## 1. Introduction

Both waste management policies and the economic theories underlying them model the behaviour of a representative company or establishment using. For example, toxic wastes such as dioxin are regulated by the mean emission volume standard measured per Nm^{3}, where the mean is estimated using data. As we will show, most establishments (particularly combustion plants) satisfy the required emission standard, while only a few exceed the regulation limit and must be checked by the authorities until regulation standards are met. But regulators must monitor all establishments incurring unnecessary costs.

Fullerton and Kinnaman 1995, among other theoretical contributions, show that taxing downstream establishments can achieve the second best policy. (See also Walls & Palmer 1998, who discuss more general market conditions.) Recent research shows that regulating downstream establishments promotes research and development by firms in upstream stages of a supply chain under certain market conditions (Calcott & Walls, 2000; Greaker & Rosendahl, 2008). These theoretical implications are important for policy making about how to design a tax system, but these theories also assume a typical producer and the regulation standard with respect to their mean emissions of waste materials. In practice, however, even though the coefficients of variation for the distributions of heavy metals in fly ash found in municipal solid waste are known to reach 50% (Nakamura et al., 1996), little statistical evidence in the published literature exists on the variation in industrial establishments’ waste generation and reuse-recycling per unit production, which is basic information required for economic and ecological design and general policy decisions.

In this paper we fill this gap in the literature and show the distributions of generation rates for various types of wastes and by-products in the production processes of establishments in Japanese manufacturing industries. We use the METI survey data (Survey on the Industrial Waste and By-Products, Japanese Ministry of Economy, Trade and Industry, 2005 and 2006). This survey gives the amounts of 37 types of industrial wastes generated for four different levels of the production processes (generation, intermediate reduction, reuse-recycle, and disposal to landfill) at 5048 establishments.[1] -

We have linked the METI survey data with the Japanese Input-Output (I-O) table. Using this linked data and the data on energy/CO_{2} requirements in industrial waste treatment, we are able to calculate the induced amounts of industrial wastes.[2] -
For example, waste oil and waste plastic are generated in large quantities at 3080 and 3694 establishments, respectively. Estimated amounts of waste oil and waste plastic generated range, respectively, between 0 and 2.50 and between 0 and 2.11 (metric) tonnes per million yen of output. On the other hand, waste ferroalloy slag is produced at only 11 establishments, and its quantity ranges from 5.8 to 64.6 tonnes per million yen of output. We estimate that production of every car with a 2000cc engine or its equivalent induces, for example, 0.051 tonnes of all types of wastes combined in hot rolling processes and 0.677 tonnes of all types of wastes combined in iron steel making in upstream production activities. We estimate that a 2000cc equivalent automobile production generates 1.49 tonnes of all types of wastes combined. We believe that these averages and the distributions for waste generation rates along a production supply chain provide (currently unused) useful information for policy makers for further reductions in the generation of waste materials.

## 2. Using the input-output analysis for evaluating waste management policies

### 2.1. Economic input-output-LCA: the theoretical background

The input-output analysis is a powerful tool to evaluate environmental impacts within an interdependent economic system (Leontief 1970, Baumol and Wolff 1994). When production of a final product requires intermediate goods (e.g. parts), inter-industry effects along a supply chain generate various wastes in stages of the life cycle of the final product.

The input-output (I-O) table is like a recipe of all economic activities for a national economy. Each column describes all the inputs used for an immediate economic activity, such as producing an automobile, supplying services such as education. It covers all economic activities and I-O relations are described in monetary terms. Recently publicly available I-O tables have been applied to the Economic Input-Output Life Cycle Assessment (EIO-LCA) (Hendrickson et al., 2006; Suh, 2010). Eiolca.net summarizes limitations of EIO-LCA compared to Process-Based LCA.

One such limitation that EIO-LCA is difficult to apply to an open economy is overcome by using the methods given by us (Hayami & Nakamura, 2007). The most apparent disadvantage of EIO-LCA is that product assessments contain aggregate data containing uncertainty as Eiolca.net describes. Assume there are n commodities (including services) in an economy, each of which is an input for production of other commodities. A typical producer *k* produces output x_{j}^{(k)} of *j*-th commodity, which requires as inputs *X*_{ij}^{(k)}, where *i=1,2,...,n*. Governments provide the official I-O table with aggregate figures for all producers of *j*-th commodity *x*_{j}*=∑*_{k=1}^{mj}*x*_{i}^{(k)}, where *m*_{j} is the number of producers of the *j*-th commodity. The same aggregation procedure is applied to inputs as follows: *X*_{ij}*=∑*_{k=1}^{mj}
*X*_{ij}^{(k)}. EIO-LCA assumes that matrix of input coefficients *A*_{ij} defined below is stable and represents a typical producer’s activity.

But these input coefficients *A*_{ij} are different from producer *k*’s input coefficients *A*_{ij}

Similarly, by applying EIO-LCA to waste management with the same assumptions made above, we get the amount of waste *i* generated in producing output *x*_{j} (we consider 37 waste materials as defined below):

Similarly, producer (*k)* generates *i*-th waste producing the *j*-th product:

Japan Ministry of Economy, Trade and Industry (METI) conducts an annual survey that reports the amounts of 37 types of wastes observed in 4 stages: amounts generated by final production, *W*_{ij}^{(k)}; amounts of reduction in intermediate steps of production, *V*_{ij}^{(k)}; amounts recycled, *U*_{ij}^{(k)}; and amounts sent for landfill, *T*_{ij}^{(k)}*.*[3] -
The most important assumption in our I-O analysis is that input coefficients and waste coefficient per output remain constant over time. If we can show empirically that these coefficients have narrow bell shape distributions, then the relative stability of these coefficients follows. In this paper, we will show using our data how the coefficients of waste generation W_{ij}^{(k)} distribute.

Using input coefficients, A_{ij}, we can calculate the demand for goods made in stages of upstream sectors of a supply chain. Unit production of j-th sector output induces production of i-th sector whose output is given by A_{ij}. Similarly production of A_{ij} induces production of A_{ki} A_{ij} in k-th sector. Repeating this, we can obtain output induced for any stage in upstream portions of a supply chain. Formally, multiplication of the I-O coefficients matrix A from left gives us induced output for all relevant goods and services in the immediate upstream stage of a supply chain.

where

By multiplying production output for final production (downstream) stage and subsequent upstream stages (f, Af,...) by waste generation matrix W, we obtain the amounts of waste generated in the corresponding stages of a supply chain: Wf, WAf, WA^{2}f,....

### 2.2. Construction of a linked data set

We briefly describe the procedure we used to link the Wastes and By-products Survey (WBS) data to the I-O table. We first note that the definition of a sector is different between the two data sets. WBS is based on the Japan Standard Industry Classification (JSIC) system, but the I-O table uses its own more detailed classification system so that the stability of I-O coefficients over time is preserved. JSIC codes are divided into one or more of 401 I-O sectors, using the allocation matrix given in the appendix tables of the I-O table. This allocation method depends on the sales figures reported for different products of each establishment in WBS. One difficulty we encountered was for the steel industry sector. The steel industry in the I-O table is divided into 13 sectors and two related sectors (coal products and self power generation). Many of these I-O sectors belong to a single establishment in WBS because of their continuous casting production, and there are no sales figures reported on WBS for transactions for these I-O sector goods since these transactions occur within the same establishment. To properly allocate output of steel industry establishments in WBS among relevant I-O sectors, we have collected needed information by interviewing the Japan Iron and Steel Federation and the Nippon Slag Association. We then modified the allocation table to reflect our information.

Secondly, in order to obtain the total amounts of industrial wastes in Japan, we multiplied the amounts derived from WBS by the proportionality constant since WBS is a survey and does not cover all Japanese establishments. The proportionality constant for each sector was obtained by comparing sales figures for the sector from the Census of Manufacturers data and WBS. Sectors of these two data sets are comparable since both use the JSIC system to define their sectors.

Table 1 lists 37 types of industrial wastes discussed in this paper. Industrial wastes in Japan are classified into (1) 37 types given in Table 1 and (2) especially regulated industrial wastes. Special industrial wastes in the latter category (2) are highly hazardous and include material contaminated with PCB, asbestos, strong acid with pH less than 2, strong alkali with pH higher than 12.5, highly inflammable waste oil and infectious wastes. WBS excludes wastes in category (2) that need to be treated separately. Industrial wastes other than those in category (2) include certain toxic substances (e.g. heavy metals, Pb, Cd) that must be treated properly.

For each establishment and each type of waste, the following material balance equation must hold:

All wastes are measured by weight in metric tonnes, and output x_{j}^{(k)} is measured in monetary unit (in 1 million yen).

## 3. The estimated results

### 3.1. Distributions of unit waste generation rates

The first objective of this paper is to estimate the statistical distributions of waste generation rates among establishments.

Table 2 presents descriptive statistics for these waste generation rates, W_{ij}^{(k)}/x_{j}^{(k)}, for waste of type i for establishment k in sector j. The number of observations (Nobs) denotes the number of establishment with non-zero production, x_{j}^{(k)}>0. Waste plastics other than synthetic rubber have the largest number of observations, which means waste plastics are the most common industrial waste. For all industrial wastes except waste animal-solidified, the sample mean is larger than the median, and the maximum value is far larger than the sample mean. This means that the distributions of unit waste generation rates W/x are asymmetric to left, with a few smaller values occur with very high frequencies and a long tail for large values.

Several typical shapes of statistical distributions are shown in Figures 1a and 1b. Figure 1a shows the distributions for waste moulding sands and iron and steel slag. Iron and steel slag does not have a large distance between the mean and the median, but it has a large maximum, 22.22 tonnes per 1 million yen, which is 12 times as large as the mean, 1.859 tonnes per 1 million yen. Standard deviation (SD) is larger than the mean, and the coefficient of variation is 1.44. Figure 1b shows two of common types of distributions for W/x for wastepaper and waste plastics, which concentrate around 0. Both have the median of 0.005 tonnes per 1 million yen of production. But the mean is 0.069 tonnes for wastepaper and 0.027 for waste plastics, with a maximum, 2.631 for wastepaper, and 2.114 for waste plastics. Extremely large maximum values may reflect irregular production and inventory practices at some establishments.

Figure 2 shows that the distributions for recycling rates for inorganic sludge and polishing sand. Both figures have concentrations around 0 and 1. This means that establishments face an all or nothing choice. Once a waste material is recycled, the establishment should choose recycling all wastes. This result follows because of the high initial cost of recycling equipment and the availability of outsourcing. But outsourcing is not available if the establishment location is far from the center of the recycling industry. As a result, the final disposal method (landfill here) is also highly concentrated around 0 and 1, as in Figure 3.

We have tried statistical fitting of these empirical distributions derived here with only a partial success. First, we tried to use the Gamma distribution to fit observed distributions for unit generation rate, W/x. But only 7 out of 37 distributions for industrial waste have been found not to be significantly different from the Gamma distribution. An appropriate theoretical distribution to fit the empirical distributions for recycling ratio, U/W, is the Beta distribution since recycling rations range between 0 and1. But our test of the goodness of fit rejected the Beta distribution for all cases.

Bootstrap resampling can calculate confidence intervals for the unit waste generation rate, W/x, from estimated empirical distributions. Table 3 shows simulated confidence intervals and the mean. The empirical distribution of W_{ij}^{(k)}/x_{j}^{(k)} used is based on observations from WBS 2005 and 2006. We used as re-sampling size 5000 for non-parametric estimation. The simulated mean uses weighs of output and our results correspond to unit waste generating rate W/x.[4] -
We find that six out of seven wastes show the same statistical characteristics: (1)the median is smaller than the mean; and (2)the distributions have a long tail. But iron-steel slag (193 observations) has a nearly symmetric distribution as shown in Figure 4a. According to the central limit theorem, the distribution of a sample mean with a finite variance converges to the normal distribution. But our statistical test of the goodness of fit does not support gamma or normal distributions. The convergence in distribution to the normal distribution is not seen for distributions of other wastes either as shown in Figure 4b. The distribution for a positive random variable becomes exponential at the maximum entropy; in the present case a statistical test rejects the exponential distribution also.

Results for the distributions of the recycling rate using the same procedure as before are given in Table 4 and Figures 5a and 5b. Compared to distributions for the waste generation rates, distributions for the recycling rates are nearly symmetric. And the figures are clearly different from those given in Figure 2 for population the distributions (histograms) of the waste generation rate. This difference arises because, in case of distributions for recycling rates, there is the effect of aggregation of recycling rates. The sample mean is almost the same value as the sample median in Table 4. We can conclude that, for the distributions for recycling rates, U/W, for all sectors, observed values are close to both the mean and median of the simulated value and their confidence intervals are symmetric.

These results on the distributions of unit waste generation rate W/x and recycling rate U/W imply that the potential problems in policy making from assuming the representative (average) waste management activity come mostly from the distributions for unit waste generation rates W/x. The mean assumed in theory does not always reflect the typical intensity of waste generation. It also means that regulations based on the mean of a representative establishment does not always give effective regulations to the majority of establishments. Most of the establishments can clear the regulation standard, because the standard is based on the mean of the distribution. But as we have shown, the mean does not capture the essential property of the distributions underlying the waste generation rate.

### 3.2. Upstream waste generation: Calculation from the input-output analysis

The second objective of this paper is to estimate the amounts of waste generated in various stages of production along a supply chain, starting from downstream production the final product to upstream production of supplies. We us the I-O table linked to the WBS data set explained in Section 2.1 above. Tables 5 and 6, respectively, describe the total amounts of wastes generated average production supply chains for cellular phones and passenger car production in Japan in 2000. In both cases, pig iron is the most significant contributor of industrial waste. This is because production of pig iron generates heavy wastes such as iron-steel slag. The second most significant contributor is electricity for cell phones and passenger car final assembly for passenger cars. The total amounts of wastes generated are about 410 thousand tonnes for cellular phones and over 9 million tonnes for passenger car production. The cellular phone assembly sector generates relatively small amounts of wastes but the passenger car assembly sector generates large amounts of wastes.

One of the most important wastes generated in producing pig iron is iron-steel slag, whose unit generation rate distributes in a rather narrow range, has a symmetric distribution as shown in Figure 4a and its variance is smaller compared to other wastes generated in any other sectors. Unit waste generation rate for iron and steel slag lies between 1.4132 and 2.7613 at a 95% level (Table 3).

Electricity sector also generates a significant amount of waste material, fly ash. The distribution for its unit waste generation rate is shown in Figure 6, with its 95% confidence interval (0.040, 0.110). Another waste, ferroalloy slag is generated by production supply chain stages for both cell phones and passenger cars. Its unit waste generation rate has a rather irregular distribution as shown in Figure 6, with its 95% confidence interval being very wide and given by (2.47, 34.96). This suggests that waste management policies based on point estimates for the unit waste generation rate for ferroalloy waste may lead to quite erroneous implications in practice.

We have shown that unit waste generation rates for various wastes generated by production supply chains distribute in different manners, sometimes with large variances and asymmetric ways. This means serious limitations about the accuracy of policy decision making relying on point estimates for the waste generation by production supply chains as we do in EIO-LCA and other types of life cycle analyses.

Given this limitation in mind, we may still be able to use information on waste generation in upstream production stages. Table 7 shows the total amounts of all wastes combined and amounts of CO_{2} emissions in the final (direct) assembly stage, a few upstream stages and all stages combined of the average production supply chain for passenger cars with 2000cc engines. Table 6 gives information about the stages which generate more waste than others. Generally waste materials tend to be generated evenly along stages of a supply chain while CO_{2} emissions tend to be generated more unevenly and fluctuate widely along stages of a supply chain. From policy perspectives, we conclude that application of production process LCA is more difficult for CO_{2} emissions than for generation of the 37 waste materials.

## 4. Conclusion

Using the datasets that recently became available, we have obtained empirical distributions for generation, recycling and landfill rates for the 37 types of waste materials that are generated in the production processes of Japanese manufacturing establishments. Some of the statistics reported are for the total amounts of all the wastes combined to save space. Many empirical distributions obtained are not symmetric and have a long tail with the mean much larger than the median, making it inappropriate for policy decision making based on the mean generation rates. For example, if the regulation level is set at the industry mean, it is likely that most establishments satisfy the regulation level without efforts while a few large violators exceed the level by a big margin. In such a case it is more cost effective to set the regulation standard at a level much higher than the mean, thus saving the monitoring costs at most establishments while spending efforts to identify the few violators.

In the second part of the paper we have shown how to estimate the amounts of wastes generated along stages of the average production supply chain and then given estimates for production processes of cellular phones and passenger cars. We have repeated this for emissions of carbon dioxide. In this supply chain analysis, we have shown that, given the large amounts of wastes generated in stages of upstream production supply chains, it is misleading to formulate waste management policies based only on the wastes generated in the final demand stages of supply chains. Our estimation results suggest that, in setting waste management policies, policy makers need to consider (1)not only the wastes generated from the final assembly stage but also the wastes generated from upstream stages of production supply chains and (2)such policies need to have different regulation standards for upstream stages depending on the final sector product and also the waste being considered to be regulated. For example, we have found that the amounts of CO_{2} emissions vary significantly from one stage to another of the Japanese production supply chain for passenger cars.

## 5. Endnotes

An earlier version of this paper was presented at the 18^{th} International Input-Output Association Conference held at the University of Sydney in Australia, June 20-25, 2010. Preparation of the datasets used was done using Programming Language Pyhon 2.7 and statistical analyses were done using R 2.12.1. Further details are available by e-mailing: hayami@sanken.keio.ac.jp.