Demand for waste as fuel in the swedish district heating sector: A production function approach

Waste Management 29 (2009) 285–292

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Demand for waste as fuel in the swedish district heating sector: A production function approach Örjan Furtenback * Department of Forest Economics, SLU, SE-901 83 Umea, Sweden

a r t i c l e

i n f o

Article history: Accepted 27 February 2008 Available online 28 April 2008

a b s t r a c t This paper evaluates inter-fuel substitution in the Swedish district heating industry by analyzing almost all the district heating plants in Sweden in the period 1989–2003, specifically those plants incinerating waste. A multi-output plant-specific production function is estimated using panel data methods. A procedure for weighting the elasticities of factor demand to produce a single matrix for the whole industry is introduced. The price of waste is assumed to increase in response to the energy and CO2 tax on waste-to-energy incineration that was introduced in Sweden on 1 July 2006. Analysis of the plants involved in waste incineration indicates that an increase in the net price of waste by 10% is likely to reduce the demand for waste by 4.2%, and increase the demand for bio-fuels, fossil fuels, other fuels and electricity by 5.5%, 6.0%, 6.0% and 6.0%, respectively. Ó 2008 Elsevier Ltd. All rights reserved.

1. Introduction 1.1. Swedish waste management Under the Swedish waste management system, formal responsibility for handling and disposing of waste is divided between:  local authorities, who are responsible for handling household waste;  manufacturers of commodities, who are responsible for waste associated with their respective products;  other waste generators, in practice, non-manufacturing industries and businesses. Domestic household waste is typically managed by local authorities at their own facilities. Waste arising from the manufacturing sector is also often handled by local government bodies and, as such, the manufacturer’s responsibility is effectively transferred to the local authorities, whose role may encompass the management of various complex waste streams (e.g., the separation of electronic waste) and incineration. Within Sweden, private commercial organizations have the main responsibility for recycling waste. Incineration accounted for 46.7% of the total amount of household waste processed in Sweden in 2004.1 Plants burning household refuse also incinerate waste originating from other sources. * Tel.: +46 90 786 8311. E-mail address: [email protected] 1 Compiled from data acquired from Avfall Sverige (Swedish Waste Management). 0956-053X/$ - see front matter Ó 2008 Elsevier Ltd. All rights reserved. doi:10.1016/j.wasman.2008.02.027

Of the total waste stream incinerated, household waste accounted for 59%, the industrial waste sector accounted for 36%, and 5% originated from imported waste. Some incineration plants store waste (often in compacted bales) when the weather is warm and heating demands are low; the waste can then be incinerated during colder periods, when more energy is needed. 1.2. Taxation and other regulations Waste originating from Swedish households increased from 3.5 to 4.2 Mton per annum over the period 1994–2004, equivalent to an increase of approximately 16% per capita. During this period there was also a radical change in the way waste was handled. As can be seen in Fig. 1, the amount of waste disposed of in landfill declined markedly, and this type of disposal has been gradually replaced by a growing combination of incineration, recycling and biological waste treatment options. A ban on the disposal of waste in landfills came into force on 1 January 2002, although municipal authorities could apply for exemptions for a specific period of time (Swedish statutes, 2001). On 1 July 2006, new carbon dioxide (CO2) and energy taxes were introduced. One goal of these taxes was to harmonize the energy taxation system applied to fossil fuel used for district heating. Despite mixed household waste containing an average of 14% plastics (Profu, 2005), up until July 2006 it was regarded as bio-fuel and thereby exempted from both CO2 and energy taxes. These taxes apply to the incineration of waste for heating purposes, which emits CO2 (Swedish statutes, 2006). Another goal of the tax policy, and of the landfill ban which preceded it, was to promote the objectives of Sweden’s hierarchical waste management strategy (Commission of

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Fig. 1. Changes in Swedish waste management practices between 1994 and 2004.1

the European Communities, 2005). The overall aim of this strategy is to extract the maximum practical benefit from products during their lifetimes, while generating the minimum amount of waste. The waste hierarchy ranks available options for dealing with waste. Both the ban on landfill disposal and the taxes on waste incineration are aimed at shifting the bulk of waste management up the hierarchy, to other, more desirable, means of management. This study explores the substitutions in fuel inputs that are likely to occur in the district heating industry in response to the taxes imposed. The rate of the taxes varies, depending on the type of incineration plant and its environmental performance. If electric power is produced together with heat, as in combined heat and power plants, the level of taxation is reduced. A combined heat and power plant that produces electric power equivalent to 5% of its combined output pays the same tax for energy and CO2 production (3524 SEK/tonne CO2, 388 €/tonne CO2) as a district heating plant. In 2003, waste incineration-based combined heat and power plants generated 5983 GWh of energy for district heating with no electric power generation, and 176 GWh of power with some associated electricity power generation. These data indicate that most (more than 97%) of the waste incinerated in Sweden is purely for district heating, and does not produce extra electricity. Thus, most of the Swedish waste incineration industry is likely to fall within the tougher tax regime. One of the reasons for electricity production being low compared to heat production is because of the many impurities in the waste fuel. The temperature of the steam in the boiler cannot exceed 400 °C without incurring high maintenance costs due to corrosion, as described, for example, by Korobitsyn et al. (1999). Since the average energy content of household waste is 2.9 MWh per tonne, with a CO2 rating stipulated at 12.6% of weight (according to the tax specification), it has been calculated that the total taxation will amount to 15.4 SEK (1.7 €) per MWh of waste fuel used by the district heating industry. The tax scheme is illustrated in Table 1. 1.3. District heating plants in Sweden District heating is well established in Sweden and its share of heat supply is among the highest in Europe. District heating in Sweden accounts for more than 40% of the total heat demand for apartment blocks, detached houses and buildings (Swedish Energy Agency, 2001). In 2003 there were approximately 300 district heat-

Fig. 2. Changes in proportions of energy sources used from 1989 to 2004. — - — waste; —- —- bio fuel; —— fossil fuel – – – – – electricity, ......... other fuel.

ing plants in Sweden, about 25 of which were waste incineration plants. These waste incineration plants accounted for roughly 26% of the total district heating output. The fuels used in power generation have changed over time. Fig. 2 shows the changes in the proportions of different energy sources used in district heating plants from 1989 to 2003. The aggregated data for all of the plants (Fig. 2a) indicate that, while the proportions of fossil fuel and electricity used have declined, proportions of bio-fuels have increased. For the waste incineration plants (Fig. 2b) the trends are somewhat different. Waste incineration and use of bio-fuel increased until the year 2002, then biofuel use started to decline while waste incineration continued to increase. These data are consistent with predictions made by Sahlin et al. (2004) regarding the consequences of the ban on landfill disposal. As for all plants, the use of electricity by the district heating plants declined during this period. Both sets of data clearly indicate that the proportional use of electricity has declined, which probably reflects the fact that electricity is used mainly in peak production conditions, for example when it is very cold. From this data, an energy efficiency of 0.85 with a standard deviation of 0.09 was calculated for all the plants over the period 1989–2004. The most important environmental problems associated with waste incineration are flue gas emissions and the ash production. The flue gases contain hazardous substances such as heavy metals (e.g., lead, cadmium and mercury), dioxins and dust. Today, waste incineration facilities have advanced flue gas cleaning systems. Any hazardous substances mainly end up in the flue gas ash. This ash is classified as hazardous waste and must be landfilled in special ways. Fly ash amounts to around 4% of the total weight of the

Table 1 Energy and taxes (on 1 July 2006) in SEK (€) per tonne CO2 produced by waste incineration (assumed by the legislation to equal 12.6%, w/w, of the waste incinerated)

Heat only Heat and electrical power Heat and electrical power

Energy tax

CO2 tax

Tax reduction

Electrical power (% total output)

150 (16.5) 0 150 (16.5)

3374 (371) 3374 (371) 3374 (371)

0 19–79% 0

0 5–15% <5%

Ö. Furtenback / Waste Management 29 (2009) 285–292

waste; bottom ash amounts to about 19% and is mostly landfilled even though it could be used for road construction and for covering landfills (Swedish Association of Waste Management, 2001). 1.4. Related studies The study by Sahlin et al. (2007) investigated whether the tax on waste incineration increased the incentive to recycle materials, including biological treatment. They developed a spreadsheet model to estimate the marginal cost of treatment alternatives to waste incineration. Their result indicates a 9% increase in biological treatment and less than 1% increase in total material recycling. Nilsson et al. (2005) evaluated the environmental effects of assumed changes in waste flows, due to different waste incineration tax levels. Three evaluation methods were applied to four waste management strategy alternatives. The results showed modest environmental improvements with a waste incineration tax of 400 SEK/tonne waste (44 €/tonne), compared to the ‘‘potential to achieve more far-reaching goals concerning optimization of energy recovery and reduction of greenhouse gas emissions”. In contrast, this study is focused on the substitution of fuel inputs that will take place in response to the new tax. A study by Brännlund and Lundgren (2004) explored inter-fuel substitution in district heating plants in Sweden using a dynamic model (waste was not included as a fuel). All own-price elasticities were found to be negative and all cross-price elasticities to be positive. They also found that the fuel mix used in plants is adjusted quickly in response to changes in relative fuel prices. In an investigation by Brännlund and Kriström (2001), the impact of energy taxation on the Swedish district heating industry was examined using a static model. They used a similar approach to the one adopted in this study, which is also based on a static model for estimating the production function parameters, but they did not specifically consider waste as an input to the incineration industry. The resulting elasticities from the cited study were as expected: the own-price elasticities were negative and the cross-price elasticities were positive. A more detailed analysis of production functions was presented by Galatin (1968), who assessed thermal power generation plants in the USA, which used comparable technologies to those used in modern Swedish district heating plants. Stoughton et al. (1980) developed an algorithm for planning the generation mix of a power system for a specified target year. This algorithm can be used, inter alia, to calculate industrial fuel substitution in response to a tax on the use of a particular type of fuel. However, its use in this context requires knowledge of the capacity constraints for all the different types of boilers deployed at the different district heating plants. In a paper by Sahlin et al. (2004) the impact of the ban on disposing of waste in landfills was investigated. They found that this ban increased the use of waste fuel in the district heating industry and reduced the demand for other fuels, particularly bio-fuel. This investigation was performed using panel estimation methods to evaluate data acquired from Svensk Fjärrvärme AB (the Swedish District Heating Association). The study reveals that price changes for waste fuel have the expected result, i.e., negative ownprice and positive cross-price elasticities. To our knowledge this is the first time the price elasticities of waste incineration have been analyzed. 1.5. Outline Following this introduction, Section 2 provides a theoretical model for a profit-maximizing power plant. The data and the empirical model are discussed in greater detail in Section 3. The results of estimations are presented in Section 4, a discussion of the results is provided in Section 5 and conclusions in Section 6.

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1.6. Purpose The purpose of this study is to investigate inter-fuel substitution in Swedish district heating plants as a response to changes in the net price of waste. The net price of waste for the waste incineration industry is changing in response to new taxes on waste incineration. While the operators of waste incinerators charge fees for handling and disposing of waste, they also use it as a fuel. This industrial enterprise is modeled as a multi-output production system, in which the plants both generate energy (for district heating) and provide a waste disposal service. The waste incinerator plants are therefore considered as bearing extra costs for the handling and disposal of the waste they receive as a fuel input. This implies that the waste incineration industry incurs a net cost for the waste it utilizes. 2. Theoretical considerations Plants incinerating waste usually receive some form of financial compensation for accepting household waste. The purchasers of a waste incineration service are often the municipal authorities responsible for collecting waste. Thus, waste can be both an input and output for the incineration industry. Here it is assumed that certain costs are incurred by the plants incinerating waste. This implies that the firm pays a net price for waste. Thus, the plants provide three services: district heating, waste incineration and (in some cases at least) electricity generation. The generation of electricity is henceforth disregarded. Assuming that a heat-producing operation is using primary inputs (i.e., labor and capital) and fuel inputs, the plant-level heat production function can be represented by ydh it ¼ f ðxwit ; xit ; Lit ; K it Þ where i and t are indices for the plant and time, respectively, xit is a vector of different kinds of fuel inputs other than waste, xwit is the waste fuel input, Lit and Kit are labor and capital respectively, and ydh it represents the production of heat. The production of waste incineration, ywi it , is simply represented by ywi it ¼ xwit It is assumed that the plant behaves as a short run profit maximizer, i.e., Y  wnet pdh ; pxit ; wit ; rit it ; pit   wi   dh w x ¼ max pdh ð1Þ it yit  pit  pit xwit  pit xit  wit Lit  r it K it x;L

w where pwi it is the price of waste incineration, pit is the price (special wi w ¼ p  p , is the net price of waste, cost) of handling waste, pwnet it it it x pdh it is the output price of district heating, pit is the price vector of input fuels, wit represents wages, and rit is the price of capital. By solving the profit maximization problem as in Eq. (1), the price elasticities of demand can be obtained. This is illustrated in Appendix 1. These elasticities are of major interest in this study. Considering the first law of thermodynamics, it seems reasonable to assume that the output, in the form of heat energy, could be fully characterized by the input fuel vector, since all quantities are in energy units. It can be argued that there is very little potential for substitution between the fuel input vector on the one side and labor and capital on the other. The rationale for this is that it is difficult, in the short run, to substitute some of the fuel inputs for either capital or labor while retaining the ability to produce the same amount of output heat. It would be desirable to test this separability, and this has been attempted by several authors, for example, Berndt and Wood (1975) and Blackorby et al. (1977). However, due to a lack of relevant data, the separability between

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the fuel input vector on the one side and labor and capital on the other has to be assumed here, and it is recognized that this is a limitation of this analysis. This rather crude assumption means that the production of heat, in the form of energy, is assumed to be determined solely by the energy content of the input fuels; this is not such an unrealistic assumption. This is taken into consideration in the model and the production function can be restated with a Leontief assumption, where the inputs are entered in nested fixed proportions: ydh it ¼ f ðxit ; Lit ; K it Þ ¼ minðagðLit ; K it Þ; bhðxit ÞÞ where g describes the part of the production function that includes capital and labor, and h incorporates the transformation of different fuels into heat. Here, and in the rest of the paper, the waste fuel is incorporated into the vector xit. a and b are constants greater than zero. Given this assumption, and assuming that the plant’s operators are aiming to maximize their profits (in terms of Shepard’s lemma theory operating at the kink of the isoquant), when choices of inputs and output are optimal: ydh it ¼ agðLit ; K it Þ ¼ bhðxit Þ With this separation, the parameters for the fuel component of the production function can be calculated separately, as follows: ydh it ¼ bhðxit Þ

ð2Þ

3. Data and the empirical model The data set contains measured values for all energy outputs and inputs for almost2 all of the district heating plants operating in Sweden from 1989 to 2003. Unfortunately, there are no data on labor, capital or the market price of any other inputs. A common way to empirically estimate conditional demand and the elasticity of demand is to use the duality between cost and technology, which specifies the cost function. The conditional supply and demand can be obtained as functions of price, fixed capital, and the level of production by applying Shepard’s lemma. Another way to extract the required estimates from the available data is to determine the production function directly, using quantitative data pertaining to inputs. Following the steps of Zellner et al. (1966), it is assumed that the production function is stochastic, so that disturbances are due to factors such as the weather or unpredictable variations in machine or labor performance. It is further assumed that plant managers aim to maximize the expected profits, and the prices are either known with certainty or statistically independent of the production function disturbance. It is further assumed that disturbances to the profit-maximizing conditions partly result from uncertainty in the production function and partly from ‘‘human errors”, and that these contributors are considered statistically independent. Based on these assumptions Zellner et al. (1966), showed that the Cobb-Douglas production function can be estimated using a single equation and that the resulting order of least squares (OLS) estimates are consistent and unbiased. Since no information on prices was available, we made the assumption that incineration technology can be approximated with a Cobb–Douglas production function. Eq. (2) can now be further specified as Y xak ð3Þ ydh it ¼ bhðxit Þ ¼ c kit

nized that the Cobb–Douglas functional form has two major drawbacks: it requires all inputs to be positively employed and it has a unitary elasticity of substitution for all levels of factor use. The first problem is addressed in Appendix 2. The second constraint could, of course, be circumvented by using a more flexible functional form, such as a normal quadratic-, translog- or generalized Leontief functional form. Alternatively, with the Cobb-Douglas functional form, elasticities of demand can be determined solely by the parameters of the production function, without considering prices or quantities; this is especially relevant in cases such as this, where the data are subject to the limitations detailed above. The number of different fuel inputs in the data set is very large. Thus, to facilitate their interpretation, the data need to be aggregated. The fuel aggregations considered here are: waste, bio-fuel, fossil fuel, other fuels and electricity. The ‘‘fossil fuel” aggregate consists of those inputs to production that were already subject to CO2 and energy taxes before the introduction of the tax on waste incineration. The aggregate term ‘‘other fuels” comprises residual heated water from other industries, heat pumps, solar power and a small percentage of unspecified input fuels. These aggregations facilitate comparison with the findings presented by Brännlund and Kriström (2001), who used a similar aggregation approach. However, one difference between this and the cited study is that here, waste is treated as a separate input. One complication is that some of the aggregated fuels were not used in some of the plants in some years. This is a drawback since the Cobb–Douglas production function will fail when some inputs amount to zero. This problem, known as the zero-observation problem, can be addressed in a number of ways, one of which is to select a subset of data, with input quantities that are not zero, and to base estimates of parameters on this subset. However, an obvious drawback of this approach is that a potentially significant percentage of the total observations (which might provide crucial information) are ignored. Another approach, proposed by Battese (1997), is based on dummy variables and uses all observations. This approach is used in this study and is described in detail in Appendix 2. Using this technique, the data are partitioned depending on the combination of fuels used. One might say that the parameters for several different production functions are estimated. There is one function for each combination of inputs used. The functions differ with respect to their intercept parameters for the dummy variables and the variables used in the combination. The parameters for the fuel input variables are the same, but the parameters in the functions differ, depending on the combination of input fuel variables used. This approach was also adopted by Brännlund and Kriström (2001) and Brännlund and Lundgren (2004). The model, described by Eq. (3), can now further modified on the basis of the above approach (Battese, 1997). Technical progress is incorporated in the form of a time variable, and the data is partitioned into different plant size classes. Size is determined by the amount of heat output produced. The final model, in log form, for estimating parameters of the production function can now be stated as ln ydh it ¼ a0i þ þ

A few observations where deleted due to consistency problems.

XX

þ Dhit ¼



X

X

ak ln xkit

k

ask ln xkit Sit þ

s

k

xkit ¼ 2

hh Dhit þ

h2H

k

With this function, range regularity conditions such as positive cost shares and negative own-price effects are conserved. It is recog-

X

X

bs Sit

s

cs Sit t þ c0 t þ eit

s

1 if input combination h is used 0 otherwise   xkit if xkit > 0 1

if

xkit ¼ 0



ð4Þ

Ö. Furtenback / Waste Management 29 (2009) 285–292

where i and t, are plant and time indices, k is the fuel input index and s the size class index. H is the set of input combinations, and h represents the specific combination index. Dhit and Sit are dummies, grouping the data according to input combination and size class. a0i represents the fixed effects parameters. ak and aSk represent the exponents in the Cobb–Douglas function for different input and size groups. c0 and cS are the time effect parameters allowing for technological progress. bS and hh are the intercept shift parameters with respect to size class and input combination dummy variables.

eskl ¼

D% Q skl D% pl

ð7Þ

where P

%

D

Q skl

Dqsh kl ¼ P sh qk h2H

ð8Þ

h2H

and

3.1. Weighting of elasticities

sh % sh Dqsh kl ¼ ekl D pl  qk

The derivation of own- and cross-price elasticity of factor demand is detailed in Appendix 1 and can be represented by 9 8 ak þask > > > = < P ðam þas Þ  1 if k ¼ l > m m ð5Þ ¼ esh s kl a þa l > l > > if k–l > ; : P ða þa s Þ m

m

(

0

sh if qsh k ¼ 0 or ql ¼ 0

esh kl

otherwise

qsh k

Eqs. (7)–(9) together produce: P sh sh e q D% Q skl h2H kl k s ekl ¼ % ¼ P sh qk D pl

qsh l

) ð6Þ

where and represent the quantities used of fuel inputs k and l, respectively. The elasticity matrices will now have the same dimensions, with zeroes in rows and columns representing inputs that are not used. With these equal dimension matrices, a scheme for weighting the elasticities into a single matrix is constructed. The weights are based on the averaged quantities of fuel inputs used in the different size groups, and fuel input combination groups, over the time period of the study. The weighting procedure combines the concept of arc and point elasticities, where the point elasticities are combined into the overall matrix of arc elasticity. The procedure can be illustrated in two steps. The first step weights the point elasticities in Eq. (6) across the different input combinations, h, and becomes part of Eq. (10). The second step uses this result as an input for weighting the different size groups, s, and becomes part of the overall matrix of arc elasticity 11. The procedure is as follows. Consider the elasticity of demand for each size group. The elasticity, Eq. (7), can be considered to be the total percentage change in demand for input k when the price of input l changes by 1%. Note that this is the definition of arc elasticity. The total percentage change in demand for input k, Eq. (8), is the sum across the relevant Battese group of the absolute changes in demand for input k, when the price of input l changes by 1%, divided by the sum across the relevant Battese group of average use of input k. The absolute change in demand for input k when the price of input l changes by 1%, Eq. (9), is the elasticity defined in Eq. (6) multiplied by the average use of input k. Substituting Eqs. (8) and (9) into Eq. (7) yields an expression for the elasticity of demand, presented in Eq. (10).

ð9Þ

ð10Þ

h2H

m

where k, l and m are fuel input indices. The indices s and h represent the size of the group and input fuel combination, respectively. There is a matrix of elasticities for each fuel input combination, h, within each size group, S. It should be noted that when calculating the elasticity for input combination, h, only those parameters associated with that combination are used. This means that the matrices of elasticity can have different dimensions, with the dimension of the matrix determined by the number of fuel inputs used in that specific combination. Note also that these elasticities are point elasticities. In order to create a single matrix of elasticities that collectively represent the industry as a whole, the matrices are transformed to have the same dimensions. The elasticities in Eq. (5) are redefined as esh kl ,

289

D% represents the percentage change and D the absolute change, of different entities. Dqsh kl is the absolute change in demand for input k, in size class S using fuel input combination h, when the price for input l changes at the rate D% pl  qsh k is the quantity currently used in the size group s, using input combination h. H is the set of input combinations used. D% Q skl represents the percentage change in demand for each size group, aggregated over input combinations. In a similar fashion, the total elasticity of demand is calculated from the weighted elasticities for each size group. These elasticities are convenient to use since they reflect the total effect on industry demand for each factor in a single matrix. The weighting follows the same pattern as above and its mathematical form is presented below. eIkl ¼

D% Q Ikl D% pl

D% Q Ikl ¼

DQ Ikl

Q Ik P sh h2H qk

¼

 P P sh D% pl s eskl h2H qk PP sh s h2H qk

ð11Þ

Ssk , P

P sh s h2H qk X I s s ekl ¼ e S s kl k where eIkl represents the elasticity for the industry as a whole. Here SSk is defined as the proportional quantity for input fuel k over size, S, P hence s Ssk ¼ 1.

4. Estimation results 4.1. The industry as a whole Since data for almost all of the Swedish plants were included in the panel data set, the fixed effects model was considered to be the most appropriate for estimating parameters (Greene, 2003), and this was confirmed by a Hausman test with the null hypothesis predicting random effects rather than fixed effects. The chi-square value obtained was 1446.3, with 50 degrees of freedom. The number of observations for the industry as a whole was 2573 over the entire time period. The adjusted R2 value for the regression analysis was 0.988. Most of the parameters were significant at the 95% probability level, although the estimates for the waste fuel parameters were not significant. An F-test restricting all waste parameters to zero did not significantly change the overall fit of the model, indicating that these variables cannot explain the variation in production. This lack of significance is probably due to the fact that relatively few of the plants (approximately 25 out of an industry total of around

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Table 2 Descriptive statistics for plants incinerating waste (in GWh)

Production Waste Bio Fossil Electricity Other

Table 3 Estimation results (waste incinerating plants only)

Mean

Standard deviation

Minimum

Maximum

Parameter

Estimate

t-Statistic

742.8 213.5 119.3 259.0 43.9 230.6

1066.9 262.5 162.0 425.1 144.8 545.4

13.5 0.2 0.0 0.0 0.0 0.0

6602.0 983.3 966.0 2352.0 1371.0 3633.5

awaste abio afossil aelectric aother awaste,2 abio,2 afossil,2 aelectric,2 aother,2 awaste,3 abio,3 afossil,3 aelectric,3 aother,3 b2 b3

0.08 0.07 0.04 0.00* 0.00* 0.02* 0.05 0.01* 0.03* 0.01* 0.10 0.05 0.03* 0.00* 0.02* 0.48 0.26*

2.50 3.87 2.64 0.26 0.20 0.65 2.79 0.26 1.61 0.78 2.13 2.34 1.16 0.19 1.03 2.47 0.81

300) incinerated waste. Thus, since the main focus of this paper is on waste incineration, another approach was adopted.3 4.2. The waste incineration industry Since the waste fuel parameters were insignificant for all plants, a different estimation approach was adopted in which only observations for plants that incinerated waste were used. This reduces the number of data observations to 317. The size of the groups had to be modified to account for the composition of this smaller data set. It also appears that there is collinearity between the time and waste variables in this smaller data set. A simple test of correlation further strengthens this impression. The time variables were therefore excluded from the analysis. A Hausman test with the null hypothesis predicting random effects rather than fixed effects, and assuming that the individual effects are uncorrelated with the other regressors in the model, yielded a chi-square value of 451.64 with 25 degrees of freedom. The assumption of a fixed effects model was therefore considered valid. Table 2 presents statistical data relating to the different fuel mixes used in waste incineration plants over the period 1989– 2004, as depicted in Fig. 2b. The adjusted R2 value for the regression analysis was 0.995. Results of an F-test, presented in Table 4, indicated that the hypothesis that all Battese parameters are zero cannot be rejected, and this was confirmed by regressing a model without the Battese dummies. All parameters differ by less than 3% from the Battese case. This may be because much of the effect of Battese dummies is absorbed in the fixed effects. However, the dummies were present when estimating the parameters used for calculating the elasticities. This is because they are a critical part of the Battese solution to the zero-value problem. The elasticities presented in Table 5 are calculated from the parameter estimates shown in Table 3. The elasticities are nonlinear functions of the estimated parameters. This makes it difficult to obtain an analytical expression for the errors in the calculated elasticities with respect to the errors in the estimated parameters. Therefore, the variances of the calculated elasticities were estimated using the bootstrap technique.4

Note: The numbers in the indices are equivalent to the s indices in Eq. (4). They represent the size groups [0, 175], [175, 550] and [550, 1] GWh.

Table 4 F-Test of model restrictions (waste incinerating plants only) F-Test

Value

Critical value

No No No No

50.98 0.78* 3.53 14.58

1.43 1.98 1.87 2.64

fixed effects (43, 248) Battese (8, 248) size effects (10, 248) waste (3, 248)

The results from this estimation are reported as t-statistics in parentheses in Table 5. Table 5 shows that own-price elasticities are negative and cross-price elasticities are positive, except in the case of electricity. As can be seen from the t-statistics, all elasticities are significant except for the cross-price elasticities for electricity. The insignificant cross-price elasticity for electricity is probably due to its small share of input. This is also indicated by the small size of these cross-price elasticities. The results suggest that the waste incinerating industry will respond to an increased waste fuel price by decreasing its use of waste in favor of other inputs, such as bio-fuel and fossil fuel, but the substitution is inelastic. It is also noteworthy that the magnitude of the cross-price elasticities are largest for waste, implying that the waste incinerating part of the district heating industry is most prone to substitution for other fuels when the price of waste increases. 5. Discussion

3

Several different approaches have been taken to estimate parameters using data for the whole industry, inter alia, excluding time, or the interaction between time and size. The insignificance of the waste parameters, however, seems to stem from the small impact that this sector of the industry has on the industry as a whole. 4 In short, this is done in the following manner: After estimating the parameters of the model, we re-sample the 317 observations with replacement. Adding this resampled vector of residuals to the fitted part of the regression gives us a set of pseudo-data for the endogenous variable. Estimating the parameters of the model based on pseudo-data and the right hand side variables gives a new parameter vector and a new set of weighted elasticities calculated according to Section 3.1. This procedure is repeated 10,000 times, which gives us 10,000 estimates of weighted elasticities. The variances of the estimated elasticities are then simply calculated as the variance in each pseudo-sample of elasticities. Comparing the 10,000 re-sample procedure with a 1000 re-sample procedure demonstrates very small changes in the variances. This indicates that the bootstrap method converges and that most elasticities are significant. For an overview of this technique see, for example, Efron and Tibshirani (1993).

This study investigates fuel input substitution in response to changes in the net price of waste used in the waste incinerating part of the Swedish district heating industry. The net price of waste for the waste incineration industry is expected to change in response to the recent introduction of a tax on the incineration of waste. The results suggest that the waste incinerating industry will respond to the increased price of waste fuel by decreasing its use of waste in favor of other inputs, such as bio-fuel and fossil fuel. The response is inelastic, partly because when waste incinerating capacity is installed it is better to use it. Thus, the average cost is probably still low while the marginal cost will increase. Furthermore, the incinerator may be able to shift the burden to the buyer of the waste disposal service. If one assumes that the industry will bear the whole burden of the tax, it is straightforward to simulate its impact on the

291

Ö. Furtenback / Waste Management 29 (2009) 285–292 Table 5 Total elasticity of demand (waste incinerating plants only) Share Waste fuels Bio-fuels Fossil fuels Electric fuel Other

0.25 0.14 0.30 0.05 0.27

pwaste 0.42 0.55 0.60 0.60 0.60

pbio (6.64) (9.30) (8.98) (8.74) (8.79)

0.11 0.85 0.10 0.11 0.08

pfossil (4.00) (27.64) (3.47) (3.54) (3.13)

pelectric

0.30 0.32 0.69 0.33 0.29

(6.14) (6.22) (13.08) (5.51) (5.69)

*

0.07 (1.88) 0.09* (1.87) 0.08* (1.79) 1.07 (16.68) 0.05* (1.76)

pother 0.08 0.07 0.08 0.08 0.92

(2.63) (2.25) (2.71) (2.59) (29.93)

Note: Figures in parentheses indicate t-statistics, obtained by bootstrapping.

industry’s substitution in fuel usage using the results from this paper. It is quite possible, however, that the waste incineration industry will be able to shift at least part of the tax downwards, onto the municipal authorities buying the waste incineration service. This is suggested by Profu (2006), who found that the tax on waste incineration leads to higher incineration gate fees. It may also be possible for the waste incineration sector to shift the tax burden upwards, to the purchasers of district heating. This effect might not be significant, however, due to the relatively small proportion (26%) of district heating output arising from the waste incineration industry. Further studies on the elasticity of demand for district heating are needed to determine who will bear the tax burden. It is also possible that the tax will have an impact on the investment behavior where waste incineration is currently not in place and where there is an exemption to the ban on landfill. Here, the increased cost of waste incineration due to the tax is likely to reduce the likelihood of investment in new facilities for waste incineration. Of course the rebate on tax that a combined heat and electricity plant will receive is likely to encourage such investments, but these types of facilities are more expensive to set up compared to heat only generation plants. The above scenario is validated by the results of Holmgren and Gebremedhin (2004). The author is aware of the simplifications in the model presented in this paper. It is recognized that a more flexible form of the production function would yield a more representative result. It may also be incorrect to assume that prices are statistically independent of the error related to the production process. For example, stochastic processes related to the weather may influence both district heating outputs and their price. It is further recognized that the assumption of separability of the fuel input vector on the one side, and labor and capital on the other, would have much stronger foundations if it could be rigorously tested. Nevertheless, this study provides indications of likely consequences of the recently introduced waste incineration taxation policy, but further investigations are required to overcome some of the limitations of this study. Given the wider governmental aims of the taxation policy (i.e., to stimulate reuse and recycling of waste), further studies on long-term structural changes, i.e., general equilibrium modeling, might also provide a better understanding of the implications of such a policy. 6. Conclusions The main implication of a tax on waste incineration, according to this study, is that the use of waste as fuel will decrease, with concomitant increases in the use of alternative fuels. The results here indicate that if the net price of waste increases by 10% while other prices remain constant, then the demand for waste will decrease by approximately 4.2%, while demand for bio-fuel, fossil fuel, other fuels and electricity will increase by 5.5%, 6.0%, 6.0% and 6.0%, respectively. The resulting increase in the use of biofuels, for example, might be seen positively from a policy maker’s perspective. On the other hand, the increased use of fossil fuels is unlikely to be welcomed by policy makers.

The results of this study are consistent with those reported by Brännlund and Lundgren (2004) and Brännlund and Kriström (2001), i.e., own-price elasticities are negative and cross-price elasticities are positive. The magnitudes of the elasticities determined in these studies differ to some degree, but this is not surprising since the studies have different formats. Acknowledgements Comments from Tommy Lundgren, Bengt Kriström, Sören Wibe and Runar Brännlund are gratefully acknowledged. The author would also like to thank Magnus Sjöström for his assistance in data acquisition. Appendix 1. Elasticities of factor demand In economics and business studies, the price elasticity of demand (PED) is an elasticity that measures the nature and degree of the relationship between changes in quantity demand for a good and changes in its price. Mathematically, the PED is the ratio of the relative (or percent) change in quantity demanded to the relative change in price. For example, if, when the price of a certain good decreases by 10%, the quantity demanded increases by 20%, the PED for that good will be 2. Below we describe how the elasticities of factor demand are derived in this particular study. Restating the profit-maximizing problem, Eq. (1), without plant and time indices Y ðA:1Þ ðpy ; px ; w; rÞ ¼ maxfpy y  px x  wL  rKg x;L

assuming inputs enter in nested fixed proportions y ¼ f ðx; L; KÞ ¼ minðagðL; KÞ; bhðxÞÞ plants operate at the kink of the isoquant, according to the assumption of profit maximization y ¼ agðL; KÞ ¼ bhðxÞ the profit maximization problem, (A.1), can be reduced to Y ðpy ; px Þ ¼ maxfpy bhðxÞ  px d  wL  rKg x

ðA:2Þ

Having limited or no information on competitiveness of the output markets for district heating and waste incineration, we adopt a restricted profit maximization scheme in which the outputs are fixed. This reduces the profit maximization problem, (A.2), to a problem of cost minimization, Varian (1992, p. 26). cðpx ; yÞ ¼ min px x x

ðA:3Þ

such that y ¼ bhðxÞ

By taking the antilog of the estimable production function in Eq. (4), where s and h represent the divisions into the size and fuel input combination, we get: Y ak þas s s sh xk k bh ðx; tÞ ¼ ysh ðx; tÞ ¼ ea0þhh þb þtðc0 þc Þ ysh ðx; tÞ ¼ Ash ðtÞ

Y k

k a þask

xkk

ðA:4Þ

292

Ö. Furtenback / Waste Management 29 (2009) 285–292

By solving problem (A.3) using (A.4) as an expression for the production function we get the cost function, Varian (1992, ch. 4): sh

x

sh

c ðp ; tjy Þ ¼

1

s

Y

Ash ðtÞ

k

pxk ak þ ask

P ak þak m

ðam þaS Þ m

ðA:5Þ

Applying Shepard’s lemma to (A.5) we get the demand function: x sh xsh k ðp ; tjy Þ ¼

ask

sh

sh

ak þ oc c  x ¼P s opxk m ðam þ am Þ pk

ðA:6Þ

The own- and cross-price elasticity of demand is given by repeated use of Shepard’s lemma in (A.6): esh kk ¼

oxsh px ak þ ask k 1  k ¼P s opxk xsh m ðam þ am Þ k

esh kl ¼

oxsh px al þ asl k  l ¼P s opxl xsh m ðam þ am Þ k

where k – l. Appendix B. The zero-value problem Assume a data set for an industry that can be characterized by a Cobb–Douglas production function. The data contain quantified information on one output yi, and two inputs x1i and x2i. One of the inputs, x1, is greater than zero for all observations, the other input, x2, has zero values for some of the observations. The regression model can be written as ln yi ¼ a0 þ a1 ln x1i þ a2 ln x2i þ ei ; i ¼ 1; . . . ; n1

ðA:7Þ

n1 ¼ number of observations with x2 > 0

ðA:8Þ

ln yj ¼ b0 þ a1 ln x1j þ ej ; j ¼ n1 þ 1; . . . ; n1 þ n2 ¼ n n2 ¼ number of observations with x2 ¼ 0

ðA:9Þ ðA:10Þ

Pooling (A.7) and (A.8) ln yk ¼ a0 þ ðb0  a0 ÞD2 k þ a1 ln x1k þ a2 ln x2k þ ek ;

k ¼ 1; . . . ; n ðA:11Þ

where D2k ¼ x2k ¼

 

1

if x2k ¼ 0



0 if x2k > 0  x2k if x2k > 0 1 if x2k ¼ 0

Using OLS, the parameters of (A.9) can be estimated. The number of dummy variables depends on the number of variables that are of zero value. A dummy for all combinations of zero-valued variables is required. In the above example only one dummy is required, since there can only be one combination with zero-valued

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