economic analysis).

“As best available practice it is proposed that, as a baseline, characterization factors will be calculated for infinite time without discounting. If relevant, this can also be approached by a given long period of time, e.g. 500 years for global warming or 10,000 years for radioactive waste, as practical approximations. In addition, it must be checked whether a short period will yield considerably different results; if so, it is proposed that characterization factors for a 100-year period will also be calculated. It has still to be checked whether 100 years is a useful short time period for all categories involved. Following this line, the start of the short time period (e.g. of 100 years) must be precisely defined, in particular for waste materials. Preferably the moment should be chosen that these materials reach the waste management stage and are out of reach of further direct human activity. Thus, best practice will then be expressed in a double result, thus enabling to attach different weight to events in the nearby and the far future” (Udo de Haes 1999a,72).

Given the recent paucity of research towards dynamic analysis, the efforts of this research will present a method to generate a dynamic LCI that can subsequently be used to access impacts that are best viewed within a temporal context. The details of this method are introduced and formalized in the next chapter.

[2] Wassily Leontief comments further with regards to opposing contemporary economic theory to dynamic modeling. “This possibility, methodologically rather obvious, and practically very important, has unfortunately been obscured by the fact that most of the recent attempts to determine the structural characteristics of actual economic systems have been based on some kind of statistical time-series analysis, thus giving rise to the erroneous impression that the empirical laws of change necessarily must be derived from direct observations of past developments” (Leontief 1953, 53).

[3] In (Leontief 1953, 62) Chapter 3 Dynamic Analysis – “Having mentioned these peculiar properties of the theoretical long-run dynamic equilibrium – a concept which plays a considerable role in some of the ‘purer’ theories of economic growth – one must at once say that, for purposes of empirical analysis of the actual economic development, they most probably will be of very little use.”