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An analysis of private and social gains from plastics recycling
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An analysis of private and social gains from plastics recycling
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AN ANALYSIS OF PRIVATE AND SOCIAL GAINS FROM PLASTICS RECYCLING by Scott Raymond Atkinson A Thesis Presented to the FACULTY OF THE GRADUATE SCHOOL UNIVERSITY OF SOUTHERN CALIFORNIA In Partial Fulfillment of the Requirements for the Degree MASTER OF ARTS (Economics) December 1994 1994 Scott Raymond Atkinson UNIVERSITY O F SO U TH ER N CALIFORNIA THE GRADUATE SCHOOL UNIVERSITY PARK LOS ANGELES. CALIFORNIA 9 0 0 0 7 This thesis, written by Scott Raymond Atkinson under the direction of h..XS....Thesis Committee, and approved by all its members, has been pre sented to and accepted by the Dean of The Graduate School, in partial fulfillment of the requirements for the degree of _Master_of_Arts_____________________ Dean Vigtp December 19, _ 1994 Chairman CONTENTS LIST OF TABLES AND F IG U R E ........................................................iii LIST OF A B B R E V IA T IO N S...................................................................iv 1. IN TR O D U C TIO N ....................................................................................... 1 2. IDENTIFICATION OF P R O B L E M ................................................ 5 3. PLASTICS AND WASTE M A N A G E M E N T ................................9 3.1 La n d f il l in g ............................................................................................11 3.2 SO U R C E R E D U C T I O N .............................................................................. 12 3.3 RECYCLING.................................................................................................14 4. RECYCLED PLASTICS .....................................................................17 4.1 Economies of s c a l e........................................................................... 18 5. VIRGIN PLASTICS ..............................................................................21 5.1 Analytic A p p r o a c h...........................................................................23 5.1.1 The M odel..................................................................................29 5.1.2 D ata.............................................................................................. 34 5.1.3 Separability...............................................................................39 5.2 ESTIMATION.............................................................................................. 41 5.2.1 Collinearity...............................................................................43 5.2.2 Autocorrelation........................................................................44 5.3 Results of estim atio n.................................................................... 48 5.3.1 Model Selection ...................................................................... 50 5.3.2 Regularity Conditions...........................................................54 5.4 D e r i v e d D e m a n d a n d G a i n f r o m R e c y c l i n g ....................56 6. C O NC LUSIO N..........................................................................................59 REFERENCES 62 LIST OF TABLES AND FIGURE Table Page 1. Observations and OLS Estimates of Average Total Cost in Plastics Recycling................................... 19 2. ISUR Estimates for the U.S. Virgin Plastics Industry 1958-1991 ............................................................. 49 3. AUES and Demand Elasticity Estimates for the U.S. Virgin Plastics Industry 1958-1991 .................... 56 Figure — The Inverse Demand for Aggregate Energy Input in the Virgin Plastics Industry..................... 25 iii LIST OF ABBREVIATIONS AC Average Cost AR( 1) Autoregressive of the First Order AUES Allen-Uzawa Elasticities of Substitution CPRR Center for Plastics Recycling Research CRTS Constant Returns to Scale EPA United States Environmental Protection Agency ESS Sum of Squared Errors GJ Gigajoules HC Hydrocarbons HDPE High Density Polyethylene ISUR Iterative Seemingly Unrelated Regression LDPE Low Density Polyethylene LPG Liquid Petroleum Gas MJ Megajoules MRF Material Recovery Facility MSW Municipal Solid Waste NGL Natural Gas Liquids NTC No Technical Change OECD Organization for Economic Cooperation and Development OLS Ordinary Least Squares PCR Post-Consumer Recyclate PET Polyethylene Terephthalate PP Polypropylene PS Polystyrene PVC Polyvinyl Chloride SIC Standard Industrial Classification SOC Synthetic Organic Chemical SPI Society of the Plastics Industry SUR Seemingly Unrelated Regression 1. INTRODUCTION Public interest in recycling of post-consumer waste has been accelerating in recent years and much has been written on the subject. The recycling literature focuses on such aspects of recycling as collection, sortation, reclamation technologies, and household participation.1 However, these studies typically are concerned with the supply of recycled material rather than the demand for recycled material. Additionally, only a few of the household participation studies have been examined with empirical analyses. It was the objective of two notable studies, Nestor (1992) and Westenbarger, Boyd and Jung (1991), to model the production of virgin material, with recycled material used as input, and obtain information from the elasticity estimates. While neither of these studies yields information on recycled 1 See sec. 6 for some examples o f these topics. I plastics, they nevertheless provide novel approaches to the demand-side analysis of recycling. Nestor (1992) examines the market for old newspapers and the effectiveness of existing supply-side public policies of recycling. The demand for old newspapers as an input in the production of newspapers is empirically derived. Nestor finds that this demand is highly price-inelastic and that the policies which encourage collection to boost supply are ineffective in stimulating an increased use of old newspapers in the production of newspapers. Also, it is found that the most effective policies for increasing the demand for old newsprint may be those which stimulate the overall production of newspapers. Westenbarger, Boyd and Jung (1991) also model the use of recycled material as input in the production of virgin material. The estimates are used to calculate the gains available to producers and society from increased recycling of aluminum.2 2 See see. 5.1 for further discussion o f Westenbarger, Boyd and Jung (1991). 2 Similar to Westenbarger, Boyd and Jung (1991), it is the objective of this analysis to quantify certain private and social gains which can be achieved from the recycling of one portion of the waste stream, plastics. By increasing the use of post consumer plastics as material input in the production of virgin plastics, both virgin energy and material input (Aggregate energy input) can be decreased, thereby achieving gains to industry and society.3 In order to determine these gains, the structure of cost in the virgin plastics industry is modeled and the demand for aggregate energy input is derived. The gains are calculated from the shift in demand for the aggregate energy input. Until now, no empirical study has been undertaken which focuses on the recycling of plastics, primarily because plastics recycling is so new. In addition to the virgin industry analysis, an examination of engineering estimates of costs in recycled plastics production 3 In the virgin plastics industry the material input is primarily oil and natural gas derived feedstocks, o t energy. Therefore, the “Aggregate energy input” is comprised of 3 indicates that there may be room for increased scale in plastics recycling. The increased scale of operation and lower average cost would lead to more competitively priced recycled plastics. both energy and material inputs, of which the material input is predominant. See sec. 5.1.3 for discussion of the aggregation of these two inputs. 2. IDENTIFICATION OF PROBLEM It has been estimated by the United States Environmental Protection Agency (1990, 79) that the U.S. generated 163 million metric tons of Municipal Solid Waste (MSW) in 1988, with an average growth rate of about 1.6 percent annually per capita since I960.4 Of that amount approximately 13 percent was recycled, 14 percent was incinerated and 73 percent, or 256 million cubic meters, was discarded to landfills. As of 1988, plastics comprised 9.2 percent by weight and 19.9 percent by volume of all landfilled MSW, while only 0.85 percent by weight and 1.88 percent by volume of all recycled MSW was plastic. The average percentage increase of plastics’ share in landfilled MSW is 14.9 percent annually since 1960, far greater than any other component of MSW. '"incidentally, the U.S. is by far the world’s leading producer of waste, both in total and per capita (World Resources Institute 1992, 50-52). 5 This growth in the waste stream is occurring simultaneously with a decline in available landfill space in non-rural areas. Operating landfills declined from 30,000 in 1976 to about 6,000 in 1987 (Curlee, Das, and EPA 1991, 151-154). Of those, the EPA estimates that only 3,300 were running in 1991 (World Wildlife Fund 1991, 5). While increasingly stringent environmental regulation is part of the reason for the decline (Curlee, Das, and EPA 1991, 151), public opposition to landfills due to their real and perceived toxicity undoubtedly plays a role as well. Whether or not such regulation and opposition is warranted, the decline in landfill space will at the very least lead to increased transportation costs for landfilling at greater distances from populated areas, and at most lead to nearly no landfilling at all as it becomes too costly a MSW management option. As an example, the national average private cost of landfill disposal increased 51.6 percent in one year from 1986 to 1987 to $22.44 per ton (Curlee, Das and EPA 1991, 423). 6 A market failure occurs when the manufactured items that comprise MSW do not include their marginal social cost of disposal. When the cost of disposal is not a component of the price of virgin material, a bias favoring landfilling exists which leads to less recycling and an excessive amount of landfilled MSW.5 In addition to the costs of disposal, there are costs specific to the production of virgin plastics. It can be said with some confidence that the negative environmental externalities from the natural gas and petroleum derivatives used in the manufacture of virgin plastic are much greater than those of recycled scrap production.6 There are social costs in the extraction, refinement and transportation of these energy resources which do not exist in the production of recycled material. 5 Germany has taken steps to correct for this situation with their Dualcs system in which producers and retailers are required to take back the packaging they create or participate in the Duales recycling program (see Shea 1992). 6 The recyclable portion of post-consumer waste shall herein be referred to as “scrap”, while recycled scrap will be called “post-consumer recyclate” (PCR). 7 Other biases favoring the production of plastics with virgin material exist. A favorable tax treatment, the depletion allowance, is given to industries involved in the extraction of depletable resources (Tietenberg 1992, 210-213). The depletion allowance in effect provides a tax subsidy which lowers the after tax cost of resource extraction and hence lowers the cost of virgin plastics. Two attempts to quantify this subsidy to virgin material are known to have been made: $3.5 billion in 1972 (Tietenberg 1992, 212), and $3.3 1/ton (Stone, Sagar and Ashford 1992, 54). These biases against scrap create a distinct disadvantage for the use of scrap material in the production of plastics and inhibit the use of recycled material. Although measures could be taken to correct the biases directly (e.g. through tax subsidies), the gains identified in this paper provide some justification for the use of recycled material by offsetting some of the social costs associated with the use of virgin material. 8 3. PLASTICS AND WASTE MANAGEM ENT “Plastic” is a broad term used to define many different types of petroleum-based synthetic materials called resins consisting of hydrocarbons (HC) and synthetic organic chemicals (SOC). Plastics are classified as thermosets or thermoplastics. Thermosets form a group of resins which form molecular bonds which when broken, cannot be reformed, making them less recyclable. Thermoplastics on the other hand can be melted and reformed and are the most widely used, comprising 85 percent of all plastics produced in 1987 (U.S. International Trade Commission 1992, 8-3). Thermoplastics have been further subdivided into seven categories of resin by the Society of the Plastics Industry (see Powell 1990, 40-41). These resins, referred to as commodity thermoplastics for their use in packaging and other non-durables, are: Polyethylene terephthalate (PET), High-density polyethylene (HDPE), Polyvinyl chloride (PVC), Low-density 9 polyethylene (LDPE), Polypropylene (PP), Polystyrene (PS), and “other.” Together the first six comprise 79.5 percent of all thermoplastics produced in 1987, and 67.5 percent of all plastic produced in 1987 (U.S. International Trade Commission 1992, 8- 2, 3). There are two sources of plastic waste: (1) that which occurs during the manufacturing of plastics, and (2) from post consumer use of plastic items, or scrap. The manufacturing sector only contributes about 4 percent or less of the total plastic waste stream (Curlee and Das 1991b, 349-350). The remaining 96 percent of disposed plastics is post-consumer scrap, the majority of which is comprised of the six commodity resins defined above. The options that exist for the management of MSW may be classified into three general categories: landfilling, source reduction and recycling. As will be explained below, all three methods must be utilized together for an efficient societal outcome. 10 3.1 Landfilling Landfilling is the primary way waste has traditionally been handled and as noted above, landfilling is becoming increasingly costly with plastics constituting an increasing percentage of MSW. The environmental consequences of landfilling plastics are not fully understood. Questions arise as to the degradability of plastics, what they degrade into, and how they interact with other MSW. Although landfills tend to preserve and mummify MSW rather than break it down, some anaerobic degradation does occur. This degradation results in leachate, which is what may escape into the air and ground and surface water from landfills. Plastics are not thought to contribute to air leachate but may contribute significantly to ground and surface water contamination from toxins such as: lead, cadmium, phthalate esters and antimony oxide, which are used as additives in plastics (Curlee, Das and EPA 1991, 158-175). Biodegradability of plastics has been widely touted in the literature as the answer to solid waste problems. Indeed this 1 1 approach may significantly reduce litter pollution. However, no significant degradation of biodegradable plastics occurs in the airless landfill environment. William Rathje, the noted (and possibly only) landfill archaeologist, finds upon excavation, “...a mound of guacamole discarded in 1977, hot dogs from 1972, leaves from 1964, lumber from 1956, and stacks and stacks of newspapers [dating back to 1952]...(U.S. Congress 1989, 64- 68).” It is possible that we have seen the upper limit of the landfilling rate, since it appears that the marginal social cost of landfilling has been increasing in recent years, which makes landfilling increasingly costly as we tend toward a 100 percent landfilling rate. Each of the other MSW management options of source reduction and recycling has its upper limits as well. 3.2 Source Reduction An important component of MSW management is source reduction. Although not strictly a method of managing waste, it nevertheless may reduce the quantity of waste generated. 12 If the quantity of material in the goods which find their way into MSW can be reduced before use and disposal, the social costs of both production and disposal could be decreased. There would then be less need for both landfilling and recycling as the quantity of MSW is reduced. The effectiveness of source reduction as a MSW management option is directly dependent upon the quantity of materials which need not be produced, and therefore disposed of as MSW. The decision as to which materials need not be utilized is highly subjective. For example, when materials are used as excess packaging for marketing a product, what amount of those materials is really necessary for selling the product? The profit maximizing firm simply does not typically seek to minimize MSW since disposal cost is not directly realized by the firm, and therefore will tend to overproduce packaging materials. While the potential effectiveness of source reduction could be substantial, all MSW would still not be eliminated with this approach alone. Therefore source reduction cannot negate landfilling and recycling as important MSW management options. 13 3.3 Recycling Recycling is a broad term which has been used to describe both general processes and end uses simultaneously. Four categories have been defined: Primary, Secondary, Tertiary, and Quaternary (Leidner 1981, 64-65). Primary recycling refers to scrap that can be utilized in the production of a good identical in quality to that of the scrap’s original use. Both Primary and Secondary are processed by cleaning the scrap and reforming it into PCR flake or pellets. This option is possible mainly for post-industrial plastic waste which is clean, pure scrap created during the manufacturing stage and is only recently feasible for post-consumer waste - t plastic. This is due to the difficulty in obtaining uncontam inated post-consumer scrap, while the purity of scrap produced during manufacturing is assured. Secondary recycling is the utilization of scrap as an inferior input in the production of a good. The inferior input has lower 7 For example, Coca-Cola began using PCR in some of its PET soda bottles which was a first for food contact PCR use (Keische 1991, 12); also see Leaversuch (1993). 14 purity standards than the original material. This type of recycling for plastics yields materials which compete with other raw materials such as wood, metal, and concrete, but not typically with virgin plastic.8 Tertiary recycling refers to the breaking down of scrap plastic into its various elements, or monomers, for use as basic chemicals or fuels. These fuels are sometimes then used in the quaternary process. This approach is technically appealing, but is not cost competitive with other methods of waste management (Curlee and Das 1991, 345). Quaternary recycling is the incineration of waste with recovery of heat energy.9 As with landfilling, significant public opposition is probably the key reason this option has not been utilized to a greater extent. Of chief concern are the gaseous s Some examples of products produced with Secondary recycled plastic (some currently only in Europe and Japan) include: fence posts, boat piers, curb stops, pipe, signs, furniture, lumber, pallets, retaining walls, park benches, picnic tables, road construction, flooring, storage bins, flower/tree/sand boxes, and even lobster traps (Bennett 1991, passim). 9 The incineration of waste without recovery of energy has been utilized increasingly rarely; it is not a form of recycling and therefore not further discussed. 15 emissions produced by the incinerators and the non-combustible residual which is typically landfilled and potentially hazardous as a contributor to leachate. Proponents of incineration argue that current “burner” technology is very clean in that the gaseous emissions are captured with electrostatic precipitators, scrubbers and filters. The environmental impact and thus social cost from quaternary remains controversial. As with landfilling and source reduction, recycling cannot alone be used to manage all MSW. Since not all MSW can be recycled and therefore avoid the landfill, a 100 percent rate of recycling is theoretically impossible. The optimal level for society of recycling versus landfilling is where the marginal social cost of landfilling a unit of garbage is equal to the marginal social cost of recycling a unit of garbage. With 100 percent recycling, the marginal social cost of landfilling would be zero, while the marginal social cost of recycling would not. 16 4. RECYCLED PLASTICS The technological processes involved in Primary and Secondary plastics recycling are numerous and developing. Since plastics recycling is a nascent industry, there are undoubtedly increasing returns to technical progress available in the production of PCR. An increase in demand for PCR should stimulate the development of promising technologies which are currently slow to move through the research stage. This increase in demand is crucial to the development of a market for recyclables. Many of the technologies currently in use are similar, with minor variations. The Center for Plastics Recycling Research (CPRR) has been studying the most efficient combination of process stages and operating parameters for a PET/HDPE bottle recycling pilot plant (Alex 1988; Dittman 1989; and Phillips and Alex 1990). This Primary and Secondary process involves the unbaling of the presorted, baled combination PET/HDPE bottles 17 from Material Recovery Facilities (MRFs) which are then ground, washed, hydrocyclonically separated and dried. The PET and aluminum bottle caps are further separated electrostatically, and then each resin is extruded and pelletized into PCR. The PCR is then sold to fabricators of plastics products. These CPRR data are used for all plastics recycling calculations throughout this paper. 4.1 Economies of Scale A significant opportunity may exist for increasing the competitiveness of PCR with other materials. By lowering the average total cost (AC) to produce PCR, it may be priced more competitively with substitute materials. By simply increasing output, a firm operating at increasing returns to scale can decrease AC. AC in plastics recycling is calculated from data on input cost at three levels of output: 5, 10, and 20 million pounds. The data are detailed engineering estimates from Alex (1988), Dittman (1989), and Phillips and Alex (1990). The modeling of 18 AC in plastics recycling technology is accomplished by simply fitting a rectangular hyperbolic (reciprocal) curve through the AC data points with ordinary least squares (OLS). Table 1 lists: the output observations, corresponding AC, adjusted R2, the parameter coefficients, t-statistics, and the functional form. The variables cb, y, and rj represent both of the parameter estimates and millions of pounds of PCR output, respectively. Table 1.—Observations and OLS Estimates of Average Total Cost in Plastics Recycling n AC 1 R 2 A a) A r Model 5 0.34 10 0.27 0.9974 0.19834 700,094.94 AC = S+y(l/rjf) 20 0.24 (56.577)** (27.490)* Note: values in parentheses are the corresponding t-statistics. AC is in $ per pound. * Significant at the 5 percent level. ** Significant at the 2 percent level. Based on this approach, it is found that increasing returns to scale appear to exist in plastics recycling throughout the domain 19 of the data. Although admittedly unreliable, the slope of the AC curve becomes relatively flat at over 100 million pounds of output, which is well outside the domain of the sample. Only two of 44 leading plastics recyclers identified by Tito (1991, 59) and Bennett (1991, passim) using this kind of technology (Martin Color-Fi and Wellman) were known to produce at the 100 million pounds per year level in 1990, all the others produced far less. At the very least, it can be said that 20 million pounds of output is likely not the minimum optimal scale of operation in plastics recycling using the CPRR technology. 20 5. V IR G IN P L A S T IC S Four main categories of inputs may be identified in the production of virgin plastics: capital, labor, energy, and feedstock. The feedstock input is a material input which consists mainly of various hydrocarbons (HC) and synthetic organic chemicals (SOC). The energy and feedstock inputs are intertwined in that some feedstocks are interchangeable with fuels used for heat and power in production. There are two sources from which the HC are derived: raw natural gas and crude oil. For the former source, dry natural gas is cooled and compressed into natural gas liquids (NGL) which consist primarily of ethane, propane and butane (U.S. Department of Commerce 1963-1987). The latter source of plastics feedstock, crude oil, is refined into three petroleum products: liquefied petroleum gas (LPG), gas oil and naphtha. The plastics industry converts these three petroleum products and the NGL into ethylene, propylene, butylene, 21 butadiene and others through a high temperature process known as “cracking.” The Organization for Economic Cooperation and Development (OECD) (1985, 28) estimates that the HC utilized by the U.S. plastics industry are about 30.35 percent derived from NGL, 16.29 percent from LPG, 28.75 percent from gas oil, and 24.6 percent from naphtha. The major SOC utilized are: styrene, vinyl chloride monomer, acrylonitrile, phenol, acrylates, toluene, xylene and benzene (U.S. Department of Commerce 1963-1987). These are largely derived from naphtha in the oil refining process which are then combined with the HC derivatives through a process called polymerization to produce various types of plastics. The materials comprising the greatest share of feedstock expenditure in order of importance are ethylene, styrene, vinyl chloride monomer and propylene. Combined, the above four account for one-half of all feedstock expenditures by the industry (U.S. Department of Commerce 1963-1987). 22 5.1 Analytic Approach The primary objective of this paper is to determine the potential benefit to the virgin plastics industry and to society by comparing the industry’s total energy usage (energy and feedstock inputs) with how much the industry would have used had a portion of operations been devoted to producing recycled rather than virgin plastic. In order to quantify this benefit, the cost structure of the virgin plastics industry is modeled and estimated. The quantity of aggregate energy input and corresponding own-price elasticity of demand are then calculated, and the resulting factor demand curve is derived. This approach in quantifying the gains from recycling is closely based on that of Westenbarger, Boyd and Jung (1991), wherein a translog cost function is employed to obtain the derived demand for electricity input in the aluminum industry. The gains are then calculated from the decreased electricity input demand which occurs from the increased recycling of aluminum. 23 It was felt however that the empirical portion of Westenbarger, Boyd and Jung was insufficiently rigorous in a few areas. One of the most serious problems is the severe lack of degrees of freedom in their models. This not only leads to unreliable estimates, but their hypothesis tests of autocorrelation and model selection have very little power. In addition, the use of the Durbin-Watson test statistic to check for the existence of autocorrelation may not be appropriate in multiple equation models (Judge et al. 1985, 493-496). Their use of the likelihood ratio test statistic as a model selection criterion is questionable since there is evidence that the statistic performs poorly in small samples (Judge et al. 1985, 475). Also, they attempt to measure economies of scale with the empirical estimates from time series data.1 0 Lastly, no check for the satisfaction of the concavity regularity condition is made.1 1 l0Sec sec. 5,1.1. 1 1 See sec. 5.3.2. 24 Appropriate methods to correct for these deficiencies are used throughout this analysis of the plastics industry. In the Figure, the inverse demand curve for aggregate energy input in the virgin plastics industry is initially given by DD. The industry is presumed to be in equilibrium at point a where the derived quantity demanded is q0 at price p0. The long-run supply of energy and feedstock to the virgin industry is P P o 0 Fig. The Inverse Demand for Aggregate Energy Input in the Virgin Plastics Industry. 25 represented by p0S and is assumed to be perfectly elastic at least over the relevant range qj to qo. The assumption of perfect supply elasticity is made because only 2.8 percent of U.S. total aggregate energy resources consumed were demanded by the U.S. virgin plastics industry in 1991.1 2 A decrease from q0 to qi yields a 0.027 percent decrease in U.S. total aggregate energy resources consumed. This small change in quantity demanded probably would not measurably affect the price of these energy resources. The virgin industry ostensibly could obtain post-consumer scrap plastic from MRFs and process it into PCR which would then be sold to fabricators to make products. This displaces both the energy used for power and the oil and natural gas feedstock which would have been utilized to produce an equivalent amount of virgin plastic. In order for PCR to replace any virgin plastic, and thus reduce energy and material demand, PCR must be produced 1 2 Calculations from U.S. Department of Energy (1992) and results o f sec. 5.4. 26 virtually at virgin quality levels. Since PCR can currently be produced only in limited amounts at virgin quality, the percentage of recycled output which is assumed to supplant virgin output is one percent, or 276,583 tons. The percentage of all virgin plastic produced in 1991 that was recycled is estimated at 1.1 percent (304,242 tons) by the EPA (1991, 11). However, only a portion of the amount actually recycled was returned to near virgin quality.1 3 A new quantity of aggregate energy qi is then demanded and the demand curve DD shifts inward along p0S to D'D' where a new equilibrium is reached at point b. The area qi6rarq0 represents resources the industry no longer must use and would thus be freed for alternative uses. The area abc is a gain realized by society by meeting price p0 rather than p as quantity demanded becomes qt. Point c represents the virgin industry’s willingness to have paid p at DD in order to achieve qi in the absence of recycling. The price and 13The one percent was certainly achievable at that time, considering the aforementioned biases against PCR in the market. 27 quantity combination at point c could have been achieved by an exogenous supply shock which would have decreased supply, shifting p0S upward. The potential benefit from recycling has been identified a priori based on input expenditure information for each industry. 1 4 Both technologies utilize approximately equal amounts of electricity per pound of output, 1.8763 megajoules (MJ) per kilogram (kg) for virgin, and 2.1905 MJ/kg for recycled. However, the virgin industry additionally uses fuels for heat and power at the equivalent of 9.5223 MJ/kg of output, and non-power feedstock input at the equivalent of 22.7574 MJ/kg. Thus it appears that a large benefit can be achieved from recycling a priori. The private gain to industry and the social gain identified above each partially mitigate the social costs of the production and disposal of plastics. M Calculations of virgin input from U.S. Department of Commerce (1958-9 la), of recycled input from Alex (1988), Dittman (1989), and Phillips and Alex (1990), and of output from Modern Plastics Inc. (1959-92), passim. Non-power feedstock usage is based on U.S. Department o f Energy (1991) survey responses o f firms in the virgin plastics industry for 1988. 28 5.1.1 The Model The transcendental logarithmic (translog) cost function, due to Christensen, Jorgenson and Lau (1971, 1973), is one of the most commonly used specifications in the neoclassical producer modeling literature. It is for this reason, and accordingly because its properties are well established, that the translog is used here. The translog cost function is defined as: 'u\npM p} /= i i= \ j= \ In#lny + £ t Inp , + % J3yy(\ny)2 + p y tt lny+ i 2 , i= l i= 1 where C is the total cost of production in the plastics industry, p is a vector of N input prices, y represents total output, and t is time, a proxy for technical change, where /=1,2,...,T. The J3s are unknown parameters to be estimated. Following Diewert (1974), the translog cost function largely satisfies various desirable conditions which are: consistency, flexibility, linearity, and parsimony. Consistency means that the (1) lnC(p,j>,/) s £o + Z A ln # + j0„lny + A *+2 29 cost function C(p,y,t) must be consistent with several regularity properties of cost functions. Two properties which are satisfied a priori are that C{p,y,t) is non-negative and continuous from below in y, C{p,y,i) must also be: (a) linearly homogenous in p, which is imposed, (b) non-decreasing in y and in p, and (c) concave in p. The conformity of (b) and (c) must be examined post-estimation. Flexibility means that cfp,^,*) should have enough parameters to provide a second order approximation to an arbitrary twice continuously differentiable function. Linearity of the unknown parameters in the cost function simply facilitates estimation. Finally, parsimony means that c(p,y,/) has the minimal number of parameters required to achieve flexibility (Diewert 1974). As stated in property (a), linear homogeneity of the cost function in p is imposed. This property will be satisfied with the following linear restrictions on the parameters: 30 v Jt, A # , ( 2 ) £ a = i , z X = o, = Z A r = o . 1 = 1 In addition to these restrictions, symmetry is also imposed by assuming p ij = pji. Differentiating equation (I) with respect to the Inp t and applying Shephard’s lemma (Shephard 1953) yields, where S( is the share of total cost contributed by the /th input, and < 7, is the quantity of the /th input demanded. The S-s must also sum to unity and this is maintained for all t observations. In order to derive the needed own-price elasticity of demand for the aggregate energy input, the Allen (1938) and Uzawa (1962) partial elasticities of substitution (AUES) need to be derived first. Uzawa (1962) illustrates that the AUES can be obtained directly from the cost function via, m d lnC dC PL = q i P L K ) s used to test H0: p n = - 0 (no autocorrelation). Since lm = 6.4909 > ^(O.OS) = 5.9915 , we reject ff0 and conclude that autocorrelation is significant. Also, stationarity appears to hold since logarithmic values for the data are used and the autocorrelation values arc less than 1 in absolute value. 45 r i r f oji for t = s where E\ult\ = 0 , E\ul(u} 0 otherwise The complete post-transformation covariance matrix is £[uu'] = S® /r , while the covariance matrix for the pre transformation residuals e is is[ee']=Q. It is necessary to assume that R be diagonal due to the finite sample. After transforming the data, several degrees of freedom would be lost since additional parameters would be created with R non-diagonal.25 A A Like R , the covariance matrix 2 is also an estimate. The ISUR estimator and covariance estimates for b are given by (13) p = [ ^ ( ^ 1® /r)^]“1 X'(2-1® /r)y , oij = T~'(yi ~ Jf/ft) (y, - ^;Py) , for i,j= 1 ,2 where the first iteration is performed with OLS, which yields b. The parameter and covariance OLS estimates are then used in a 2SThis finding is supported by Doran and Griffiths (1983, 189). 46 second iteration made with ISUR to form new estimates. The iterations are continued until convergence is achieved. A In order to find R, ISUR is applied and the residuals (14) e, = y, — Xfjij , i = 1,2 are obtained. From these residuals, p n and p2 % are derived via (15) A = S f . 24 « .,- i/ S L ^ - 1 • '=1.2. A A Then R is used to form a transformation matrix P which transforms the complete autocorrelated covariance matrix Q and A A A satisfies POP' = 2 ® / and is defined as (16) P = dtt 0 0 • o' “ A _ A "Pit 1 0 • • 0 P i 1 A 0 A , where P u = 0 A -Pa 1 • • 0 A , and = 0 " A -^1 ■ ^ 2 2 - • * • . 0 -& 21 ^22- 0 0 0 • • 1 A where the elements of A are the transformation parameters for the first observation in each equation. A is calculated via triangular decomposition of £ and V, where V = ^edjeJiJ, 47 andvec(K) =(/-/?®7i)-1vec(s)(Graybill 1969, 298-300). Ai becomes a matrix of zeros because a21 is found to be zero. A A The transformed observations are y* = Py, andX* = PX. ISUR is then applied to these new, transformed observations to arrive A/ at the final estimates. 5.3 Results of Estimation Each of the four models defined in (1), (2), (3), and (6) are estimated and compared. The results of the estimations are listed in Table 2. For Model A, five of the 15 parameters appear to be significant as indicated by the asymptotic t-statistics. Two summary statistics, /^2andfc, are given in the lower section of the table. The second, fc, is discussed in section 5.3.1. The first is due to McElroy (1977, 384) and is given by (17) J£ = l-u '(irl®/)u/y*'(^1® A-)r» where A- = /r -jj'/7\ and j =(l,l,...,l)'. 2 6 A test of the transformed residuals using the Im statistic defined supra n. 24, where Hq- p ii = P i 2 = 0, yields bn = 0.2473 < x l (0.25) = 5.9915. Thus, we fail to reject H0 and conclude that autocorrelation is no longer significant. 48 Table 2.— ISUR Estimates for the U.S. Virgin Plastics Industry 1958-1991 Model A Model B Model C Model D Parameters Unrestricted CRTS & NTC NTC NTC & Homothetic Pa 0.5045 -3.5350 0.9511 0.8561 r u (0.0986) (-48.0004) (1.1031) (0.9680) fix 0.9855 0.8038 0.9912 0.8310 (19.5103) (14.5227) (24.5020) (21.4076) P e 0.0145 0.1962 0.0088 0.1690 (0.2864) (3.5457) (0.2188) (4.3542) P v 0.1410 1.0000 0.0857 0.1325 r y (0.1295) — (0.4850) (0.7293) fit 0.3279 — — — (1.6745) — — — fix'E -0.0801 -0.1128 -0,0726 -0.0576 (-7.3110) (-20.4273) (-9,0051) (-7.9361) fix x -0.0202 -0.0898 -0.0166 -0.0765 (-0.9004) (-7.0032) (-1.2540) (-8.3832) P t e 0.1003 0.2026 0.0892 0.1340 (6.0155) (20.9613) (8.0216) (12.9390) -0.0496 . . -0.0504 — • (-3.3213) — (-5.1867) -- fi-vv 0.0496 — 0,0504 — t'L.y (3.3208) — (5.1860) — fixt 0.0003 — — (0.1907) -- — fi%t -0.0003 — .. — (-0.1905) -- — — 0.0704 .. 0.0679 0.0544 r y y (0.6619) — (4.2701) (3.3457) fiyt -0.0425 — — — / (-1.4739) — — — P tt 0.0041 -- — .. (0.8789) — k — Summary Statistics 0.99072 0.97566 0.98924 0.98826 fc — 7.8049 1.7405 1.7843 f{0.05) — 1.998 2.295 2.08 ffO.10) — 1.71 1.9 1,765 Note: Parameter estimates are listed first, Followed by the asymptotic t- statistics in parentheses. 49 The measure is: a monotonic transform of the f-statistic given in (18), is the ratio of the conditional to the unconditional transformed variation in y* about its mean y*, and is bounded on [0,1] (McEIroy 1977, 384). The measure is based on the transformed observations of y*, and the transformed residuals u. This goodness of fit measure was developed for sets of equations which have transformed observations. All of the models have very high values for suggesting the models and the data fit each other well. 5.3.1 Model Selection The f-test statistic, fc, is used to decide if a restricted version of Model A from (6) is superior to Model A. Two models are compared with each test, the unrestricted Model A (A) and a restricted one (R). The statistic fc is defined as (r -Zp')(ZGz)-'(r - Z p ) /j { r - X ’0](£-l® i)(y -X -p )l(M T -k ) (ESS,-ESS A)/J ESSJ (M T -k ) ~ 50 A where Zp = r is a set of linear coefficient restrictions, G = , J is the difference in the degrees of freedom between A and R for all M equations, and the error sum of squares (ESS) is subscripted for each A and R model.2 7 Of those models defined in (6), Model B is the most restricted. The null hypothesis used to determine if B is a better specification than A is Hq . (py- 1 ) = /?, = p Xy = Pxy = Pxt = Pt, = P}y = pyt = P„ = 0, against the alternative hypothesis HA: at least one terms above is non-zero. The fc statistic is calculated, and the result from Table 2 shows that the joint imposition of CRTS and NTC is not supported by the data. Since fc>f(o.o5)>f(o.io), H0 is rejected even at the 10 percent level of significance and thus Model B is not an improvement over A. Upon further examination of the results for Model A, it is evident that only the cross price-output parameters p Xy and/?£,, 27The first part o f (18) in matrix notation is from Judge et al. (1985, 472-476), the second part is from Ramanathan (1989, 171). 51 are significant, while all other H0 parameters (including the cross price-time terms Pjq m d fa ) are insignificant. It appears then that CRTS may be erroneously specified, whereas NTC may not be. Model C then specifies NTC only. The null hypothesis is then H0: p t = p ^ — p K — p yt = p„ = 0. This time H0 cannot be rejected even at the 10 percent significance level because f{0.05)> f(0.10}> fc * 28 Model D maintains NTC and homotheticity, thus H0 : Pt = Pxy = P?y - P x t - f a = Pyt = Pn = 0• The results, f(o.o5)>fc>f(o.io) indicate that while H0 cannot be rejected at the 5 percent level, H0 is narrowly rejected at the 10 percent level. The choice between Models C and D is not obvious when examining only the above results. If the simpler Model D is chosen, two parameters could be eliminated which increases degrees of freedom. On the other hand the f-test results slightly favor Model C. 2 8 It is probable that any technical change effect that may have existed has been eliminated by transforming the data in the autocorrelation correction process. 52 In order to further compare the two models, Model C becomes the unrestricted model. An f-test of H0: p%y ~ p^y- 0 is performed which yields fc ~ 2.594. HQ cannot be rejected at the 5 percent level since f(o.o5) = 3.174, however H0 is rejected at the 10 percent level since f(o.io) = 2.405. Although the decision between the two models remains somewhat arbitrary, Model C will be selected as best for two reasons. The first reason is simply that the f-tests favor Model C at the 10 percent level, and these tests take into account both the reduction in ESS and the increase in degrees of freedom. The second reason is that since the interaction terms PxyandpTy are significant, Model D may be misspecified. Some evidence that misspecification may exist in Model D appears when the six- tenths factor rule is considered. The six-tenths factor rule is of the form / A = I G {QA jQB)°6, where / is plant investment cost, Q is production capacity, and A and B are identical plants with QA * QB,2 9 This engineering rule 29From Chapman (1991, 125), Skinner and Rogers (1968, 104), and OECD (1969, 59- 60), all with differing notation. Plant investment cost (/) and production capacity (O) arc 53 is widely used within the petrochemical industry to determine the cost of a proposed plant A based on the proposed capacity of A and the existing capacity and cost of B. Lau (1986, 1547) states that “[the use of] the six-tenths factor rule is inconsistent with the use of functional forms for production functions that are homothetic, unless all other inputs also satisfy the six-tenths factor rule...” This is because under the homothetic specification of Model D the cross price-output terms, and/?E > , are zero, so no relationship between capital and output can exist, six-tenths or otherwise. However, it is probable that some relationship between capital and output does exist since the six-tenths factor rule is so extensively applied within the industry. Therefore, >9jtyandp^y should not be eliminated. 5.3.2 Regularity Conditions It has been shown (notably by Wales 1977; Caves and Christensen 1980; Barnett and Lee 1985; and Diewert and Wales loosely interpreted by Lau (1986, 1547) as capital expenditures (KpK) and output (y), respectively. 54 1987) that the translog globally violates the concavity in prices property frequently in applied econometric work. It is therefore important to examine Model C for satisfaction of concavity, if not globally, at least in a neighborhood of observations (Wales 1977, 191). Concavity of Model C in input prices is checked for following a procedure from Diewert and Wales (1987, 47-48). The concavity property will be satisfied if the second order partial derivatives of cost with respect to prices, V^Cfo.jy) is negative semidefinite. This is evaluated by determining whether or not (a T - [ s* + ( s*)2 ] Px Pt ~ S.kSt Px Pt ~ SxS-z ( f c f - is negative semidefinite. For Model C, the first principal minor of the determinant of V F is negative and the second principal minor is positive for all observations. Therefore, concavity is satisfied globally. Additionally, it is found that C{\>,y,i) is non decreasing in both y and p. 55 5.4 Derived Demand and Gain from Recycling Once the appropriate model has been chosen, the AUES and elasticities of demand can be derived (see Table 3). Since the elasticities do not vary much over the years, only the values from 1959, 1975 and 1991 are reported. As would be expected Table 3.--AUES and Demand Elasticity Estimates for the U.S. Virgin Plastics Industry 1958-1991 Axx ^xx sx x sxx sxx Sxx 1959 -0.632 -1.048 0.095 -0.397 -0.389 0.060 0.035 1975 -0.627 -1.054 0.094 -0.396 -0.389 0.059 0.035 1991 -0.673 -0.992 0.103 -0.413 -0.383 0.063 0.040 Note that 1959 is used since the transformed first observation leads to quite different point estimates than for all the other years. in a two input model, JC and X behave as substitutes. Also expected, the own-price elasticities of demand for % and X are both negative, and the cross-price elasticities are positive. The X own-price elasticity of demand, %£, in 1991 is found to be somewhat inelastic at -0.383. Both DD and D'D' are modeled 56 with constant elasticity demand curves such that q% ={<f>Prf™ where < f > is the intercept term. The quantity of X employed in 1991 is arrived at by applying that part of (3) where q% = S^Cjp%. Referring back to the Figure, the quantity of X consumed in 1991, q0, is then calculated to be 2.4086X109 gigajoules (GJ), or 87 GJ per ton of output.3 0 When q0 is multiplied by the $8.18 paid per GJ in 1991, p0, it is found that the industry paid $19.7 billion for X. When only one percent of virgin output, or 276,583.5 tons is substituted in favor of recycled output, the new quantity of X demanded, q1 } becomes 2.3851xl09 GJ. Consequently, the derived demand curve DD shifts to D'D1 and the area represents a gain of $192,220,167. The gain (avoided loss) represented by area abc is (20) -qi6c*q0 = $316,175,295. 3 0 Comparatively, the 1988 derived demand was 1,1975 x 108 GJ greater than that reported for 1988 by U.S. Department of Energy (1991). The OECD (1985, 23) reports 87 GJ/ton o f output for polyethylene (the largest share of output which includes HDPE, LDPE, and PET), 97 GJ/ton for PP, and 105 GJ/ton for PS. 57 The total benefit is then equal to $508,395,462 for 1991. A 90% confidence interval for this total benefit ranges from $355,075,889 to $793,43 1,725. 58 6. CONCLUSION An increasing interest in recycling of post-consumer waste has led to research into many different aspects of the subject. This interest in recycling frequently stems from a desire to alleviate the social costs surrounding the disposal of post consumer waste, although in the case of plastics the social costs of the production of virgin materials may be more significant. The many other issues of recycling not examined here, such as: collection, sortation, reclamation systems and household participation, can produce additional efficiencies in the operation of the market for recycled material. For instance, the sortation of recyclables may soon be highly automated and accept multiple types of differently sized materials (e.g. Dinger 1992a,b), and reclamation systems are continually evolving. A major improvement in the collection of MSW and recyclables can be achieved with weight and volume pricing of household garbage, which can stimulate household participation while 59 reducing MSW (e.g. Hong, Adams, and Love 1993; and Duggal, Saltzman, and Williams 1991). An additional component of household participation is consumer demand for goods produced with PCR. If the demand for PCR is not sufficiently and consistently high, the market for scrap will not develop to the point where PCR can be priced competitively with substitute materials. Also, unless the quality of the recycled material is at least equal to that of virgin, demand by consumers and producers for PCR will remain low. This study has quantified private and social gains which can be achieved in the production of plastics. 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Washington D.C.: World Wildlife Fund & The Conservation Foundation. Zellner, Arnold. 1962. An Efficient Method for Estimating Seemingly Unrelated Regressions and Tests for Aggregation Bias. Journal of the American Statistical Association 57 (June): 585-612. 73 INFORMATION TO USERS This manuscript has been reproduced from the microfilm master. UMI films the text directly from the original or copy submitted. Thus, some thesis and dissertation copies are in typewriter face, while others may be from any type of computer printer. The quality of this reproduction is dependent upon the quality of the copy submitted. Broken or indistinct print, colored or poor quality illustrations and photographs, print bleed through, substandard margins, and improper alignment can adversely affect reproduction. In the unlikely event that the author did not send UMI a complete manuscript and there are missing pages, these will be noted. 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Asset Metadata
Creator
Atkinson, Scott Raymond
(author)
Core Title
An analysis of private and social gains from plastics recycling
School
Graduate School
Degree
Master of Arts
Degree Program
Economics
Degree Conferral Date
1994-12
Publisher
University of Southern California
(original),
University of Southern California. Libraries
(digital)
Tag
economics, general,engineering, sanitary and municipal,environmental sciences,OAI-PMH Harvest,plastics technology
Language
English
Contributor
Digitized by ProQuest
(provenance)
Advisor
Cason, Timothy N. (
committee chair
), Mui, Vai-Lam (
committee member
), Trefftz, Kenneth L. (
committee member
)
Permanent Link (DOI)
https://doi.org/10.25549/usctheses-c18-849
Unique identifier
UC11357896
Identifier
1376444.pdf (filename),usctheses-c18-849 (legacy record id)
Legacy Identifier
1376444-0.pdf
Dmrecord
849
Document Type
Thesis
Rights
Atkinson, Scott Raymond
Type
texts
Source
University of Southern California
(contributing entity),
University of Southern California Dissertations and Theses
(collection)
Access Conditions
The author retains rights to his/her dissertation, thesis or other graduate work according to U.S. copyright law. Electronic access is being provided by the USC Libraries in agreement with the au...
Repository Name
University of Southern California Digital Library
Repository Location
USC Digital Library, University of Southern California, University Park Campus, Los Angeles, California 90089, USA
Tags
economics, general
engineering, sanitary and municipal
environmental sciences
plastics technology