Environ. Sci. Technol. 2007, 41, 1024-1031
A Mixed-Unit Input-Output Model for Environmental Life-Cycle Assessment and Material Flow Analysis TROY HAWKINS, CHRIS HENDRICKSON,* CORTNEY HIGGINS, AND H. SCOTT MATTHEWS Green Design Institute, Department of Civil and Environmental Engineering, Carnegie Mellon University, Pittsburgh, Pennsylvania 15213 SANGWON SUH Department of Bioproducts and Biosystems Engineering, University of Minnesota, St. Paul, Minnesota 55108
Materials flow analysis models have traditionally been used to track the production, use, and consumption of materials. Economic input-output modeling has been used for environmental systems analysis, with a primary benefit being the capability to estimate direct and indirect economic and environmental impacts across the entire supply chain of production in an economy. We combine these two types of models to create a mixed-unit inputoutput model that is able to better track economic transactions and material flows throughout the economy associated with changes in production. A 13 by 13 economic inputoutput direct requirements matrix developed by the U.S. Bureau of Economic Analysis is augmented with material flow data derived from those published by the U.S. Geological Survey in the formulation of illustrative mixedunit input-output models for lead and cadmium. The resulting model provides the capabilities of both material flow and input-output models, with detailed material tracking through entire supply chains in response to any monetary or material demand. Examples of these models are provided along with a discussion of uncertainty and extensions to these models.
Introduction Economic input-output models have been widely used for tracing the supply chain impacts of producing goods and services, both in terms of dollar transactions (1) and environmental impacts (i.e., emissions and resource use) (2-13). For example, an economic input-output, life-cycle assessment (EIO-LCA) model is in active use on the Internet (14). Since 2000, the www.eiolca.net website has logged over 900 000 model uses (over 15 000 per month) for academic and research purposes. While government agencies in the United States (15) and elsewhere (16-18) provide comprehensive, national, inputoutput (IO) tables of monetary transactions, the inputoutputframework can also be used to quantify physical flows. Ayres and Kneese (19) and Kneese et al. (20) applied the mass-balance principle to input-output analysis forming a * Corresponding author phone: 412-268-2940; fax: 412-268-7813; e-mail:
[email protected]. 1024
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basic framework for modeling physical flows. During the energy crises of the 1970s mixed-unit input-output techniques were used in a number of energy analyses (21-25). Leontief (26) introduced a pollution sector with emission flows into a national model. Duchin (27, 28) presented an extended input-output model based upon physical quantities and prices. Suh (29) demonstrated how to integrate process-specific physical flow data with monetary inputoutput models and noted the advantages of the input-output models in accounting for circularity of flows in environmental life-cycle assessment. Konijn et al. (30) and Hoekstra (31) have utilized both physical and monetary units in an inputoutput table in tracing the resources flows in a national economy introducing the mixed-unit input-output model. Lin (32) provides an example of coke making for an enterprise specific input-output model. Thus, input-output models have been shown to be useful for materials flow analyses, tracking the movements of particular materials or energy through industrial processes, product use, and natural reservoirs (13, 33-37). In this paper, we present a mixed-unit input-output (MUIO) model including economic transactions and flows of lead and cadmium for the U.S. Our intent is to present an MUIO model created by using material flow data published by the U.S. Geological Survey (USGS) (38) and dollar transactions data from the U.S. Bureau of Economic Analysis (BEA) monetary IO model (15), and to explore its usefulness for environmental life-cycle analysis. By including a comprehensive representation of national production, full supply chain effects may be traced. At the same time, the introduction of process-specific material flow sectors allows more detailed analyses and consideration of different materials use scenarios. A Mixed-Unit Input-Output Life-Cycle Assessment Model (MUIO-LCA). An economic input-output model represents the total output of an economic sector, xi, as equal to the sum of the demand for that sector’s output from the other sectors that comprise the rest of the economy (zij) plus the final or “household” demand for the output of that sector, yi (39): n
xi ) zi1 + zi2 + zi3 + ... + zin + yi )
∑z
ij
+ yi
(1)
j)1
Equation 1 implies that the z and y values together represent all of the demand for the output of sector i. While economic input-output models generally consider output and demand in monetary terms, these values could also be expressed in whatever units apply to the output and demand for the given sector. In this study, physical units will also be used to describe the output of sectors that produce heavy metals and products containing these metals. In an input-output model, the entire economy can be expressed as a series of n equations representing the output of each sector of the economy.
x1 ) z11 + z12 + z13 + ... + z1n + y1 x2 ) z21 + z22 + z23 + ... + z2n + y2 : xn ) zn1 + zn2 + zn3 + ... + znn + yn
(2)
Note that we have one equation and a unique set of z values for each sector of the economy (thus imax ) jmax ) n). By rearranging each of these equations we could represent total 10.1021/es060871u CCC: $37.00
2007 American Chemical Society Published on Web 12/21/2006
output in terms of the fraction of each sector’s (j) total output supplied by sector i.
x1 )
z11 z12 z1j z1n x + x + ... + x + ... + x + y1 x1 1 x2 2 xj j xn n :
zi1 zi2 zij zin xi ) x1 + x2 + ... + xj + ... + x + yi x1 x2 xj xn n : xn )
zn1 zn2 znj znn x + x + ... + x + ... + x + yn (3) x1 1 x2 2 xj j xn n
These fractions of total output are commonly referred to as the direct requirement coefficients (aij).
zij aij ) xj
(4)
If we solve each of the equations for final demand we find that the result has this form:
Returning to our original set of equations used to describe the sectors of the economy (eq 2), sectors could be disaggregated to account for a portion of their output in terms of physical flows by adding rows and columns to this set of equations. In the new equations, the total sectoral output (xim) and final demand (yim) would be defined as the masses of specific material outputs, while the demand values (zijm) are the masses of the specific material inputs to the sector. For example, in the case of the nickel cadmium battery manufacturing sector, total output and final demand are the mass of cadmium contained in nickel cadmium batteries produced and sold to consumers in the U.S. respectively while the intermediate demand values are the mass of cadmium contained in inputs supplied to battery manufacturers by other sectors of the economy. m m m m m xm 1 ) z11 + z12 + ... + z1j + ... + z1n + y1 (mass) m m m m m xm 2 ) z21 + z22 + ... + z2j + ... + z2n + y2 (mass) $ $ x$3 ) z$31 + z$32 + ... + z3j + ... + z3n + y$3 (dollar)
:
y1 ) (1 - a11)x1 - a12x2 - ... - a13x3 - ... - a1nxn
$ $ x$n ) zn1 + zn2 + ... + z$nj + ... + z$nn + y$n (dollar)
y2 ) - a21x1 + (1 - a22)x2 - ... - a2jxj - ... - a2nxn : yi ) - ai1x1 - ... - aijxj - ... + (1 - aii)xi - ... - a2nxn : yn ) - an1x1 - an2x2 - ... - anjxj - ... + (1 - ann)xn (5) This series of equations can be expressed more simply in matrix terms as follows:
y ) (I - A) x
(6)
where y is the vector containing the final demand (yi) for each sector; I is the identity matrix of dimensions n by n (An identity matrix contains one in each diagonal element and zero in all other elements); A is the matrix containing each of the direct requirements coefficients (aij) which also has dimensions n by n; and x is the vector of total output (xi) for each sector. If we wish to calculate the total sectoral output (or changes in total outputs) for a particular final demand (y), then we can solve the matrix equation:
x ) (I - A)-1 y
When a sector representing a physical flow is added to the set of equations, the dollar value of the inputs to and outputs from the physical flow sector should be subtracted from the monetary transactions of the sector to which this flow previously belonged. This prevents accounting for the material flow in both physical and monetary units within the economy. For a more detailed discussion of this procedure, see ref 29. Although sectors in an ideal IO model are defined such that each sector produces only one output, in most cases a sector can be disaggregated into two sectors each of which produces a different output (2, 29, 41, 42). A supplyand-use framework for creating an IO model can be used to account for the secondary outputs produced by certain sectors (40, 43). A set of equations with mixed-units, such as eq 8, results in a mixed-unit direct requirements matrix (A*) that can be partitioned by the units of each entry. If the direct requirements matrix is based on a set of equations that are sorted so that those based on mass units (i.e., metric tonnes) are listed before those based on monetary units (i.e., $) then it will be partitioned as shown in eq 9 (29).
Direct Requirements ) A* )
(7)
Each entry in the (I - A)-1 matrix represented in this equation gives the total demand for a sector’s output associated with a one-unit increase in final demand from the associated sector. The (I - A)-1 matrix is commonly referred to as the total requirements matrix or the Leontief Inverse. If the matrices are not square (if i * j) then more complicated techniques are required to solve for the total sectoral output (x) (40). Because this model consists of a series of linear equations, it assumes that the total demand scales linearly with production level. In general, model results obtained from an IO model are appropriate for marginal changes in production level and, in many cases, suffice for larger changes as well. However, in cases where economies of scale are affected or different technologies are implemented adjustments may need to be made before implementing the IO model.
(8)
(
P CD CU A′
)
With entries defined as follows:
Physical Transactions (P): aPij )
zm ij xm j
)
Mass output of sector i demanded by sector j Total mass output of sector j
Upstream Requirements (CU): aU ij )
z$ij xm j
)
Dollar output of sector i demanded by sector j Total mass output of sector j
Downstream Requirements (CD): aD ij )
zm ij x$j
)
Mass output of sector i demanded by sector j Total dollar output of sector j
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TABLE 1. Physical Flow Data Used for Construction of the Lead Mixed-Unit Physical Flow Matrix, P (103 Metric Tons). lead mining lead mining lead primary smelting lead secondary smelting lead sheeting lead solder lead oxides new storage batteries end-of-life storage batteries a
lead lead new end-of-life imports primary secondary lead lead lead storage storage and release smelting smelting sheeting solder oxides batteries batteries of stocks
0 0
424 0
0 63.7
0 19.1
0
0
0
0 0 0 0
0 0 0 0
0
0
-17.8 -328
exports, flows to monetary sectors and accumulation total of stocks productiona
0 0
0 279
0 175
0 0
42.2 88.3
0
9.58
549
454
0
0
0 0 0 0
0 0 0 0
0 0 0 0
0 0 0 0
0 0 761 0
0 0 0 0
0 0 0 0
19.1 9.58 67 1390
19.1 9.58 828 1,390
991
0
0
0
0
0
0
0
991
100
448 329 1,110
Total production amounts are the sum of the rows and are comparable to total outputs reported in refs 46 and 47.
Monetary Transactions (A′): aAij )
z$ij x$j
)
Dollar output of sector i demanded by sector j Total dollar output of sector j
Entries in the northwest (upper left) quadrant of the mixedunit direct requirements matrix represent the ratio of material consumed by the column sector j to the total material output of sector j. Similarly, the southeast (lower right) quadrant represents the economic dollar per dollar direct requirements. In our examples these dollar per dollar direct requirements (A′) have been obtained by subtracting the value of each physical flow from the entry in the monetary transactions matrix (Z), which was calculated as the product of the monetary direct requirements matrix (A) and the total output vector (x) from the BEA (15) corresponding to the sector with which the physical flow was previously associated. The northeast and southwest quadrants represent the interactions between the physical and monetary economies described in the other sectors. The northeast sector, whose entries have units of mass per dollar, gives the ratio of the amount of physical sector material output consumed by the monetary sectors to the total output of that sector which has units of dollars (44, 45). The southwest sector provides the ratio of monetary sector output purchased by each physical sector to the total output of that sector which is measured in physical units. This quadrant has units of dollars per mass. Sectors in the southwest and northeast quadrants have been referred to as the upstream and downstream requirements, respectively (29). Entries in the southwest quadrant relate to purchases from the monetary transaction sectors by the physical (mass unit) transaction sectors. These represent the demands of the mass unit sectors on the economic (monetary unit) sectors or the upstream requirements. The northeast quadrant indicates purchases made by the monetary sectors from the physical sectors. Entries in this quadrant tell us about demand placed on the physical economy from the outside or the downstream requirements (44, 45). Once the mixed-unit direct requirements matrix (eq 9) has been derived, the total requirements can be calculated in the same way as it was for the strictly monetary matrix according to eq 7. The interpretation of the (I - A)-1 matrix or the Leontief Inverse is also the same as in the monetary case although the mixed-unit Leontief Inverse is not dimensionless, rather it is partitioned in the same way as the mixed-unit direct requirements described above. For a stepby-step explanation of how the direct and total requirements matrices used in the following examples were calculated see the Supporting Information for this article. 1026
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FIGURE 1. Estimated lead extraction, refined lead demand (primary and secondary), and imports associated with $10 million final demand in each of 12 domestic monetary sectors obtained from the MUIO model. Case Study: Lead Flows Due to Additional Final Demand. To illustrate the use of the mixed-unit model, a 1997 U.S. MUIO model based upon twelve domestic economic sectors, one noncomparable import sector, and seven lead flow sectors was assembled. Noncomparable imports are goods purchased by U.S. residents abroad and service imports with no domestic counterparts, such as port expenditures by U.S. airlines in other countries. The resulting 20 by 20 sector model was sufficiently small (with 400 entries) to permit calculations within spreadsheet software. The economic transaction data (used to derive the A′ portion of the mixedunit direct requirements matrix in eq 9) were provided by BEA (15) and the physical flow data were based upon data published by the U.S. Geological Survey (46, 47). Table 1 shows the physical flow matrix, where the entry 424 in the first row indicates a total flow of 424 000 tonnes from lead mining into lead primary smelting sectors (estimated from data in Table 1 and Table 12 in the 1998 USGS Minerals Yearbook, ref 47). The interaction matrices (CU and CD) were estimated from price and output data (refer to Supporting Information A for details). Lead is a toxic material that has received considerable regulatory and scientific interest (48, 49). Lead has been used in the U.S. in a variety of products over the last century, with the dominant uses for the past 50 years being in gasoline and lead-acid batteries. Lead has useful chemical properties such as a low melting point, high density, acid resistance, and chemical stability that contribute to its use in radiation shielding, ammunition, and as an additive in paints and other
TABLE 2. Total Estimated Lead and Monetary Output Required to Produce $10 Million Additional Final Demand in Each of the 12 Domestic Monetary Sectors. nat. res. and construc- manufacmining tion turing
trade
educ. trans. prof.and and and informa- financial business health leisure and other utilities tion services services services hospitality services
Pb Flow Sectors (tonnes Pb) 0.21 0.41 0.38 0.11 0.16 0.32 0.30 0.082
Pb mining Pb primary smelting Pb secondary smelting Pb sheeting Pb solder Pb oxides new storage batteries end-of-life storage batteries
0.69 0.53
1.3 1.0
3.2 2.5
1.1
1.6
5.0
0.33
0.64
0.59
0.006 0.008 0.80 1.3
0.19 0.036 1.2 2.0
0.024 0.034 3.7 6.2
0.003 0.002 0.24 0.41
0.005 0.005 0.48 0.80
1.0
1.4
4.4
0.29
0.57
natural resources and mining construction manufacturing trade transportation and utilities information financial services professional and business services education and health services leisure and hospitality other services other noncomparable imports
13.06
0.67
Dollar Flow Sectors (U.S. $1997 million) 1.6 0.15 1.1 0.23 0.09
0.19 0.15
0.37 0.29
0.62 0.48
0.57 0.44
0.087 0.067
0.16
0.30
0.58
1.0
0.89
0.13
0.004 0.004 0.44 0.74
0.003 0.001 0.12 0.20
0.003 0.002 0.22 0.38
0.005 0.004 0.43 0.73
0.006 0.007 0.72 1.2
0.006 0.006 0.66 1.1
0.002 0.001 0.10 0.17
0.53
0.14
0.27
0.52
0.86
0.79
0.12
0.16
0.23
0.56
0.33
0.10
0.062 1.0 0.22 0.31
0.10 2.0 0.35 0.38
0.11 3.3 0.62 0.61
0.10 3.0 0.52 0.47
0.076 0.45 0.084 0.16
0.40 1.4 1.4
0.37 1.3 1.2
0.42 1.2 1.3
0.048 0.15 0.23
0.013
0.014
0.001
0.13
0.015
0.077 3.6 0.69 0.81
10.05 5.3 1.3 0.64
0.071 16.73 1.1 0.93
0.26 2.1 1.3
0.38 1.1 1.7
0.39 1.1 1.7
0.40 1.1 1.9
0.35 1.1 1.4
0.007
0.008
0.012
0.011
0.021
0.018
0.005
0.011
10.09
0.13
0.11
0.15
0.12
0.19
0.21
0.10
0.16
0.20
10.36
0.18 0.14 0.074
0.26 0.15 0.063
0.27 0.23 0.12
0.15 0.15 0.073
0.18 0.20 0.21
0.22 0.15 0.24
0.10 0.091 0.065
0.16 0.13 0.053
0.14 0.19 0.035
0.19 0.16 0.05
1.31
3.16
0.212
Totals 0.411 0.382
0.105
0.195
0.374
0.623
0.568
0.0867
1.79
4.97
0.331
0.644
0.599
0.163
0.305
0.585
0.977
0.891
0.134
0.868
2.10
0.141
0.273
0.254
0.0701
0.130
0.249
0.414
0.378
0.0577
9.91
9.86
9.88
9.34
9.88
9.77
9.93
9.90
9.91
Pb extraction from 0.690 the environment (tonnes) primary and secondary 1.08 refined Pb (tonnes) total imports of lead 0.459 (tonnes) value added (U.S. 10.0 $1997 million)
0.066 0.11 1.1 2.2 10.35 0.47 0.48 11.33
other
materials. Its redox chemistry makes it suitable for use in electrochemical batteries. Evidence of the detrimental health effects of airborne and ingested lead catalyzed a phase-out of lead additives to gasoline beginning in 1976 and the ban of lead additives in paint in 1978. The removal of tetraethyl lead from gasoline is widely viewed as a significant environmental achievement (50, 51). However, lead is still in use in numerous products, especially lead-acid batteries in automobiles. Using the full model system, Figure 1 shows the estimated lead extraction, refined lead demand, and imports associated with an increase of $10 million final demand (∆y) in each of the 12 domestic dollar transaction sectors. Lead extraction refers to the total lead content of lead ore concentrates mined as a result of the additional final demand while refined lead demand indicates the output of primary and secondary lead. Imports are calculated using the imported fraction of the lead content of the output of each sector. For example, $10 million in additional final demand for professional and business services increases lead extraction by 0.195 tonnes, refined lead production by 0.305 tonnes, and lead imports by 0.130 tonnes. As expected, the lead requirements are greatest for manufacturing and construction with the smallest requirements for service-oriented sectors such as trade,
0.066 2.0 0.34 0.35 12.26 0.93 1.5
10.1
0.12 0.54 0.13 0.28 0.22 12.10 0.94
0.49 0.87 11.47
10.19 0.025 0.19 10.04 0.043 0.017
10.3
professional and business services, financial services, and other. The finer detail in the physical flow sectors can be seen in Table 2 where column headings represent the sector from which an additional $10 million final demand has been applied while the row entries correspond to total output produced by each sector throughout the entire supply chain to meet the additional final demand. For example, the entry at the intersection of the lead mining row and manufacturing column indicates that 3.2 tonnes of lead output from lead mining is consumed throughout the supply chain in order to produce an additional $10 million final demand for manufacturing output. In contrast, only 0.19 tonnes of lead mining is required to produce an additional $10 million final demand for professional and business services. These total industry output values could easily be combined with emissions factors (expressed in releases per tonne or per dollar of output) to aid in estimating the environmental releases as well as human or ecosystem health impacts resulting from a change in consumption behavior. The MUIO model provides a simple framework for the organization of complex material flow data and allows for the detailed estimation of material flows due to economic or material demands. Results of the MUIO model provide the total physical and monetary output required to supply VOL. 41, NO. 3, 2007 / ENVIRONMENTAL SCIENCE & TECHNOLOGY
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FIGURE 2. Estimated lead flows associated with $10 million additional final demand in the manufacturing sector. All flows are provided in tonnes. an additional final demand by sector and stage in the supply chain. In Figure 2 the results of the MUIO model for $10 million additional final demand in manufacturing are presented in the flow chart format commonly used for presentation of MFA results. The value provided in each box represents the total mass of lead output from each sector. In cases where material from one process is used by another the same material is accounted for more than once. For example 3.2 tonnes of lead from mining are used to produce 2.5 tonnes output from primary smelting. The difference between these values is assumed to be the amount of lead in waste resulting from primary smelting. The output of primary smelting serves as an input to the manufacturing processes (lead sheeting, lead solder, lead oxides, and new lead-acid storage batteries) represented within the dotted box. The production of new lead-acid storage batteries consumes 3.4 tonnes of lead in lead oxides and at least an additional 2.8 tonnes of refined lead (output of primary and secondary smelting). We can also see that end-of-life (EOL) storage batteries are an important source of lead for manufacturing. If EOL storage batteries were not available for recycling, demand for mined lead would more than double. Figure 3 provides another perspective on the same data. Direct outputs shown in Figure 3 refer to those demanded by manufacturing from all other sectors (including manufacturing itself) in the first level of the supply chain while indirect outputs are those required by all sectors throughout their entire supply chains to provide the initial output demanded by manufacturing.
Direct Output ) A*y
(10)
Indirect Output ) (I - A*)-1 y - A*y
(11)
The total height of each bar in Figure 3 corresponds to an entry in the manufacturing column of Table 2. The largest lead requirement comes from the storage batteries sector followed by lead secondary smelting (lead recycling). The total flow of lead mined, smelted, produced, and reclaimed is represented. The largest monetary output is associated with the manufacturing sector itself, including the $10 million final demand increment. Case Study: Cadmium Flows Due to Additional Final Demand. Cadmium is also a toxic material of considerable 1028
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FIGURE 3. Model results for lead and monetary output required to supply an additional $10 million final demand for manufacturing output. Output directly required by manufacturing is represented by the hashed areas while dotted gray regions depict the indirect supply chain output. interest (52-56). New (primary) cadmium is typically produced as a byproduct of zinc and lead mining and smelting. The International Metals Reclamation Company (INMETCO) is the only producer of recycled cadmium currently operating in the U.S. (57). Their facility in Ellwood City, Pennsylvania processes used nickel-cadmium batteries as well as industrial residues such as the electric arc furnace dusts resulting from steel production. The major use for cadmium is in nickelcadmium batteries, accounting for roughly 80% of cadmium use (57). As with lead, we used the twelve domestic and one noncomparable imports sector economic model and extended it with seven cadmium product sectors, with flows based upon U.S. Geological Survey data and interaction matrices estimated from output and price data (58). The result is a 20 by 20 sector MUIO model for cadmium in the U.S. economy. Detailed descriptions of the matrix partitions for the cadmium model are available as Supporting Information. To illustrate the model, Table 3 shows the change in output (∆x) resulting from an increase in final demand (∆y) of $10 million for each of the twelve domestic economic sectors. Table 3 can be interpreted in the same way as Table 2. The cadmium flows associated with a given dollar output are not very large because the relatively small mass of cadmium consumed by the U.S. economy has been spread across the large output of the aggregate economic sectors represented in this 13 by 13 summary level model. For example, $10 million additional final demand for construction (column 4) results in total demand of $10.05 million for construction (with the extra $50 thousand due to indirect demands) and $5.3 million for manufacturing. In addition, the $10 million in construction final demand results in output of 5 kg of cadmium from contained in zinc concentrates from zinc and lead mining and 4.6 kg of cadmium from primary zinc smelting and cadmium recovery. As with the lead case, the largest increases in cadmium production result from the incremental manufacturing demand. The direct and indirect supply chain output required to supply a $10 million final demand for manufacturing sector output is depicted in Figure 4. The total height of each bar should correspond to the entries in the manufacturing column of Table 3. Not surprisingly the greatest cadmium demand occurs in the zinc and lead mining sector which mines cadmium along with zinc and lead ores. A slightly smaller mass of cadmium is produced by the primary zinc smelting and cadmium recovery sector. The difference between the cadmium content of smelting output and that
TABLE 3. Total Estimated Cadmium and Monetary Output Required to Produce $10 Million Additional Final Demand in Each of the 12 Domestic Monetary Sectors nat. res. and construc- manufacmining tion turing
Zn and Pb mining primary Zn smelting and Cd recovery secondary Cd, INMETCO electric arc furnace dust new manufacturing scrap Cd compounds end-of-life NiCd batteries
natural resources and mining construction manufacturing trade transportation and utilities information financial services professional and business services education and health services leisure and hospitality other services Other noncomparable imports
trade
educ. trans. prof.and and leisure and informa- financial business health and hospi- other utilities tion services services services tality services
other
3.4
5.0
16
Cd Flow Sectors (kg Cd) 1.0 2.0 1.9
3.2
4.6
15
0.97
1.9
1.8
0.47
0.89
1.7
2.9
2.6
0.39
0.31
0.45
1.4
0.09
0.18
0.17
0.045
0.086
0.17
0.28
0.25
0.04
0.021
0.031
0.10
0.006
0.013
0.012
0.003
0.006
0.011
0.02
0.02
0.00
0.005
0.008
0.024
0.002
0.003
0.003
0.001
0.001
0.03
0.00
0.00
0.000
0.89 0.28
1.3 0.41
4.1 1.3
0.27 0.09
0.53 0.17
0.49 0.15
0.13 0.041
0.25 0.079
0.48 0.15
0.80 0.25
0.73 0.23
0.11 0.03
0.67
1.6
Dollar Flow Sectors (U.S. $1997 million) 0.15 1.1 0.23
0.087
0.16
0.23
0.56
0.33
0.10
0.077 3.6 0.70 0.82
10.05 5.3 1.3 0.64
0.071 16.69 1.1 0.92
0.12 0.54 0.13 0.28
0.062 1.0 0.22 0.31
0.10 2.0 0.35 0.38
0.11 3.3 0.62 0.61
0.10 3.0 0.52 0.47
0.076 0.45 0.084 0.16
0.26 2.1
0.38 1.1
0.39 1.1
0.40 1.1
0.35 1.1
12.26 0.93
0.22 12.10
0.49 0.88
0.40 1.4
0.37 1.3
0.42 1.2
0.048 0.15
1.3
1.7
1.7
1.9
1.4
1.5
0.94
11.47
1.4
1.2
1.3
0.23
0.007
0.008
0.012
0.011
0.021
0.018
0.005
0.011
10.09
0.013
0.014
0.001
0.13
0.11
0.15
0.12
0.19
0.21
0.10
0.16
0.20
0.13
0.015
0.18 0.15 0.074
0.26 0.15 0.063
0.27 0.23 0.12
0.15 0.15 0.073
0.18 0.20 0.21
0.22 0.15 0.24
0.10 0.091 0.065
0.16 0.13 0.053
0.14 0.19 0.035
0.19 0.16 0.048
13.07
cadmium extraction 3.4 from the environment, (kg Cd) primary and secondary 3.5 refined Cd (Kg) total imports 1.33 of Cd (Kg Cd) value added, (U.S. $1997 million) 10.0
0.066 0.11 1.1 2.2 10.35 0.47 0.48 11.3
0.066 2.0 0.34 0.35
0.51
0.96
1.8
3.1
2.8
0.42
10.36
10.19 0.025 0.19 10.04 0.043 0.017
5.0
16
1.0
Totals 2.0
1.9
0.51
0.96
1.8
3.1
2.8
0.42
5.1
16
1.1
2.1
1.9
0.52
0.98
1.9
3.1
2.9
0.43
0.732
0.196
0.373
0.715
1.19
1.09
0.163
9.88
9.77
9.93
9.91
9.92
1.94
6.10
0.405
0.787
9.91
9.88
9.88
9.34
of the mining sector is disposed of in waste material. Secondary cadmium is produced from end-of-life nickel cadmium batteries as well as electric arc furnace dusts resulting from steel recycling and new scrap produced by manufacturing processes.
Discussion The mixed-unit models have significant uncertainty associated with them, stemming from the economic transactions models, the physical flow matrices, and the interaction matrices. Many of the sources of uncertainty are well-known, such as the age of underlying data, the assumption that input requirements scale linearly with changes in final demand (2, 59-61), and the assumption that the input structure required to produce imported goods is the same as that of U.S. industries (60). Although the mixed-unit model adds uncertainty associated with the physical flow and interaction matrices, the physical flow sectors allow more detailed estimates of specific material flows due to particular demands. The use of an IO framework to track material flows allows
10.1
10.3
the user to track the indirect, supply chain flows which would be more difficult to determine using a process model. In deriving a mixed-unit transactions matrix from the monetary transactions matrix published by the BEA, the dollar value of each physical flow should be subtracted from the monetary transactions within which it was previously included (2). In our models, this was done by using an estimated price to calculate the dollar value of each physical flow. This correction becomes more important for detailed models with more sectors than the example case described here. The detailed U.S. monetary IO models contain roughly 500 sectors. Although both cadmium and lead are primarily used in rechargeable batteries, important differences between their material flows can be seen in our models. The scale of lead flows through the U.S. economy is roughly 3 orders of magnitude larger than the flows of cadmium. Also a much higher fraction of lead is recycled (62). Because of the welldeveloped infrastructure for the collection and recovery of lead-acid batteries, U.S. secondary lead production supplies VOL. 41, NO. 3, 2007 / ENVIRONMENTAL SCIENCE & TECHNOLOGY
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that can be used to obtain detailed estimates of particular material flows due to the production and purchase of specific goods and services, these extensions represent an opportunity for more detailed supply chain management and life-cycle assessment.
Acknowledgments This material is based upon work supported by the U.S. National Science Foundation under grant no. 0328870. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the National Science Foundation. Special thanks to Mitch Small, Lester Lave, Fran McMichael, and several anonymous referees for their comments and criticism.
Supporting Information Available FIGURE 4. Model results for cadmium and monetary output required to supply an additional $10 million final demand for manufacturing sector output. Output directly required by manufacturing is represented by the hashed areas while dotted gray regions depict the indirect supply chain output. New manufacturing scrap refers to cadmium recovered from manufacturing processes (rather than post consumer products).
a large portion of lead demand, while only a small fraction of cadmium consumed in U.S. manufacturing is sourced from recycled material owing to its use in small portable re chargeable batteries whose collection rates are lower (38, 63). The recycling rate for large nickel-cadmium batteries used for uninterruptible power systems is 80%, nearly that of lead-acid SLI batteries; however, this use accounts for only 20% of the mass of cadmium used in batteries (64). The use of both cadmium and lead in U.S. manufacturing has been decreasing in recent years in response to concerns about their toxicity. There are several extensions that can be made to make the mixed-unit models more useful for supply chain and life-cycle analysis. For example, disaggregating the economic (monetary) sectors can provide the opportunity for much better detail on interaction terms and the impact of specific new goods and services. While our example of a $10 million demand increment in manufacturing is of general interest, most life cycle assessment work is concerned with more specific sector outputs. The BEA provides a U.S. input-output table with nearly 500 sectors (15) which has been used to create the EIO-LCA model (14). An MUIO model at this scale is currently under development using the same physical flow sectors presented here. It should be able to augment other environmental impact vectors in the www.eiolca.net model (2, 14) for use in scoping life cycle assessment and material flow analyses. Although the separate models for lead and cadmium were presented here, process data for several metals could be combined in a single MUIO model capable of simultaneously tracking multiple metal flows. This method could also be used in the formulation of an energy MUIO model based on energy flows throughout the supply chain. Representing physical flows in terms of mass or energy units can reduce the uncertainty associated with price in monetary IO models and allows researchers and policy-makers to directly model the flows they are interested in. A MUIO model also provides a means of quickly assessing the supply chain impacts of technology changes affecting the physical input structure of a process. Disaggregating the environmental emission flows into different media or locations would also be helpful in assessing human exposures. While we have demonstrated the estimation and use of mixed-unit input-output models 1030
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A detailed explanation of how the lead and cadmium MUIO models were constructed as well as the transactions (Z), direct requirements (A*) and total requirements (I - A*)-1 matrices. This material is available free of charge via the Internet at http://pubs.acs.org.
Literature Cited (1) Leontief, W. Input-Output Economics; Oxford University Press: Oxford, England, 1986. (2) Hendrickson, C. T.; Lave, L. B.; Matthews, H. S. Environmental Life-Cycle Assessment of Goods and Services: An Input-Output Approach; Resources for the Future: Washington, D.C., 2006. (3) Lave, L. B.; Cobas-Flores, E.; Hendrickson, C. T.; McMichael, F. C. Using input-output analysis to estimate economy-wide discharges. Environ. Sci. Technol. 1995, 29 (9), 420A-426A. (4) Hendrickson, C. T.; Horvath, A.; Joshi, S.; Lave, L. B. Economic input-output methods for environmental life-cycle assessment. Environ. Sci. Technol. 1998, 32 (4), 184A-191A. (5) Dietzenbacher, E. Waste treatment in physical input-output anlaysis. Ecol. Economics 2005, 55, 11-23. (6) Hendrickson, C. T.; Horvath, A. Resource use and environmental emissions of U.S. construction sectors. J. Construct. Eng. Manage. 2000, 126, 38-44. (7) Kagawa, S.; Inamura, H.; Moriguchi, Y. A Simple multi-regional input-output account for waste analysis. Economic Syst. Res. 2004, 16, 1-20. (8) Hubacek, K.; Giljum, S. Applying physical input-output analysis to estimate land appropriation (ecological footprints) of international trade activities. Ecol. Economics 2003, 44, 137-151. (9) Kondo, Y.; Nakamura, S. Evaluating alternative life-cycle strategies for electrical appliances by the waste input-output model. Int. J. LCA 2004, 9, 236-246. (10) Nakamura, S.; Kondo, Y. Input-output analysis of waste management. J. Ind. Ecol. 2002, 6, 39-64. (11) Proops, J.; Faber, M.; Wagenhals, G. Reducing CO2 Emissions: A Comparative Input-Output Study for Germany and the UK; Springer-Verlag: Heidelberg, 1993. (12) van der Voet, E.; Guine´e, J.; Udo de Haes, H. Heavy Metals: A Problem Solved? Methods and Models to Evaluate Policy Strategies for Heavy Metals; Kluwer Academic: Dordrecht, 2000. (13) Takase, K.; Kondo, Y.; Washizu, A. An analysis of sustainable consumption by the waste input-output model. J. Ind. Ecol. 2005, 9, (1-2), 201-219. (14) Green Design Institute. Carnegie Mellon University Environmental Input-Output Life-Cycle Assessment Model. www.eiolca.net (accessed July 2006). (15) U.S. Bureau of Economic Analysis Benchmark Input-Output Accounts. http://www.bea.gov/bea/dn2/home/benchmark.htm (accessed March 21), (16) Statistics Canada. Input-Output Structure of the Canadian Economy in Current Prices; Statistics Canada: Ottawa, Ontario, Canada, 2006. (17) National Statistics United Kingdom Input-Output United Kingdom Accounts. http://www.statistics.gov.uk/about/methodology_by_theme/inputoutput/ (accessed July 2006), (18) Australian Bureau of Statistics Australian National Accounts: Input-Output Tables. http://www.abs.gov.au/AUSSTATS/abs@ .nsf/productsbytitle/EE991BE3CB4C77BBCA256EC1007FB811? OpenDocument (accessed July 2006),
(19) Ayres, R. U.; Kneese, A. V. Production, Consumption and Externalities. Am. Economic Rev. 1969, 59, 282-297. (20) Kneese, A. V.; Ayres, R. U.; d’Arge, R. C. Economics and the Environment: A Material Balance Approach; Resources for the Future: Washington D.C., 1970. (21) Bullard, C.; Herendeen, R. Energy impact of consumption decisions. Proc. IEEE 1975, 63 (3), 484-493. (22) Bullard, C.; Penner, P.; Pilati, D. Net Energy analysis: Handbook for combining process and input-output analysis. Resour. Energy 1978, 1 (3), 267-313. (23) Casler, S.; Wilbur, S. Energy input output analysissa simple guide. Resour. Energy 1984, 6 (2), 187-201. (24) Hannon, B.; Stein, R. G.; Segal, B. Z.; Serber, D. Energy and labor in construction sector. Science 1978, 202 (4370), 837-847. (25) Herendeen, R. A. Input-output techniques and energy cost of commodities. Energy Policy 1978, 6 (2), 162-165. (26) Leontief, W. Environmental repercussions and the economic structure: An input-output approach. Rev. Economics Stat. 1970, 52 (3), 262-271. (27) Duchin, F. Input-Output Economics and Material Flows. http:// www.economics.rpi.edu/www/workingpapers/rpi0424.pdf (accessed April 2006), (28) Weisz, H.; Duchin, F. Physical and Monetary Input-Output Analysis: What Makes the Difference? http://www.economics.rpi.edu/www/workingpapers/rpi0422.pdf (accessed April 2006), (29) Suh, S. Functions, Commodities and environmental impacts in an ecological-economic model. Ecol. Economics 2004, 48 (4), 451-467. (30) Konijn, P.; de Bohr, S.; van Dalen, J. Input-output analysis of material flows with applications to iron, steel and zinc. Struct. Change Economic Dyn. 1997, 8, 129-153. (31) Hoekstra, R. Structural Change of the Physical Economy: Decomposition Analysis of the Physical and Hybrid InputOutput Tables; Free University: Amsterdam, 2003. (32) Chen, C.; Newman, J.; Newman, R.; Rada, R.; Lin, X.; Polenske, K. R. Input-output modeling of production processes for business management. Struct. Change Economic Dyn. 1998, 9, 205-226. (33) National Research Council. Material Count: The Case for Material Flows Analysis; National Academies Press: Washington, DC, 2004; p 144. (34) Bailey, R.; Allen, J. K.; Bras, B. Applying ecological input-output flow analysis to material flows in industrial systems part I: Tracing flows. J. Ind. Ecol. 2004, 8 (1-2.), 45-68. (35) Bailey, R.; Bras, B.; Allen, J. Applying ecological input-output flow analysis to material flows in industrial systems part II: Flow metrics. J. Ind. Ecol. 2004, 8 (1-2.), 69-91. (36) Ayres, R. U.; Ayres, L. U. Handbook of Industrial Ecology; Edward Elgar Publishing Ltd.: Cheltenham, UK, 2001. (37) Baccini, P.; Brunner, P. H. Metabolism of the Anthroposphere; Springer: Berlin, 1991. (38) U.S. Geological Survey Minerals Yearbook 1997: Vol. I, Metals and Minerals. http://minerals.usgs.gov/minerals/pubs/commodity/myb/ (accessed June 2006), (39) Leontief, W. Quantitative input-output relations in the economic system of the united states. Rev. Economic Stat. 1936, 18, 105125. (40) Miller, R. E.; Blair, P. D. Input-Output Analysis: Frontiers and Extensions; Prentice Hall: Englewood Cliffs, NJ, 1985. (41) Joshi, S. Product environmental life-cycle assessment using input-output techniques. J. Ind. Ecol. 2000, 3 (2, 3), 95-120. (42) Wolsky, A. Disaggregating input-output models. Rev. Econ. Stat. 1984, 66 (2), 283-291. (43) Stone, R.; Bacharach, M.; Bates, J. Input-Output Relationships, 1951-1966; Chapman & Hall: London, 1963; Vol. 3. (44) Suh, S. Reply: Downstream cut-offs in integrated hybrid lifecycle assessment. Ecol. Econ. 2006, 59 (1), 7-12.
(45) Peters, G.; Hertwich, E. A comment on “functions, commodities and environmental impacts in an ecological-economic model”. Ecol. Econ. 2006, 59 (1), 1-6. (46) USGS Minerals Yearbook 1997; U.S. Geological Survey, U.S. Department of Interior: Reston, VA, 2000. (47) USGS Minerals Yearbook 1998; U.S. Geological Survey, U.S. Department of Interior: Reston, VA, 2000. (48) NRC, Lead in the Human Environment; National Academy Press: Washington, DC, 1980. (49) National Research Council. Measuring Lead Exposure in Infants, Children and Other Sensitive Population; National Academy Press: Washington, DC, 1993. (50) Rabinowitz, M. B.; Needleman, H. L. Temporal trends in the lead concentrations of umbilical cord blood. Science 1982, 216 (4553), 1429-1431. (51) Thomas, V. M.; Socolow, R. H.; Fanelli, J. J.; Spiro, T. G. Effects of reducing lead in gasoline: An analysis of the international experience. Environ. Sci. Technol. 1999, 33 (22), 3942-3948. (52) Johannesson, M.; Anheden, M.; Arrhenius, E.; Dahl, J.; Ericson, S.; Hindreson, A.; Nielson, B.; Obernberger, I.; Riddell-Black, D. The Market Implication of Integrated Management for Heavy Metal Flows for Bioenergy Use in the European Union; Department of Biology and Environmental Science, Kalmar University: Kalmar, Sweden, 2002. (53) Ikeda, M.; Zhang, Z. -W.; Moon, C. -S.; Shimbo, S.; Watanabe, T.; Nakatsuka, T.; Matsuda-Inoguchi, N.; Higashikawa, K. Possible effects of environmental cadmium exposure on kidney function in the japanese general population. Int. Arch. Occup. Environ. Health 2000, 73, 15-25. (54) ATSDR, Toxicological Profile for Cadmium., U.S. Department of Health and Human Services, Agency for Toxic Substances and Disease Registry: Washington, DC, 1999; p 400. (55) USEPA, Integrated Risk Information System (IRIS) Cadmium; U.S. Environmental Protection Agency: Washington, DC, 1995. (56) Nawrot, T.; Plusquin, M.; Hogervorst, J.; Roels, H. A.; Celis, H.; Thijs, L.; Vangonsveld, J.; VanHecke, E.; Staessen, J. A. Environmental exposure to cadmium and risk of cancer: A prospective population-based study. Lancet Oncology 2006, 7, 119-126. (57) USGS Minerals Yearbook 2004; U.S. Geological Survey, Department of the Interior: Washington, DC, 2005. (58) Hawkins, T. Closing the loop on cadmium: An assessment of the material cycle of cadmium in the U.S. Int. J. Life Cycle Assess. 2006, 11 (1), 38-48. (59) Lenzen, M.; Treloar, G. Differential convergence of life-cycle inventories toward upstream production layers implications for life-cycle assessment. J. Ind. Ecol. 2003, 6 (3-4), 137-160. (60) Lenzen, M. Errors in conventional and input-output-based lifecycle inventories. J. Ind. Ecol. 2001, 4 (4), 127-148. (61) Duchin, F.; Levine, S. H. Human Ecology: Industrial Ecology. http://www.economics.rpi.edu/www/workingpapers/ rpi0603.pdf (accessed June 2006), (62) Battery Council International National Recycling Rate Study. http://www.batterycouncil.org/BCIRecylingRateStudyReport.pdf (accessed July 2006), (63) Fishbein, B. Industry Program to Collect Nickel-Cadmium (NiCd) Batteries. http://www.informinc.org/recyclenicd.php (accessed July 2006), (64) Plachy, J. Cadmium Recycling in the United States in 2000; U.S. Geological Survey: Reston, VA, 2003.
Received for review April 11, 2006. Revised manuscript received September 25, 2006. Accepted October 19, 2006. ES060871U
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