Proc. Nati. Acad. Sci. USAVol. 89, pp. 851-855, February 1992Colloquium Paper

This paper was presented at a colloquium entitled "Industrial Ecology," organized by C. Kumar N. Patel, held May20 and 21, 1991, at the National Academy of Sciences, Washington, DC.

Industrial input-output analysis: Implications for industrial ecology(economic model/economic database/scenario analysis)

FAYE DUCHINInstitute for Economic Analysis, New York University, 269 Mercer Street, New York, NY 10003

ABSTRACT Industrial ecology will need to develop fun-damentally new approaches to reducing, reusing, and recyclingwastes. Industrial ecology will also require an analytic frame-work for examining the implications for the economic system asa whole of each potential web of industrial changes. A suitableframework is furnished by structural economics, which situatesthe economy within the physical world. This approach is basedon dynamic analysis rather than static concepts ofequilibrium,and optimization assumptions are used selectively rather thanas the general solution mechanism. Input-output economics,an important formal model within structural economics, cantrace the stocks and flows of energy and other materials fromextraction through production and consumption to recycling ordisposal. An input-output computation, including wastes, ispresented; it illustrates the separate but integrated analysis ofphysical stocks and flows and of prices and costs. This paperalso describes the major advances that have been made in thelast decade in the extension of input-output economics toaddress increasingly complex questions, notably the fully dy-namic physical/price/income model and the engineer-ing/input-output data base. Economists need to be able toassess the costs of cleaning up and to develop incentive schemesto increase the likelihood this will happen. To do this, econo-mists need to take on the difficult "how" questions thatconcern industrial ecologists since the cost, and indeed thewider implications, of cleaning up depends upon how it is done.Structural economics, and modern input-output models anddata bases, in particular, can help meet this challenge.

1. Introduction

Ayres (1) conceived of industrial metabolism as a systemsapproach to modifying the production, use, and disposal ofgoods to greatly reduce the generation of wastes by applyinglessons from the natural world. This is also the basic idea inwhat Frosch and Gallopoulos (2) have called industrial ecol-ogy. Industrial ecology is intimately related to human ecologybecause significant reductions in waste will require changesin people's private and social habits and not only in industriallife cycle planning and production. Industrial ecology, how-ever, provides a useful starting point.Although it is generally difficult tojudge the future success

of a new concept, industrial ecology appears uncommonlypromising. Reducing waste can simultaneously conserveenergy and other materials of mineral and biological origin,save money, and reduce pollution. The biological metaphorcan suggest specific ideas for efficient ways of processingmaterials, and the biosystem also serves as an importantexample of a complex system that has evolved in such a way

that wastes are reduced and recycled as the system proceedsto a higher degree of organization. There is no reason tobelieve, however, that the principles ofindustrial ecology willautomatically be adopted.

Natural systems evolve over long stretches of time, andfalse starts are weeded out by trial and error. Actual out-comes may be optimal responses to particular narrowlydefined problems; but it is not clear what the "optimal"evolution of an entire ecosystem might mean, and there is nomechanism assuring its occurrence. In human affairs, socialinstitutions are dominant agents of selection. They alsoproceed by trial and error and are able to respond optimallyto certain problems, especially problems that are narrowlydefined and have short-time horizons. In particular, theeconomic marketplace is an efficient mechanism for selectingalternatives that are immediately profitable (i.e., cost saving)for individual decision makers. The marketplace is certainlynot the only relevant institution: Ayres (3), for example, hasargued the importance of the role of government in assuringthe ecologically sound evolution of an economy. Nonethe-less, an outcome that contradicts the logic of the marketplaceover the long term is not likely to be sustainable.The challenge to industrial ecology, then, is 2-fold. (i)

Industrial ecology needs to generate workable concepts andactual methods for reducing wastes, and recycling those thatare generated, in a wide range of situations. The subjectmatter of industrial ecology is likely to involve studies anddemonstrations regarding technical changes in manufac-turing activities (particularly those concerning the processingof materials for the production of goods) combined with anincreased role for maintenance and repair activities in the useof these goods and new service activities (particularly thoserelated to designing, installing, and operating new systems).Some of these changes may be sufficiently profitable from ashort-term private point of view that they will be adoptedwith little if any political or legal involvement. These, how-ever, are not necessarily the most important options from asystem-wide or from a long-term point of view.

(ii) Industrial ecology also needs to include a coherentoperational framework for examining potential long-termadvantages and disadvantages of alternative webs of indus-trial changes and identifying the short-term bottlenecks thatmay emerge. These studies will provide the kind of informa-tion required both for public debate and decision making andfor private calculations about requirements and opportuni-ties. These debates, decisions, and calculations are necessaryfor the development of markets and as input to the variousother social institutions that have a stake in industrial ecol-ogy.

Industrial ecology can benefit from several decades' worthofexperience with the analysis of industrial interdependence.This body of work makes use of operational system-wide

Abbreviation: BOD, biological oxygen demand.

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Proc. Natl. Acad. Sci. USA 89 (1992)

frameworks for describing and analyzing the interrelation-ships among individual production processes and the asso-ciated flows of materials. The following sections of this paperdescribe an input-output framework that can play this role.Section 2 contains a description of structural economics,which provides a conceptual context for the input-outputmodel of an economy. A simple but illustrative input-outputcomputation is given in Section 3, and Section 4 describesmore elaborate models and some relevant applications. Thefinal section explores the ways in which a modern, dynamicinput-output model and data base can contribute to advancesin industrial ecology.

2. Structural Economics

Like industrial ecology, structural economics is an emergingframework combining old and new ideas to help understandand deal with current issues, including environmental pollu-tion. The differences between structural economics and"mainstream" economics are mainly differences of empha-sis. One broad perspective about structural economics isoffered in the editorial statement of ref. 4. What follows is amore personal view.

Structural economics is concerned with a detailed, disag-gregated description of an entire economy in terms of itsconcrete and observable constituent parts and their interre-lationships. Prominent among these constituents is the ma-terial infrastructure of a society. This includes not onlynatural objects like soil and those made of bricks and mortarbut also more abstract components of an economic systemsuch as specific technologies and social institutions. Becausesome of these components are not fundamentally economicobjects (unlike prices or interest rates, which are), the workof the structural economist typically crosses disciplinaryborders.A structural perspective can be formalized in a mathemat-

ical model; in fact, the input-output modeling framework thatwill be discussed below is a prominent example. However,structural economists explicitly acknowledge qualitative is-sues that are often difficult to formalize but essential to takeinto account, at the outset, in the formulation of the importantrelevant questions and, later, in the evaluation of formalresults. Structural economists study the material world and,because of this empirical commitment, are concerned withinformation and data; these are described and measured inphysical units [e.g., tons (1 ton = 908 kg)] as well as in moneyvalues when the latter have meaning. Even a formal database, to be analyzed with a formal model, is built largely "byhand" and not manipulated only mechanically.

Structural economics is concerned with structural changeand, therefore, with dynamics rather than only, or mainly,with static analysis or with "equilibrium" states. Because ofthe empirical foundation, the interest is with real historicaltime and with the future as much as the past. Interest istypically in the longer term more than the short term, and thefocus on technological and institutional structures provides afirm basis-a "handle"-for projecting parameters severaldecades into the future according to alternative assumptionsabout structural changes.Many of the economic mechanisms are the same as in

mainstream (or neoclassical) economics but with one funda-mental difference. In neoclassical economic models, a vari-ety of optimization problems are solved simultaneously un-der a system of constraints that is expected to yield a uniquesolution. (In the application of game theory to economicproblems, the multiplicity of Nash equilibria is a matter ofgreat concern.) The formal structural economic models, onthe other hand, are used so as to yield a set of possiblesolutions rather than a single optimal one. Within the set,trade-offs are believed to operate that are not reducible to a

monetary bottom line. In addition, economic feedback mech-anisms are generally believed by structural economists to bemore complex than the work of neoclassical economistswould suggest. A critically important example is the substi-tution of less expensive for more expensive inputs both inpersonal consumption and in production. Structural econo-mists believe that the most important instances of changinginput structures involve process change and the substitutionof inputs not one by one, but of a set of inputs for another set.Furthermore, the resulting input structure has to be plausiblefrom a physical point of view and not just be of lower cost.Structural economics is not a complete and closed system butis open to mechanisms of change originating outside theeconomy. A notable example is technological innovation, thetypical source of alternative sets of inputs.The formalism of structural economics includes the input-

output model and data base. The simplest and, even today,the most widely used form of the model is the open staticversion, which represents the interdependence among theproductive sectors of an economy. This interdependencefollows from the fact that each sector's output provides inputfor the other sectors (and itself).The input-output data base, again in its simplest form, is

derived directly from the official input-output tables that areprepared periodically by the national statistical offices (U.S.Department of Commerce) of more than 100 countries. Thesetables quantify for a given year the flows of goods andservices, and of capital and labor, from one sector to the othersectors and to final users. In virtually all cases the officialtables are prepared exclusively in money values. They followthe standard industrial classifications and may disaggregatean economy into as few as a dozen or up to several hundred(or more) distinct sectors. The simplest static input-outputmodel is widely used, with these tables, in governmentagencies, the private sector, and by researchers, sometimeswithin a more complete modeling framework such as a

computable general equilibrium model or an econometricmacroeconomic model. An alternative framework based onthe increasingly popular dynamic input-output model, bettersuited for industrial ecology, is described in a later section.A modern input-output data base that relies on direct tech-nical information measured in physical units and on account-ing tables is also taken up below.

3. An Example Input-Output Computation

Applications of the static input-output model form a largebody of literature; Leontief (5) provides an advanced intro-duction to this type of computation. There are three basicequations; their use will be illustrated in the following ex-

ample:

(I - A)x = y.

(I - A')p = v.

p'y = V 'X.

[1]

[2]

[3]

The equations relate A, the matrix of structural input-outputcoefficients (generally derived from an official input-outputflow table), and the four vectors representing output (x),prices (p), deliveries to final users (y), and factor costs (orvalue-added) per unit of output (v). (A' is the transpose of A,and I is the identity matrix.)To illustrate the use of the simple model, consider a

four-sector economy producing food products (F), machinesand tools (M), and two categories of waste water containinghigh (H) and low (L) levels, respectively, of dissolved or

suspended biological solids. For each gallon (1 gallon = 3.78liters) of high-biological-oxygen-demand (BOD) water

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Proc. Natl. Acad. Sci. USA 89 (1992) 853

treated in sector H, a fraction of a gallon of low-BOD wateris sent for treatment in sector L; and, for each gallon treatedby sector L, a fraction remains requiring further treatment.All four sectors dump some sludge into the environment.The economy is described by the following input-output

matrix:

F M H L0.4 0.3 0 0 F0.2 0.3 0.2 0.1 M

A= 0.4 0 0 0 Ho0.4 0.1 0.3 0.2] L

Thus, for example, the food-producing sector (F) requires 0.4ton of food inputs and 0.2 machine to produce a ton of foodand in the process generates 0.4 x 100 gallons each of high-and low-BOD waste water. (This is seen by reading down thefirst column.) If final deliveries and value-added are asfollows

[10] d [1013 ~~~~~~~10

Y ~ and [250

we can calculate total output, unit prices, and total incomeusing Eq. 1-3:

25.217.0

x = 10.1 I

18.5]

11066

P = 73

I-33-and p'y = v'x = $1294.

Finally, if residuals per unit of output (per 100 gallonstreated in the case of sectors H and L) are given by

0.051

0

S= 0.050.02]

then s'x = 2.1 tons of sludge.This means that if 10 tons of food and three machines are

delivered to final users and all waste water is subjected totreatment, then the economy will need to produce 25 tons offood products and 17 machines, 10 x 100 gallons ofhigh-BODand 18.5 x 100 gallons oflow-BOD water will be treated, and2.1 tons of sludge will be dumped. Given the labor and capitalcosts per unit of output (v), unit prices are $110 per ton offood, $66 per machine, and $73 and $33, respectively, fortreating 100 gallons of high- and low-BOD water. Totalnational income is $1294. Note that no waste water is emptiedinto the environment in this example.Now let us assume that the society is prepared to tolerate

that 2 x 100 gallons each of high- and low-BOD water beemptied into the environment without treatment while con-sumers still require 10 tons of food and three machines.

This can be represented by allowing final users to "accept"the dirty water, and

10

whereas A, s, and v remain unchanged. In this case, about20% of the high-BOD water and 11% of the low-BOD waterwill not be treated. The output vector is now computed to be

24.5115.7

x 7.9

L14.61This means that slightly less food and fewer machines arerequired, and significantly less waste water is treated, than inthe first scenario. The amount of residual sludge can becomputed to fall from 2.1 to 1.9 tons. Less work is done,prices decline, and national income falls from $1294 (in theother computation) to $1092. The two scenarios can now becompared:

Scenario 1: $1294 income and2.1 tons of residual sludge.

Scenario 2: $1092 income,200 gallons of high-BOD wastewater dumped,200 gallons of low-BOD wastewater dumped,and 1.9 tons of residual sludge.

Thus for an additional outlay of $202 (covering the pro-duction costs of an additional 0.7 ton of food, 1.4 machines,and the processing of an additional 2.3 x 100 gallons ofhigh-BOD water and 3.9 x 100 gallons of low-BOD water)and the toleration of an additional 0.2 ton of sludge, it ispossible to avoid dumping 200 gallons each of high- andlow-BOD waste water.Note in this comparison that the amount of consumption

remains the same at 10 tons of food and three machines. Inthis example, prices are higher when more water is treated:almost 20o higher for a ton of food ($110 compared to $92)but only 6% higher for treating a ton of low-BOD water.Complete flow tables with unit prices for the two scenariosare given in Tables 1 and 2.

It will sometimes be the case, as in this example, thatincreased processing of wastes will be accompanied bydisposal of (i) smaller quantities of raw pollutants, (ii) greaterquantities of concentrated residuals, and (iii) greater costs.Of course, there will also be opportunities for reducing theuse of water and the accumulation of solids in it or ofrecovering economically useful products from the wastestream. In these cases, less pollution can be consistent withlower rather than higher costs.

In this framework there is no attempt to find the "optimal"amount of water to dump or even to determine which of thetwo scenarios is "better" because this is deemed to be notexclusively an economic decision. The method makes itpossible to examine the physical and economic implicationsof technically feasible scenarios rather than screening out allbut one. It is in particular possible to experiment withchanges in input structures that might reduce water usage inproduction or recover products of economic value. Use ofthis framework requires that more information be obtainedand manipulated by the analyst and that a more complex setof results, involving economic and environmental trade-offs,

Table 1. Scenario 1: Flow table corresponding to economyrequiring the treatment of all waste water

Sector value Row

Sector Unit F M H L y totalF Tons 10.1 5.1 0 0 10 25.2M Machines 5.0 5.1 2.0 1.9 3 17.0H 100 gallons 10.1 0 0 0 0 10.1L 100 gallons 10.1 1.7 3.0 3.7 0 18.5v'x $ 251.6 169.9 503.2 369.6 - 1294.3Sludge Tons 1.3 0.0 0.5 0.4 2.1Price $ per unit 109.6 66.0 73.2 33.3Data are from Duchin (6).

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Proc. Natl. Acad. Sci. USA 89 (1992)

Table 2. Scenario 2: Flow table corresponding to economytolerating the dumping of some waste water

Sector value Row

Sector Unit F M H L y total

F Tons 9.8 4.7 0.0 0.0 10 24.5M Machines 4.9 4.7 1.6 1.5 3 15.7H 100 gallons 9.8 0.0 0.0 0.0 -2 7.9L 100 gallons 9.8 1.6 2.3 2.9 -2 14.6v'x $ 245.0 156.6 392.9 297.9 - 1092.4Sludge Tons 1.2 0.0 0.4 0.3 - 1.9Price $ per unit 91.9 57.7 69.9 31.4

These unit prices are obtained by reducing the third and fourthrows of the matrix A by 20% and 11%, respectively, before compu-tation. In the corresponding physical model [where y' = (10 3 0 0)],the solution is identical to that shown in the table except that thewater dumped is credited directly to each sector rather than to finalusers.

be evaluated. Hopefully, a deeper understanding of thetrade-offs is obtained. The results and conclusions can sub-sequently be simplified for other purposes.

4. A More Complete Input-Output Framework

Over the past decade considerable progress has been made inextending the input-output framework beyond the simplestatic model and the accounting data base. The scope of themodel has been broadened to be able to address a larger partof the complexity of the real-world issues in a systematic andintegrated fashion; these are summarized by Duchin (7). Thedata base has been extended in parallel: the data structure isno longer a simple matrix and the nature of the data has beentransformed to accommodate not only accounting data, de-scribing business transactions that took place in the past, butalso technical information obtained directly from technicalsources.The single most important extension to the model has been

the dynamic input-output model, which provides a frame-work for describing and analyzing changes in the economyover historical time. The dynamic physical model representsstocks of specific capital goods and investment in them whilethe corresponding costs and returns are explicit in the dy-namic price model. The changing technical coefficients inboth models, taken up again below, represent technologicalchanges. The model and data base jointly provide an ex-tremely rich framework for investigating the potential con-tributions of specific recommendations issuing from indus-trial ecology.An operational version of the dynamic input-output model

is relatively recent (8) and was first applied to the UnitedStates economy to analyze the economic implications ofcomputer-based automation from 1963 to 2000 (and for thedynamic price and income distribution models; see ref. 10).Variants of this model have since been built and applied inseveral European economies. The present renaissance ofinterest in the properties of this model within the input-output literature suggests that there will be a shift also in theapplied work from a static to a dynamic analysis.A second extension is an optimization framework for

identifying the least-cost technological options faced bydifferent sectors of the economy. This model has recentlybeen applied to the United States economy to investigate thetechnological choices made from 1963 to 2000 (11). Amongother results, this work helps to distinguish the circumstancesunder which formal optimization is usefully employed andthose in which its automatic use would be highly misleading:the latter is true, for example, for the choice of technology ininstances of qualitative changes in output.

A third major extension is a model of the world economythat includes international flows of goods, services, financialcapital, and people. There are several models of the worldeconomy in operation today although there is still a signifi-cant gap between the theory of international exchanges andits implementation. The World Model and World Database,the input-output framework under development at the Insti-tute for Economic Analysis, is being used to investigatestrategies for environmentally sound economic developmentover the next 50 years (United Nations Contract CPTS/CON/103/90; see also ref. 12).The incorporation of technological information into an

input-output database is an area that is ripe for significantdevelopment especially in Japan where the collaboration ofengineers with economists is being systematically supported.Early work along these lines was carried out at the BattelleColumbus Laboratories; an example is their report on theeconomic effects of metallic corrosion (13). Subsequent workat the Institute for Economic Analysis also incorporated anddocumented technical information, especially about comput-er-based automation, and a formal data structure for absorb-ing this kind of information is described by Duchin (14). Anapproach for the kind of studies that will be needed for datadevelopment, this one focused on the conversion of biolog-ical materials and wastes to useful products, is described byDuchin (15).

5. Implications for Industrial Ecology

Raw materials undergo various stages of processing intofinished products whose life cycle can end in different ways.The use of the constituent materials can be reduced at thesource and materials used can be recovered for reuse insimilar applications or, at least, in less demanding applica-tions. The following questions will surely be posed to econ-omists:

* How much will it cost to reduce wastes of particularmaterials?

* Will the value of the benefits be greater than the cost?* Who would end up paying?* What financial incentives, tax schemes, legislation, and

international agreements could assure that the "opti-mal" amount of recycling takes place?

These questions are undeniably important and will need tobe addressed in many specific instances. However, beforeplausible credible answers that provide a firm basis forlong-term action can be forthcoming, there is a prior set ofquestions that needs to be addressed: How would this sourcereduction and recycling be achieved?

This question of "how" has been largely ignored, orrepresented mainly symbolically, by economists for twodifferent but mutually reinforcing reasons. First, an eco-nomic analysis is generally based on the conviction thatindividual decision makers have the right and are the bestinformed parties to decide for themselves the "how" ques-tion: what techniques they will use for production andconsumption. The decision-makers' ingenuity to constantlyseek out the best approach consistent with cost minimizationis said to be unleashed if decision makers are provided withincentives but not constrained by prescriptions. Therefore,the analysis usually focuses on incentives and not on tech-niques. In this view, the "right" incentives can make itpossible to achieve virtually any social objectives. If theprices are right, new techniques will be forthcoming.

This type of reasoning has proven fruitful in many con-texts, especially those involving adjustments to smallchanges in the economic environment within a relativelyunconstrained physical environment. But these mechanisms

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Proc. Natl. Acad. Sci. USA 89 (1992) 855

are not adequate for dealing with problems that may requiresignificant departures from current practices and may run upagainst significant feedback between the physical and eco-nomic systems. The analysis ofalternative techniques in theirinteraction within the economic system can provide invalu-able input to industrial ecology and can also serve as the basisfor the subsequent development of incentive schemes, leg-islation, and international agreements, as well as for identi-fying bottlenecks in research and development that will notbe resolved in a timely fashion by private markets. Once thiswork has been done, the market mechanisms can often berelied upon to do their job.

If it were possible to carry out the analysis without enteringvery deeply (if at all) into the technical characteristics ofspecific methods for reducing pollution, the analysts' jobwould be greatly simplified. The fact that it is simpler is thesecond principal reason why it is usual to avoid or minimizea technical analysis. The dynamic input-output approachprovides the framework for a systematic detailed represen-tation distinguishing specific alternative techniques; but thispotential has barely been developed. In addition, the repre-sentation of specific alternative techniques requires a greatdeal of data and other information that need to be collected,evaluated, and organized. This data work is costly, time-consuming, and not the most glamorous part of an econo-mist's work. Furthermore, it requires technical expertise,usually associated with engineers and applied natural scien-tists. For a collaboration of economists with engineers andapplied natural scientists to be fruitful, economists need tolay the foundations for separate, but integrated, analyses ofphysical stocks and flows on the one hand and of costs andprices on the other. Then engineering and other technologicalconsiderations can be directly represented in physical termsand their costs can be evaluated in price computations.

It is time to take on this challenge. There is no precedentfor carrying out this type of work at a large enough scale tocome to terms with major real-world problems such as thosethat will be taken on by industrial ecology. Such an under-taking will require significant funding and an unusual insti-tutional setting in which team-based interdisciplinary re-search can flourish.

Despite the difficulties, there are compelling reasons fortaking up the "how" questions. It is simply not possible toestimate the cost of, say, a 50% increase in reuse of allmaterials without specifying how the reductions might beachieved in a particular economy. It might be infeasible byany or all means in which case any agreements to these endswill simply never be fulfilled. In cases where there are severalfeasible approaches, the different alternatives will feed backon other sectors, on the environment, and on the standard ofliving in substantially different ways that need to be includedin a realistic analysis.Once plausible scenarios about how to proceed are formu-

lated and quantified, the monetary and nonmonetary costsand benefits need to be computed. On the basis of theseresults, those scenarios with results that prove interestingfrom both environmental and economic points of view can beidentified. Scenario outcomes can help inform realistic bus-

iness strategies and environmental targets with the under-standing that these strategies and targets are potentiallyachievable. There is no reason to attempt to impose adoptionof the particular technologies represented in the scenarios;the marketplace may be able to do better now and is likely tobe able to do better in the future. Dynamic price and incomemodels can at this point be used to experiment with alterna-tive incentive schemes, based on comparing the costs ofproceeding in different ways, and tax schemes, based onsocial consensus about who pays for what.The importance of a physical basis for economic analysis

is particularly clear when one is concerned with alternativearrangements for the handling of materials and their effectson the environment. However, the advantages of asking the"how" question, and of calculating physical as well aseconomic outcomes, will also enable a more realistic assess-ment of production alternatives more generally. The familiarobjectives, say a particular target rate of growth of the grossdomestic product, can be achieved only by specific concreteactions. The latter may require production, domestically orabroad, of selected capital goods to be used in specific sectorsof the economy. Different approaches to satisfying food,material, and energy requirements, in particular, impactnutrition and health, the resource base, and the quality andavailability of soil and water. Within a dynamic input-outputframework, we can begin the investigation of different phys-ical arrangements and their economic implications.

1. Ayres, R. (1989) in Technology and Environment, eds. Ausu-bel, J. H. & Sladovitch, H. E. (Natl. Acad. Press, Washing-ton), pp. 23-29.

2. Frosch, R. A. & Gallopoulos, N. E. (1990) Toward an Indus-trial Ecology (General Motors Research Labs., Warren, MI),Publ. No. GMR-6959.

3. Ayres, R. (1991) Struct. Change Econ. Dyn. 2, in press.4. Duchin, F., Erber, G., Landesmann, M., Nakamura, S. &

Vercelli, A. (1991) Struct. Change Econ. Dyn. 1, 1-3.5. Leontief, W. (1986) in Encyclopedia ofMaterials, Science and

Engineering, ed. Bever, M. B. (Pergamon, Oxford), pp. 2339-2349.

6. Duchin, F. (1990) Struct. Change Econ. Dyn. 1, 243-261.7. Duchin, F. (1988) in Input-Output Analysis: Current Develop-

ments, ed. Ciaschini, M. (Chapman & Hall, London), pp.113-128.

8. Duchin, F. & Szyld, D. (1985) Metroeconomica 37, 269-282.9. Leontief, W. & Duchin, F. (1986) The Future Impact of

Automation on Workers (Oxford Univ. Press, New York).10. Duchin, F. & Lange, G.-M. (1992) Econ. Syst. Res. 4, in press.11. Duchin, F. & Lange, G.-M. (1991) Technological Choices,

TheirImplicationsfor the U.S. Economy, 1963-2000: Report onthe Construction Application ofan Engineering/Input-OutputModel Database, Final Report to the National Science Foun-dation, Grant #ENG-8703347 (Inst. for Econ. Anal., New YorkUniversity, New York).

12. Duchin, F. (1991) in The Global Environment, eds. Takeuchi,M. & Yoshino, M. (Springer, Heidelberg), pp. 142-161.

13. National Bureau of Standards (1978) Economic Effects ofMetallic Corrosion in the U.S. (National Bureau of Standards,Washington), Publ. Nos. 511-1, 511-2, and GCR78-122.

14. Duchin, F. (1988) Eng. Comput. 4, 99-105.15. Duchin, F. (1990) Struct. Change Econ. Dyn. 1, 243-261.

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