Improved Alternatives for Estimating In-Use Material Stocks

Article pubs.acs.org/est

Improved Alternatives for Estimating In-Use Material Stocks Wei-Qiang Chen* and T.E. Graedel Center for Industrial Ecology, School of Forestry and Environmental Studies, Yale University, New Haven, Connecticut 06511, United States S Supporting Information *

ABSTRACT: Determinations of in-use material stocks are useful for exploring past patterns and future scenarios of materials use, for estimating end-of-life flows of materials, and thereby for guiding policies on recycling and sustainable management of materials. This is especially true when those determinations are conducted for individual products or product groups such as “automobiles” rather than general (and sometimes nebulous) sectors such as “transportation”. We propose four alternatives to the existing top−down and bottom−up methods for estimating in-use material stocks, with the choice depending on the focus of the study and on the available data. We illustrate with aluminum use in automobiles the robustness of and consistencies and differences among these four alternatives and demonstrate that a suitable combination of the four methods permits estimation of the in-use stock of a material contained in all products employing that material, or in-use stocks of different materials contained in a particular product. Therefore, we anticipate the estimation in the future of in-use stocks for many materials in many products or product groups, for many regions, and for longer time periods, by taking advantage of methodologies that fully employ the detailed data sets now becoming available.

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INTRODUCTION The amount of a product or product group (hereafter “product” unless otherwise noted) in active use is termed the in-use stock of the product (measured in physical units in industrial ecology) and, alternatively, net capital stock of the product (measured in monetary units in economics). Industrial ecologists also define the amount of a material contained in inuse stocks of all products employing that material as the in-use stock of the material. In-use stocks of both products and materials are essential for modern society because they provide the capacities to produce output and income, as well as various services or access to services on which we rely in our daily work and lives. The U.S. Bureau of Economic Analysis (BEA) and other governmental agencies have been estimating net capital stocks of products (which BEA terms f ixed assets and consumer durable goods) for several decades.1−3 For each product (a type of asset), there are two basic methods (Figure 1) used by BEA to estimate net capital stock:1 (1) the physical inventory method multiplies independently estimated prices with the directly counted number of physical units of the asset; (2) the perpetual inventory method calculates the net capital stock in each year as the cumulative value of gross investment flows through that year less the cumulative value of depreciation flows through that year, with the annual depreciation flow determined by historical investment flows and the average service life of that type of asset. The physical inventory method is more direct, but is only in limited use because the existing data are incomplete and because there are problems with valuating the assets.1,2 © XXXX American Chemical Society

Therefore, BEA uses the perpetual inventory method for all types of assets (except automobiles, for which enhanced data are available). There are also two basic methods employed in estimating physical in-use stocks of materials: the bottom-up method and the top-down method.4,5 The bottom-up method (Figure 1) applies a strategy similar to the physical inventory method by first gathering information on the number of physical units of each product in-use, and then multiplying those data by their respective average (or typical) material contents to infer their material in-use stocks. The top-down method (Figure 1) is similar to the perpetual inventory method in taking information on material flows and inferring in-use material stock by the cumulative difference between inflow and outflow.4,5 The material inflow and outflow in the top-down method correspond to the monetary investment flow and depreciation flow in the perpetual inventory method, respectively, and the outflow is generally modeled by combining the historical material inflows and certain assumed lifespan models. A summary of the comparison between the top-down and the bottom-up methods is given in Table 1. An advantage of the bottom-up method is that it provides information on the distribution of material stocks for specific types of products (e.g., automobiles, trucks, or refrigerators) rather than merely Received: September 4, 2014 Revised: January 7, 2015 Accepted: January 30, 2015

A

DOI: 10.1021/es504353s Environ. Sci. Technol. XXXX, XXX, XXX−XXX

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Environmental Science & Technology

metals) that are classified into general end-use sectors rather than specific products. In addition, the data are almost always at the national or territorial level. This results in several limitations to existing top-down studies: (1) In-use stocks estimated by these studies are generally for aggregated end-use sectors such as transportation or consumer durables rather than for specific products. (2) The results at country or territory level make it difficult to determine material stocks for a city, or the spatial distribution of material stocks. (3) No information on flows of products are generally collected and used, and therefore stocks of materials but not stocks of products are inferred. (4) For sectors that include many heterogeneous products, it is difficult to estimate a reasonable average product lifespan, therefore resulting in high uncertainties in stock estimations. For example, in statistics on shipments of aluminum semis by end-use in the U.S., both computers and power lines are included in the electrical engineering (EE) sector,7 but their typical service lifespans are 3−5 years and 40−50 years, respectively. (5) The methods of classifying end-use sectors are material-specific but generally inconsistent among the data sources. (For example, there is a “containers and packaging” (C&P) sector and an “others” sector in the U.S. aluminum statistics,7−9 while the iron that is used for C&P is classified in the “others” sector in many iron studies10−12) Another challenge is that some sectors identified for some metals are intermediate products rather than real end-use sectors, such as the sector called “integrated circuits” for gallium,13 resulting in difficulties in estimating lifespans. (6) The top−down method requires time-series data on inflows; in order not to underestimate the in-use stocks, these time-series data should cover a period longer than the longest lifespans of all sectors, but the time spans of industrial statistics are often limited. Aluminum is one of the metals for which in-use stocks have been extensively analyzed. Existing studies on in-use aluminum stocks are listed in Table 1, in which the models used therein are categorized into the different analytical methods. A majority of these studies used the top-down approach,9,14−20 probably because of the wide availability of data on historical semis shipments by end-use. There are only two published studies21,22 applying the bottom-up method, and they provided results for only a one-year snapshot. There are also two published studies23,24 in which the model can be categorized as the Flow-Based Using Physical Data (FBPD) method (details are described later in this paper), and they are only for automobiles. By taking advantage of physical or monetary data on stocks and flows of products that have been or are becoming available (e.g., those compiled in one of our recent studies25) and of new modeling methods (e.g., the unit physical input−output by

Figure 1. Methods for estimating net capital stocks of products and inuse stocks of products and materials.

that of very general and sometimes nebulous sectors (e.g., transportation or consumer durables). Another advantage is that the bottom-up method may allow determination of the spatial distribution of stocks in particular localities.6 However, to our knowledge all existing studies that apply the bottom-up method provide results only for a one-year snapshot (i.e., they lack time-series information), although analyses using this method can be dynamic too, provided that multiyear data on physical stocks of products and their material contents are available. Another limitation of these studies is that they cannot show information on outflows from in-use stocks, which may be important for analyzing the potential for materials recycling. In contrast, the advantage of the top-down method is that it provides time-series estimation of not only in-use stocks themselves but also outflows from them. A practical difficulty with existing studies that apply the top− down method to estimate in-use material stocks is that almost all data regarding material inflows are industrial statistics on shipments or apparent consumption of materials (mostly

Table 1. Comparison among Methods of Estimating In-Use Material Stocksa

a

feature

TD

BU

FBPD

SBPD

FBMD

SBMD

sector vs product level multi (M) vs one (O) year physical vs monetary based flow information available stock spatial distribution material content information lifespan information Al-related studies

sector M physical yes no no need for sector refs 9, 14−20

product M or Ob physical no maybe needed no need refs 21, 22

product M physical yes maybe needed for product this study, refs 23, 24

product M or O physical maybe maybe needed for product this study

product M monetary yes maybe needed for product this study

product M or O monetary maybe maybe needed for product this study

See Figure 1 for abbreviations. bResults provided by existing published studies are only for a one-year snapshot. B


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factors, even though the product is still in active use. Thus, exemplified by automobiles used in the U.S., we estimate a data series termed “virtual capital stock” by assuming that the economic depreciation rate is the same as the physical retirement rate, and compare this “virtual capital stock” with in-use stock and actual capital stock. Determination of Aluminum Content per Unit of Automobiles. When flows and stocks of products are indicated by physical units, the average material content is measured in material weight per physical unit of a product. When flows and stocks of products are indicated by monetary units, the average material content is measured in material weight per monetary unit of a product. In automobiles, for example, units are kilogram (kg) of aluminum use per vehicle and kg of aluminum use per 1000 constant US$ of automobiles, respectively. If data on the average price of a product are available or can be inferred, the material weight per monetary unit of a product can be converted to the material weight per physical unit of a product. We did so in this study for the average aluminum use in automobiles and compared the two data series on kg of aluminum use per vehicle. The average price of an automobile is inferred by dividing the annual monetary investments flow by the annual physical sales flow. Data on the average material content per physical unit of products are widely available in public reports, academic papers, and other publications, although locating these data can be time-consuming. Average aluminum content of a new light-duty vehicle manufactured in the United States from 1973 to 2009 has been reported in an industrial presentation,31 and these data are used in this study. For earlier years, because the automobile industry began to use aluminum in 1899,32 we estimate average aluminum content per physical unit of automobiles manufactured in the period 1901−1972 by an interpolation method, with the assumption that an automobile’s aluminum content in 1900 is zero. The average content of a material per monetary unit of a product is not directly reported by any publication, but can be estimated using the UPIOM model26−30 and the price of the concerned material. Details on the UPIOM model are described in the cited publications, and only a summary is provided here. For the ten years (1963, 1967, 1972, 1977, 1982, 1987, 1992, 1997, 2002, and 2007) for which the U.S. BEA has released detailed input−output (IO) tables,33−35 the first step , the average content of material m (which is in estimating Cm,p,f i aluminum in this study) in product p (which is automobile in this study) manufactured in year i, is to calculate the commodity by commodity direct requirements matrix Ai in year i. (Note, however, that the original U.S. IO data for years except 1963 and 1967 were compiled as Make and Use tables, and should be converted into commodity by commodity IO tables using a method detailed in the Supporting Information. In addition, the 1963 and 1967 U.S. IO tables were not compiled using the commodity-by-industry approach and thus the original IO tables were directly used.) The second step is to transform matrix Ai into matrix Ã i in which each input will become a physical component of each output:

materials (UPIOM) model developed by Nakamura and colleagues26−30), the present work seeks to achieve the following goals: (1) propose four alternatives to the existing top-down and bottom-up methods for estimating in-use material stocks, in which a combination of methods can avoid the disadvantages of top-down and bottom-up methods individually; (2) use aluminum in automobiles as an example to show the applicability and robustness of these four methods, and to explore the reasons for consistencies and differences among them; we chose aluminum and automobiles for this case study because the relevant data are widely available in the United States, which enables us to apply the case study to the four alternative methods; and (3) discuss for what materials and products in-use material stocks can be estimated using the available data and an individual or a suitable combination of these four alternatives.

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MATERIALS AND METHODS The four alternative methods we are proposing (Figure 1 and Table 1) are classified according to two groups of features: (1) flow-based vs stock-based; and (2) using physical data vs using monetary data. Details and formulas for these four methods are available in the Supporting Information of this paper. A summary of the data compilation for the illustrative example, U.S. aluminum use in automobiles, is provided in Supporting Information Table S1. Flow-Based Methods. The strategy of flow-based methods is that the annual flow into use of a material contained in a product is determined first (this is similar to the top-down method) by multiplying annual flow into use of the product by its average material content. Annual end-of-life flow out of use of the material is then estimated using a lifespan model. Finally, the in-use stock of the material is inferred by accumulating the annual difference between its flow into use and its flow out of use. Both flows and stocks of products can be measured in and indicated by either physical or monetary units. As exemplified by automobiles, the physical flow into use is the same as the annual sales to the domestic market measured in number of vehicles, while the monetary flow into use is the same as the annual domestic automobile investments measured in U.S. dollars (we use constant 2000 US$ in this study). Stock-Based Methods. The strategy of stock-based methods is that annual stock (either in-use stock or net capital stock) of a product is determined first (this is similar to the bottom-up method), and then in-use stock of a material contained in that product is estimated by multiplying the product’s stock with its average material content. In-use stock of a product (when measured in physical units) can be determined in two methods: (1) existing data can be an approximation of in-use stocks, such as the number of registered automobiles; and (2) physical data on annual flow into use of a product and a lifespan model can be used to infer in-use stock of a product. Net capital stock of a product (when measured in monetary units) can also be estimated by two methods:1 (1) the physical inventory method (that is only applied to automobiles in the U.S.); and (2) the perpetual inventory method (that can be used for all products). However, it is important to note that the economic depreciation rate is faster than the physical retirement rate for many tangible products, because flows out of use physically happen only when a product (or its component) is discarded, while economic flows out of use (depreciation) can occur due to quality decrease, aging, falling out of fashion, and other

Ã i = ΓΘ(ΦAi )

(1)

where Γ = [γ] is the yield ratio matrix with γ ϵ [0,1], Θ is the Hadamard product (the element-wise product of two matrices), and Φ = [φk] is a diagonal matrix with its kth diagonal element φk equal to unity when k is physical, and zero otherwise. C


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Figure 2. Flows and stocks of automobiles in the United States, 1900−2010: a comparison between physical data and monetary data. The Virtual Capital Stock is estimated using the same strategy as the Perpetual Inventory Method, but assuming that the economic depreciate rate is the same as the physical retirement rate (refer to Supporting Information Figure S2 for their difference).

Figure 3. Prices of automobiles and aluminum, and average aluminum content in automobiles manufactured in each year. Refer to Supporting Information Figure S3 for longer time data.

Cim,p,f = Cim,p,IO/priceim

The third step is to classify all sectors in a year’s IO table into three categories, resource sectors, material sectors, and product sectors, and then reorder and partition matrix Ã as follows: ⎛ Ã r,r Ã ,m,r Ã p,r ⎞ ⎛ 0 0 0 ⎞ i i ⎜ i ⎟ ⎜ ⎟ r,m r,m m,m p,m ̃ 0 0 ⎟ Ã = ⎜ Ã i Ã i Ã i ⎟ = ⎜ Ai ⎜ ⎟ ⎜ ⎟ ⎜ ̃ r,p ⎟ Ã im,p Ã ip,p ⎠ Ã im,p Ã ip,p ⎠ ⎝ 0 ⎝ Ai

Ã r,m i ,

Ã m,p i ,

where pricemi is the price of aluminum in year i, for which the data are compiled by U.S. Geological Survey.13 We note that the reported data or results generated by the UPIOM model reflect the average material content of annual flows into use. However, because products remaining in stocks in a certain year entered use in prior years, it is only when the average material content of newly manufactured products remains stable over time that these data or results can be regarded as the average material content of stocks in the same year. In the case that the average material content of a product increases or decreases (relatively) steadily, a method of approximating the average material content of stocks is to assume that it equals the average material content of a newly manufactured product in a certain previous year. Otherwise, the determination of the average material content of products remaining in stocks can be very complicated (details in the Supporting Information). Luckily, because the average aluminum content in automobiles experienced a relatively steady increasing trend, we assume that the average aluminum content in stocks in a certain year is the same as the average aluminum content in flows in previous years (0, 7, or 14 years for sensitivity analysis).

(2)

Ã p,p i

where only and are not zero because resources only become physical components of materials, materials only become physical components of products, and products can become components of products. The fourth step is to generate the material-composition matrix of products, Cm,p,IO , in which each element indicates the i monetary input of material m per monetary output of a product Cim,p,IO = Ã im,p (I − Ã ip,p )−1

(4)

(3)

With Cm,p,IO for i for the Cm,p,IO i

the above ten years estimated by this method, entire period 1900−2010 is derived using interpolation by assuming that aluminum input per automobile output in 1900 was zero while aluminum input per automobile output after 2007 remains stable. Finally, the weight of aluminum per monetary output of automobiles manufactured in year i in the United States for the period 1900−2010 is estimated by D


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Figure 4. Flows and stocks of aluminum contained in automobiles in the United States, 1900−2010. Refer to Figure 1 for the abbreviations of the four methods. For the stock-based methods, the average aluminum content in all in-use automobiles in year t is assumed to be the same as that in new automobiles manufactured in year t − i (i = 0, 7, or 14).

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Average Aluminum Content in Automobiles. As was done above for product flows and stocks, material flows and stocks can be compared in both physical and monetary analyses. According to a detailed industrial report,31 the average aluminum content of a new light-duty vehicle manufactured in the United States increased from 37 kg in 1973 to 148 kg in 2009 (Figure 3b). The monetary input of aluminum per monetary output of automobiles manufactured in the United States experienced an increasing trend from 1963 to 2007 as well (Figure 3a), despite some fluctuations. (Supporting Information Figure S3 shows results for the whole period 1900−2010 based on interpolation.) Results on monetary input of aluminum per monetary output of automobiles were first converted to the average weight of aluminum use per monetary output of automobiles, and then to the average weight of aluminum per physical unit of automobiles (Figure 3b). A comparison between the two temporal patterns of aluminum use per physical unit of automobiles in Figure 3b reveals that (1) the average aluminum content per automobile estimated using monetary data shows an increasing trend that verifies the lightweighting trend of automobiles described by industry31 and (2) the historical evolution of average aluminum content per automobile estimated using monetary data fluctuates around the historical evolution of average aluminum content per automobile reported by industry.31 The fluctuations result from uncertainties in data on input-output tables, aluminum prices, annual investments in automobiles, and so forth. The most significant factor is probably the price of aluminum (Figure 3b), because when aluminum price increases the average aluminum content estimated using monetary data decreases and becomes lower than the average aluminum content reported by industry,31 while when aluminum price decreases the estimated average aluminum content increases and becomes higher than the average aluminum content reported by industry.31 This result is reasonable because the automobile industry may keep an inventory of aluminum, may have long-term contracts with the aluminum industry, and may remelt new scrap inside its factories, so that it can deal with the challenges of aluminum price fluctuations. Thus, the automobile industry may purchase aluminum at a price that is more stable than the reported price. Flows and Stocks of Aluminum in Automobiles. The annual flows of aluminum contained in automobiles entering

RESULTS AND DISCUSSION Flows and Stocks of Automobiles. When data for a specific product are examined over time, stock and flow results in both physical and monetary units can be compared. Figure 2 shows annual flows and stocks of automobiles in the United States from 1900 to 2010. The historical evolution of annual sales measured in physical units of automobiles matches very well with that of annual investments in automobiles measured in constant US$. However, the two temporal patterns (Figure 2a) do not always overlap with each other due to the fluctuation of automobile prices (Figure 3a). Three consistencies in the estimation of automobile stocks can be observed from Figure 2b: (1) physical in-use stock estimated by using annual sales data and a lifespan model (paths 2 and 3 in Figure 1) matches very well with the number of automobile registrations (path 1 in Figure 1), thereby verifying the applicability of the lifespan model and its parameters for automobiles in the United States; (2) the historical evolution of net capital stock estimated by the perpetual inventory method (paths 6 and 7 in Figure 1) is almost the same as that of net capital stock estimated by the physical inventory method (paths 1 and 11 in Figure 1); and (3) physical in-use stocks and the virtual net capital stocks share basically the same pattern of historical evolution over time (Supporting Information Figure S1 also shows that in-use stocks and the actual net capital stocks share the same historical evolution trend). However, note that there is a significant difference in Figure 2b between the virtual net capital stocks and actual net capital stocks. Additionally, actual net capital stocks decrease after reaching a peak in 1988, while physical in-use stocks basically remain stable after that year. These differences occur because the economic depreciation rate is faster than the physical retirement rate for automobiles (Supporting Information Figure S2). An automobile ceases being part of the in-use stock only if it has been physically retired, in which case it completely loses its economic value as part of the net capital stock. However, an automobile may also partly lose its economic value because it is aging or it falls out of fashion, although it is still in active use. As illustrated by Supporting Information Figure S2b, an automobile has a 93% possibility of being in active use 5 years after entering use, but it has lost more than 60% of its economic value at the same time. E


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annual generation of end-of-life flows of materials, as well as end-of-life flows of products containing materials. Among the four methods proposed by this study, we regard the flow-based methods as preferable, because average material contents can be collected from publicly available information or can be estimated using input-output tables. This avoids the challenges of estimating average material content for product stocks. Compared to methods using monetary data, the advantages of using physical data include: (1) products and materials may be divided into more detailed levels and (2) uncertainties resulting from input-output tables and prices of materials and products can be avoided. However, using monetary data has its own advantages. For some countries (especially for the United States and Japan), data on annual investment flows are widely available, in sufficient detail, and for relatively long time periods. In contrast, the existence of physical data is more random and is distributed in publications for which exploration is more difficult and time-consuming. It is noted that although the SBMD method may generate results that underestimate the actual in-use material stocks, it could be a possible option for estimating in-use material stocks provided its average material content is suitably estimated, especially when a product’s information on physical stocks and flows, as well as monetary flows, are not available. Finally, we have to point out that the four methods proposed here cannot provide a good solution for determining the spatial distribution (at a resolution lower than that of countries) of in-use stocks. Thus, there could be additional benefits were one to combine our methods with those using remote sensing data and geographical information system models.36−38 We note that by taking advantage of these four methods in suitable combination, existing data may permit estimation of the in-use stock of a certain material contained in all products employing that material, or of in-use stocks of different materials contained in a certain product. For aluminum, copper, iron, and plastics that have relevant independent sectors in the U.S. input−output tables, for example, in-use stocks can possibly be estimated by using the FBMD method for products or product groups in the sectors of building and structures, transportation facilities, and machinery and equipment, of which the annual investment data have been compiled by U.S. BEA.3 Similar estimation is also possible for other metals provided each of their first-uses or end-uses reported by the U.S. Geological Survey13 match a sector in the U.S. inputoutput tables. For some products such as automobiles,39−41 home appliances,42,43 or certain electronic products,44 longterm physical data on their stocks and flows, as well as on their material contents,44−47 make it feasible to estimate in-use stocks of many materials contained in those products. Therefore, we believe it is becoming possible to build a cumulative and expandable database in which both physical and monetary data on flows and stocks of products and their material contents are incorporated. Such an achievement will enable the estimation in the future of in-use stocks of many materials in many products, for many regions, and for longer time periods (e.g., we estimate dynamic in-use stocks of aluminum in more than 100 products or product groups in the United States for the period 1960−2009 or longer in an associated study48), which will then be very useful for exploring past patterns and future scenarios of materials use, for estimating material end-of-life flows and urban mining potentials, and thereby for guiding policies on material recycling and sustainable resources management.

use in the United States in the period 1900−2010 are shown in Figure 4a. The most important finding is that results estimated using physical data and using monetary data share basically the same historical trends. However, some inconsistencies exist: (1) because of the impact of aluminum prices as discussed above, the increase in aluminum price may result in the underestimate of annual aluminum flows estimated using monetary data, thus making them lower than those estimated using physical data, and vice versa; (2) results estimated using monetary data were higher than those estimated using physical data in the period 1945−1967; this may be due to the fact that the input−output tables in the years 1963 and 1967 were only industry by industry instead of commodity by commodity; and (3) results estimated using monetary data after 2004 were lower than those using physical data. In addition to the sudden increase of aluminum price in this period, this difference may result from the fact that annual investment flows include both those in new automobiles and in second-hand automobiles. The latter can lead to the underestimate of aluminum flows because a secondhand automobile’s economic value can be much lower than that of a new one, even though they can contain the same amount of aluminum. Figure 4b compares in-use stocks of aluminum contained in automobiles as estimated by the four methods in this study. Several interesting features can be observed: (1) the historical evolutions of in-use aluminum stocks estimated using FBPD and FBMD methods share a very similar trend; (2) for the two methods using physical data, if it is assumed that the average aluminum content of stocks is the same as that of flows 7 years earlier (about half of the mean value of automobile lifespan), the results of flow-based method match very well with those of the stock-based method. However, if we assume that the average aluminum content of stocks is the same as that of flows 0 year earlier and 14 years earlier, the stock-based results are higher and lower respectively than the flow-based results. This result is reasonable because the average aluminum content has been increasing over time for automobiles manufactured in the United States and thus the average aluminum content of stocks should be lower than that of flows in the same year; (3) for the two methods using monetary data, the results of the stockbased method are always lower than those of the flow-based method; this is because the rate of economic depreciation of automobiles is much faster than the rate of their physical retirement as discussed above. Comparison and Future Applications of the Methods as Take-Home Messages. Exemplified by aluminum use in automobiles, this study demonstrates that in-use aluminum stock at the product level can be estimated using either physical or monetary data compiled independently by different institutions. The results estimated by different methods either match reasonably well with one another, or their inconsistencies can be well explained by differences in physical retirement versus economic depreciation patterns or by fluctuations in aluminum prices. The principal distinction between the four methods we propose in this study and the top-down method is that the four methods use and generate product-level information while the top-down method only uses and generates sector-level information (Table 1). Additionally, the four methods use and generate dynamic multiyear information while existing bottom-up studies only provide oneyear snapshot results (Table 1). A common advantage of the two flow-based methods is that they provide information on the F


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(17) Hatayama, H.; Yamada, H.; Daigo, I.; Matsuno, Y.; Adachi, Y. Dynamic substance flow analysis of aluminum and its alloying elements. Mater. Trans 2007, 2518−2524. (18) Liu, G.; Bangs, C. E.; Müller, D. B. Unearthing potentials for decarbonizing the U.S. aluminum cycle. Environ. Sci. Technol. 2011, 45 (22), 9515−9522. (19) Liu, G.; Müller, D. B. Centennial evolution of aluminum in-use stocks on our aluminized planet. Environ. Sci. Technol. 2013, 47, 4882− 4888. (20) McMillan, C.; Moore, M.; Keoleian, G.; Bulkley, J. Quantifying U.S. aluminum in-use stocks and their relationship with economic output. Ecol. Econ. 2010, 2606−2613. (21) Wang, J.-L.; Graedel, T. Aluminum in-use stocks in China: A bottom-up study. J. Mater. Cycles Waste Manage. 2010, 66−82. (22) Recalde, K.; Wang, J.; Graedel, T. Aluminium in-use stocks in the state of Connecticut. Resour., Conserv. Recycl. 2008, 1271−1282. (23) Cheah, L.; Heywood, J.; Kirchain, R. Aluminum stock and flows in US passenger vehicles and implications for energy use. J. Ind. Ecol. 2009, 718−734. (24) Modaresi, R.; Muller, D. B. The role of automobiles for the future of aluminum recycling. Environ. Sci. Technol. 2012, 46 (16), 8587−8594. (25) Chen, W.-Q.; Graedel, T. E. In-use product stocks link manufactured capital to natural capital. Proc. Natl. Acad. Sci. U.S.A. 2015, in press. (26) Nakamura, S.; Nakajima, K.; Kondo, Y.; Nagasaka, T. The waste input−output approach to materials flow analysisConcepts and application to base metals. J. Ind. Ecol. 2007, 11 (4), 50−63. (27) Nakamura, S.; Kondo, Y.; Matsubae, K.; Nakajima, K.; Nagasaka, T. UPIOM: A new tool of MFA and its application to the flow of iron and steel associated with car production. Environ. Sci. Technol. 2011, 45 (3), 1114−1120. (28) Kondo, Y.; Nakajima, K.; Matsubae, K.; Nakamura, S. The anatomy of capital stock: Input−output material flow analysis (MFA) of the material composition of physical stocks and its evolution over time. Rev. Metall. (Paris) 2012, 109 (5), 293−298. (29) Nakamura, S.; Nakajima, K. Waste input−output material flow analysis of metals in the Japanese economy. Mater. Trans 2005, 2550− 2553. (30) Nakamura, S.; Nakajima, K.; Yoshizawa, Y.; MatsubaeYokoyama, K.; Nagasaka, T. Analyzing polyvinyl chloride in Japan with the waste input−output material flow analysis model. J. Ind. Ecol. 2009, 13 (5), 706−717. (31) Ducker Worldwide. On aluminum content in north American light vehicles: Phase I, 2008. http://www.drivealuminum.org/researchresources/research (accessed Dec. 08, 2014). (32) The Aluminum Association. The history of aluminum in cars. http://www.aluminum.org/product-markets/automotive (accessed June 10, 2014). (33) U.S. Bureau of Economic Analysis. Input−output accounts data, 2014. http://www.bea.gov/industry/io_annual.htm (accessed June 10, 2014). (34) U.S. Bureau of Economic Analysis. Benchmark input−output data: Historical SIC data for 1977, 1972, 1967, 1963, 1958, and 1947, 2014. http://www.bea.gov/industry/io_histsic.htm (accessed June 10, 2014). (35) U.S. Bureau of Economic Analysis. Benchmark input−output data: 2002, 1997, 1992, 1987, and 1982, 2014. http://www.bea.gov/ industry/io_benchmark.htm (accessed May 30, 2014). (36) Rauch, J. Global mapping of Al, Cu, Fe, and Zn in-use stocks and in-ground resources. Proc. Natl. Acad. Sci. U.S.A. 2009, 18920− 18925. (37) Hattori, R.; Horie, S.; Hsu, F. C.; Elvidge, C. D.; Matsuno, Y. Estimation of in-use steel stock for civil engineering and building using nighttime light images. Resour., Conserv. Recycl. 2014, 83, 229−233. (38) Takahashi, K. I.; Terakado, R.; Nakamura, J.; Adachi, Y.; Elvidge, C. D.; Matsuno, Y. In-use stock analysis using satellite nighttime light observation data. Resour., Conserv. Recycl. 2010, 55 (2), 196−200.

ASSOCIATED CONTENT

S Supporting Information *

Details on methodology, data compilation, and complementary figures. This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*Tel.: +1 203 432 5475. Fax: +1 203 432 5556. E-mail: [email protected]; [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS We thank Kenichi Nakajima, Stefan Pauliuk, Marshall Jinlong Wang, and Ahmad Yusuf for providing relevant data, literature, or both and thank the editor and the anonymous reviewers for helpful comments.

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