The shadow price of substitutable sulfur in the US electric power plant: A distance function approach

Journal of Environmental Management 77 (2005) 104–110 www.elsevier.com/locate/jenvman

The shadow price of substitutable sulfur in the US electric power plant: A distance function approach Myunghun Lee* Department of International Trade, Inha University, 253 Yonghyun-dong, Nam-gu, Incheon 402-751, South Korea Received 9 March 2004; revised 6 January 2005; accepted 22 February 2005 Available online 1 July 2005

Abstract Given restrictions on sulfur dioxide emissions, a feasible long-run response could involve either an investment in improving boiler fuel-efficiency or a shift to a production process that is effective in removing sulfur dioxide. To allow for the possibility of substitution between sulfur and productive capital, we measure the shadow price of sulfur dioxide as the opportunity cost of lowering sulfur emissions in terms of forgone capital. The input distance function is estimated with data from 51 coal-fired US power units operating between 1977 and 1986. The indirect Morishima elasticities of substitution indicate that the substitutability of capital for sulfur is relatively high. The overall weighted average estimate of the shadow price of sulfur is K0.076 dollars per pound in constant 1976 dollars. q 2005 Elsevier Ltd. All rights reserved. Keywords: Shadow sulfur price; Input distance function; Indirect Morishima elasticity of substitution; Porter hypothesis; Marginal abatement cost; Internal/external trading

1. Introduction The regulation of sulfur dioxide (SO2), known as a major precursor of acid rain, has been more stringent in the US since a national standard was set by the 1970 Clean Air Act. One goal of this act was to control emissions from coal-fired power plants, which contribute more than 70% of the SO2 generated in the US Knowledge of marginal abatement costs—i.e., how much it would cost for power plants to reduce additional units of SO2—allows environmental policy-makers to establish an optimal emissions limit to maximize social net benefits. In addition, estimation of marginal abatement costs provides useful information on the potential cost savings from reallocating abatement resources under a marketable allowance system.1 * Tel.: C82 32 860 7805; fax: C82 32 876 9328. E-mail address: [email protected]. 1 In equilibrium, the marginal abatement cost would be equal across plants and would equal the price of an allowance. In the case of private trade between two plants, the net gain per unit would be the difference between their marginal costs.

0301-4797/$ - see front matter q 2005 Elsevier Ltd. All rights reserved. doi:10.1016/j.jenvman.2005.02.013

As of 1971, all new or modified coal-fired plants were required to emit no more than 1.2 pounds of SO2 per million Btu. In 1977, new plants were also required to install pollution abatement equipment such as flue gas desulfurization (FGD) systems, known as scrubbers. Earlier legislation was tightened by the 1990 Clean Air Act Amendments, which also established a specific time schedule for reducing aggregate SO2 emissions. The core of the Acid Rain Program (Title IV) is a market-based system for capping and trading SO2 allowances. There are two main approaches to estimating marginal costs of abating pollutants: the cost function approach and the distance function approach. Gollop and Roberts (1985) estimate a cost function for fossil-fueled power utilities in which a variable measuring the regulatory intensity of SO2 is included as an argument. Since regulatory intensity is a function of actual emissions, the marginal cost of emissions reduction is derived by partially differentiating the cost function with respect to the actual emissions level. However, it should be recognized that firms would likely fail to minimize their production costs in the presence of various regulations, including those intended to control pollutant emissions (Atkinson and Halvorsen, 1984; Kumbhakar, 1992; Lee, 2002). As a result, use of

M. Lee / Journal of Environmental Management 77 (2005) 104–110

a neoclassical cost function might lead to under-estimation of marginal abatement costs. Also, inconsistencies in the availability of relevant data by industry make it difficult to develop an adequate index that consistently gauges regulatory constraints across industries.2 Fa¨re et al. (1993), Coggins and Swinton (1996), and Hailu and Veeman (2000) calculate the shadow prices or marginal abatement costs of undesirable pollutants by employing a distance function, which was originally introduced by Shephard (1953, 1970). A dual relationship between the distance function and the revenue function or cost function provides a theoretical formula for the shadow prices of pollutants, which can be interpreted as the opportunity cost of reducing an additional unit of undesirable output in terms of forgone desirable output or, equivalently, as the marginal cost of pollution abatement (Coggins and Swinton, 1996; Hailu and Veeman, 2000). The use of a non-stochastic linear programming technique allows us to estimate a distance function. Though linear programming does not produce statistics for the degrees of fitness,3 it dose enable us to impose inequality restrictions associated with desirable and undesirable outputs or inputs (Hailu and Veeman, 2000). More advantages of the distance function approach over the cost function approach include the fact that information on input prices and regulatory constraints is not required, and that it is not necessary to maintain the hypothesis concerning cost minimization (Grosskopf et al., 1995).4 In addition, the use of a nonparametric data envelopment analysis makes it possible to circumvent the presence of residual autocorrelation even when time series or panal data are used (see Fa¨re et al., 1989; Yaisawarng and Klein, 1994). All literature employing a distance function measures the shadow prices of pollutants as the opportunity cost of abatement in terms of forgone outputs. But estimates of the shadow price of SO2 fail to account for the substitution possibility between sulfur and productive capital.5 Either investments in improving boiler fuel-efficiency or shifts to production processes that are effective in removing SO2 can be used to meet legal emissions limits in the long run. The more substitutable sulfur and capital are, the less costly 2

Due to lack of information, Gollop and Roberts define an unconstrained emissions rate as the average of emissions rates greater than 1.5 pounds per Mbtu. This uniform definition pays no regard to differences in allowed emissions limits and fuel-quality environments facing different firms. 3 To overcome this limitation, Grosskopf et al. (1995) use a bootstrapping methodology. Recently, a few authors including Atkinson et al. (2003) estimate the stochastic distance function. 4 However, Kolstad and Turnovsky (1998) indicate that unobservable distance functions and endogeneity of explanatory variables might cause econometric problems. 5 A referee argues that earlier papers do not explicitly specify that relationship but do not preclude such trade-offs. However, it depends upon the sample period they use. The use of cross-sectional data or a few years’ worth of panal data could hardly capture substitution between sulfur and capital occurring in the long run.

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sulfur regulation is, ceteris paribus. As a result, it would be more appropriate to estimate SO2 abatement costs as the opportunity costs of lowering sulfur in terms of forgone capital. Porter (1991) suggests that an increase in the stringency of environmental regulations may stimulate innovation, resulting in a positive impact on economic performance. This view is called the ‘Porter hypothesis’.6 A high substitutability of sulfur and capital is likely to support the Porter hypothesis in the long run. In this paper, following Kolstad and Turnovsky (1998), we quality-differentiate coal into quantities of heat, sulfur, and ash. The use of an input distance function not only permits estimation of the shadow prices of sulfur and ash in terms of forgone capital, but also the indirect elasticities of substitution between inputs, particularly the substitution possibilities of capital for sulfur. We use data from 51 coalfired units in 38 plants.7 We also compare differences in the shadow prices of sulfur between units of the same plant and between plants This paper is organized in the following manner. Section 2 defines an input distance function with ‘good’ inputs and ‘bad’ inputs and provides the formula for indirect elasticities of substitution. A methodology for estimating the shadow price of sulfur is described in Section 3. Empirical results are analyzed in Section 4. Section 5 concludes.

2. The input distance function Consider a technology that produces an output y with a N vector of inputs x 2RC . The vector of inputs not only H includes ‘good’ ones, x1 2RC , but also ‘bad’ ones, NKH x2 2RC , so that xZ[x1,x2]. Denoting B(y)Z{x: x can produce y} as the input set, we define the input distance function introduced by Shephard (1953), which measures the maximum amount by which all inputs can be proportionally reduced while maintaining the level of output (Fa¨re and Grosskopf, 1990; Hailu and Veeman, 2000): Iðy; x; tÞ Z supfdO 0 : x=d 2BðyÞg

(1)

where t is a time index allowing for technological change. Note that x2B(y) if and only if I(y, x, t)R1. The distance function is monotonically non-decreasing in x1, nonincreasing in x2, and non-increasing in y. It is also homogenous of degree one in x, i.e., increasing x by 6 Previous articles that formally analyzed the Porter hypothesis include Oates et al. (1993), Porter and van der Linde (1995), Simpson and Bradford (1996), Jaffe and Palmer (1997), Xepapadeas and de Zeeuw (1999), and Mohr (2002). All papers except Porter and van der Linde and Mohr found little strong evidence for the feasibility of the hypothesis. 7 In fact, it is individual units (generators) that are subject to the legal emission limits. However, most previous studies used company or plant level data due to lack of unit level data. This may lead to biased estimates.

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the same proportion results in an increase in the value of the distance function by a like proportion. From the definition of the input distance function, the degree of technical efficiency of the Farrell (1957) type is measured by calculating 1/I(y, x, t). Note that technically efficient production is achieved when the input distance function has a value of one. Also, the rate of technical change, defined as the rate at which inputs can be proportionally reduced over time with output held fixed, is calculated as vI(y, x, t)/vt (Hailu and Veeman, 2000). Following Blackorby and Russell (1989) and Grosskopf et al. (1995) we can compute the indirect Morishima elasticity of substitution between inputs xi and xj as Mij Z xi Iij ðy; x; tÞ=Ij ðy; x; tÞ K xi Iii ðy; x; tÞ=Ii ðy; x; tÞ

(2)

where the subscripts on the distance function represent partial derivatives with respect to inputs. Mij measures the relative change in (shadow) input prices required to support a substitution between xi and xj; a high value of Mij suggests limited substitution possibilities. In general, MijsMji because, for example, the substitutability between highand low-quality fuels is expected to be asymmetric in the production of electricity.

substitution of Eq. (4) for Px I (y, x, t) gives ws Z Cs ðy; ws ; tÞws ðy; x; tÞ:

H NKH Let ws1 2RC and ws2 2RC denote the vectors of shadow prices for ‘good’ and ‘bad’ inputs, respectively. Assume that the market price of one ‘good’ input, x1i, equals its shadow price,ws1i , for iZ1,., H. Utilizing the method used in Fa¨re et al. (1993), we can calculate the shadow prices of individual ‘bad’ inputs, x2j, for jZNKH,.,N as

ws2j Z w1i

vIðx; y; tÞ=vx2j vIðx; y; tÞ=vx1i

ln Iðx; y; tÞ Z a0 C

N X

N X N 1X 1 a ln xi ln xi’ C byy ðln yÞ2 2 iZ1 i0Z1 ii’ 2 N X

Iðy; x; tÞ Z minws fws x : C s ðy; ws ; tÞR 1g:

iZ1

(3)

The application of Shephard’s lemma yields Vx Iðy; x; tÞ Z ws ðy; x; tÞ s

(4)

N

where w 2R is a vector of shadow-cost-minimizing input prices. Consider a Lagrangian function for a shadow cost minimization problem, G Z ws x K lðIðy; x; tÞ K 1Þ: The first-order conditions with respect to the inputs are ws Z lðy; x; tÞVx Iðy; x; tÞ: Thanks to Shephard (1970) and Jacobsen (1972), we can show that l(y, x, t)ZCs(y, ws, t) at the optimum. In addition, 8 Without imposing cost minimization as a maintained hypothesis, Atkinson and Halvorsen propose a shadow cost function with unobservable shadow prices of inputs, which are measured by incorporating a multiplicative ‘distortion factor’ into the market price for each input. When the distortion factor is unity for all inputs, firms are successful in minimizing the total cost of production.

ai ln xi C by ln y

iZ1

C

Following Fa¨re and Grosskopf (1990), we derive the Shephard input distance function from the shadow cost function Cs(y, ws, t)Zminx{wsx: I(y, x, t)R1}, where ws 2 RN is the shadow input price vector of the Atkinson and Halvorsen (1984) type:8

(6)

This shadow price can be interpreted as the opportunity cost of reducing an additional unit of ‘bad’ input in terms of forgone ‘good’ input, which is equivalent to the marginal cost of pollution abatement to the producer. To compute ws2j in Eq. (6), a parameterization for I(x, y, t) is needed. Suppose that the input distance function takes a translog functional form

C

3. The shadow price of sulfur

(5)

C

N X

1 giy ln xi ln y C at t C att t2 2 ait t ln xi C byt t ln y

iZ1

(7) 0

where i and i index ‘good’ and ‘bad’ inputs. Following Aigner and Chu (1968) and Fa¨re et al. (1993), a linear programming technique can be used for the computation of the parameters in Eq. (7). The objective function is the sum of the deviations of the individual observation distance functions from the frontier value of P one: j ½ln Iðxj ; yj ; tj ÞK ln 1, where jZ1,., J indicates the observations. We minimize it under a number of constraints. First, (i) ln I (xj, yj, tj)R0, since I (xj, yj, tj)R1. Next, for the monotonicity condition, (ii) vln Iðxj ; yj ; tj Þ=vln xj1 R 0, vln Iðxj ; yj ; tj Þ=vln xj2 % 0, and vln Iðxj ; yj ; tj Þ=vln yj % 0. For the PN of linear PNhomogeneity PN in inputs, (iii) PN imposition a Z 1; a Z g Z iZ1 i i’Z1 ii’ iZ1 iy iZ1 ait Z 0. Finally, (iv) aii 0 Zai 0 i for symmetry.

4. Data and empirical results The data come from 51 coal-fired power units operated fully between 1977 and 1986.9 Since all units secured their 9 I am grateful to Kolstad and Turnovsky (1998) for providing me with this data. The detailed data construction is described in their data appendix.

M. Lee / Journal of Environmental Management 77 (2005) 104–110 Table 1 Parameter values for the input distance function Parameter a0 ak af as aa by akk akh aks aka ahh ahs aha ass

Value 0.0298 0.0433 0.9838 K0.0155 K0.0115 K0.9119 0.0046 0.0276 K0.0195 K0.0126 K0.0541 0.0270 K0.0005 K0.0059

Parameter asa aaa byy gky ghy gsy gay at att akt aht ast aat byt

Table 2 Indirect morishima elasticities of substitution (evaluated at the mean) Value K0.0014 0.0146 0.0566 0.0208 K0.0074 K0.0078 K0.0055 0.0006 0.0020 K0.0014 K0.0019 0.0005 0.0027 0.0085

initial license during the period 1971–1979, they can decide how to meet the sulfur dioxide emissions limit, switching to low-sulfur coal or by scrubbing.10 Quality-differentiating coal into quantities of heat (in Btu), sulfur, and ash, we have two ‘good’ inputs, capital (k) and heat (h), and two ‘bad’ inputs, sulfur (s) and ash (a). The quantity of capital is obtained by adjusting the sum of yearly construction costs using a Joskow and Rose (1985) method. The price of capital (wk) is constructed according to the Christensen and Jorgensen (1969) formula. The quantities of heat, sulfur, and ash are obtained from FERC Form 423. The quantity of output (y) in kWh is calculated by dividing the quantity of coal by the thermal efficiency. All variables in log form are normalized to have mean values of unity, and the time index t is normalized to have the value for the median year, 1982, set at zero. Imposing constraints of monotonicity, homogeneity, and symmetry, we estimate the parameters by measuring Eq. (7). The parameter estimates are presented in Table 1. These estimates are used to calculate the value of the input distance function for individual electric units. The average degree of technical efficiency (TE) weighted by output share is 94.5% for 51 electric units, with individual TEs varying from a low of 81.1% for P4; #1 to a high of 100% for P9; #1, P26; #1, P32; #1, P34; #2, and P36; #2; estimates for individual units are shown in the fifth column of Table 3. The output-share weighted average rate of technical change (TC), measured by the rate at which the input distance 10

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Because of the long lead times involved in plant construction, most units became operational in the late 1970s through the mid 1980s. The majority of them have chosen to purchase low-sulfur coals rather than install expensive scrubbers, indicating that SO2 emissions are nearly proportional to the quantity of sulfur. A referee suggests including SO2 emissions as a ‘bad’ output, leaving sulfur in the input set and estimating the shadow price of output. However, this might cause serious collinearity problems because both the quantity of sulfur and SO2 emissions are included in the distance function as arguments. In a general case where both coal contents and sulfur emissions are incorporated, the use of a directional distance function is appropriate (see Fa¨re and Grosskopf, 2004).

Elasticity of substitution

Value

Mkh Mhk Mks Msk Mka Mak

0.9209 1.6919 2.1479 0.1675 1.9899 1.9774

Elasticity of substitution Mhs Msh Mha Mah Msa Mas

Value

K0.6774 0.6462 1.0985 2.2696 0.7484 2.3664

function increases over time, is calculated to be 0.11%; estimates for individual units are shown in the sixth column of Table 3. Estimates of indirect Morishima elasticities of substitution between individual inputs, calculated from (2), are reported in Table 2; these are evaluated at the mean. The comparison of Mkh and Mhk informs us that the substitution of heat for productive capital is slightly easier than the reverse. The greater value of Mks over Msk, implies that the substitutability of sulfur for capital is lower than the substitutability of capital for sulfur. In particular, the smallest Msk indicates that substituting capital for sulfur would result in the slightest change in relative prices. Given a large proportion of sulfur to capital, plants could have reduced costs by investing in improving boiler fuelefficiency to lower sulfur in the long run, suggesting a likelihood of confirming the Porter hypothesis. Also, we find that Msk (Msa) is less than Mak (Mas). No difference between Mka and Mak is observed. The use of Eq. (6) enables us to estimate the shadow prices (or marginal abatement costs) of sulfur ðwss Þ and ash ðwsa Þ in terms of forgone capital. These estimates of sulfur and ash appear in the seventh and eighth columns of Table 3, respectively. The overall weighted average estimates of wss and wsa are K0.076 and K0.006 dollars per pound in constant 1976 dollars. If a national SO2 allowance market had been established for our sample of plants during the sample period, the average price of an allowance should have equalled approximately 0.076 dollars. The estimates of marginal abatement costs for SO2 vary from a low of zero for P13 unit #2, P15 unit #1, P23 unit #2, and P30 unit #1 to a high of 2.64 dollars per pound for P11 unit #1. The estimates of marginal abatement costs for ash vary from a low of zero for P25 unit #2 and P32 unit #2 to a high of 0.06 dollars per pound for P11 unit #1. A zero marginal abatement cost indicates that the plant operates on the horizontal segment of the input set if we draw the input set such that sulfur is on the horizontal axis and capital is on the vertical axis. Kolstad and Turnovsky (1998) derived marginal prices for sulfur and ash by estimating a quadratic hedonic price function with the same data. They obtained K0.071 dollars per pound for sulfur and K0.121 dollars per pound for ash. Thus, as the electric utilities purchase coal in the market,

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Table 3 Estimates of technical efficiency, rates of technical change, and shadow prices for sulfur and ash Plant P1 P2 P2 P3 P4 P5 P5 P6 P7 P8 P9 P10 P10 P11 P12 P13 P13 P14 Weighted averagea P15 P16 P17 P18 P19 P20 P21 P22 P23 P23 Weighted averagea P24 P25 P25 P26 P27 P28 P29 P29 P30 P31 P32 P32 P33 P34 P34 P35 P35 P36 P36 Weighted averagea P37 P37 P37 P38 Weighted averagea Overall unweighted average Overall weighted averagea a b

Unit no. 1 1 2 1 1 1 2 1 1 1 1 1 2 1 1 1 2 1 1 1 1 1 1 1 1 1 1 2 1 1 2 1 1 1 1 2 1 1 1 2 1 1 2 1 2 1 2 1 2 3 1

State

Region

IN

MI Great Lakes IL

OH

WI

IA MidWest MO

MN MD

FL

KY AR NC

South

AL WV

GA MS

PA

Northeast

wss (1976$/lb)

wsa (1976$/10lb)

K0.0100 0.0007 K0.0000 K0.0009 0.0100 0.0087 0.0065 0.0059 K0.0187 K0.0189 K0.0083 K0.0064 K0.0033 K0.0122 K0.0080 K0.0053 0.0060 K0.0096 0.0003 K0.0216 K0.0054 K0.0178 K0.0057 K0.0034 K0.0005 K0.0248 0.0110 K0.0018 K0.0047 0.0030 0.0031 0.0121 0.0126 K0.0089 K0.0002 0.0002 K0.0089 K0.0057 0.0088 0.0048 K0.0122 0.0077 0.0068 K0.0015 K0.0006 K0.0017 0.0054 K0.0264 K0.0050 0.0023 K0.0042 K0.0077 0.0004 0.0010 0.0058 K0.0031

K0.046 K0.200 K0.242 K0.012 K0.353 K0.331 K0.529 K0.042 K0.111 K0.042 K0.003 K0.029 K0.246 K2.635 K0.015 K0.108 K0.000 K0.106 K0.120 K0.000 K0.015 K0.026 K1.306 K0.095 K0.035 –b K0.027 K0.003 K0.000 K0.041 K0.292 K0.016 K0.006 K0.052 K0.062 K0.123 –b –b K0.000 K0.171 K0.051 K0.146 K0.046 K0.037 K0.020 K0.435 K0.130 K0.480 K0.011 K0.077 K0.035 K0.075 K0.061 K0.013 K0.046 K0.196

K0.124 K0.085 K0.245 K0.026 K0.110 K0.218 K0.316 K0.044 K0.081 K0.088 K0.002 K0.042 K0.224 K0.635 K0.030 K0.069 K0.010 K0.144 K0.122 K0.000 K0.028 K0.063 K0.404 K0.072 K0.055 –b K0.009 K0.007 K0.009 K0.041 K0.089 K0.014 K0.000 K0.106 K0.006 K0.120 –b –b K0.023 K0.049 K0.041 K0.000 K0.024 K0.049 K0.016 K0.302 K0.044 K0.267 K0.043 K0.060 K0.037 K0.080 K0.062 K0.006 K0.021 K0.096

0.0110

K0.076

K0.058

TE

TC

0.991 0.998 0.971 0.958 0.811 0.823 0.853 0.999 0.928 0.852 1.000 0.962 0.998 0.888 0.984 0.839 0.860 0.887 0.925 0.996 0.918 0.891 0.909 0.963 0.983 0.905 0.925 0.936 0.968 0.943 0.944 0.951 0.968 1.000 0.992 0.990 0.879 0.889 0.919 0.966 1.000 0.997 0.967 0.977 1.000 0.911 0.937 0.942 1.000 0.969 0.941 0.970 0.959 0.998 0.963 0.943 0.945

TE and TC are weighted by output; wss and wsa are weighted by the quantities of sulfur and ash, respectively. We cannot estimate the shadow prices of ‘bad’ inputs because the marginal product of capital approaches zero.

M. Lee / Journal of Environmental Management 77 (2005) 104–110

they receive compensation for sulfur equivalent to its real contribution, but compensation for ash in excess of its real contribution.11 We compare our estimates with previous studies for the electric power industry. Estimating a cost function for 56 electric utilities for 1973–1979, Gollop and Roberts (1985) found that the average estimate of marginal abatement costs for SO2 was approximately 0.195 dollars per pound.12 Restricting the sample to the electric plants in Wisconsin, Coggins and Swinton (1996) derived the average shadow price of SO2 (in constant 1992 dollars) in terms of forgone electricity to be about K0.133 dollars per pound.13 Assigning our sample of plants to each of the four geographic regions (Great Lakes, Midwest, South, and Northeast), we examine how significantly marginal abatement costs for SO2 differ across regions.14 A comparison of regional weighted averages of wss reveals that plants in the Great Lakes exhibit the highest mean marginal abatement costs—nearly two or more times as large as those shown in other regions. This finding could be explained by the fact that plants in the Great Lakes area faced the most severe required emission reductions over the period 1977–1986, as indicated by Gollop and Roberts (1985). Marginal abatement costs for SO2 also vary substantially within states, and we can observe differences between plants and between units within plants. In Indiana, differences in marginal costs between plants vary from 0.034 to 0.341 dollars per pound. P2 operates two units; their marginal costs differ by only 0.042 dollars per pound, meaning that the largest difference between plants is more than eight times that between units of the same plant. In Michigan, the difference in marginal costs between P5 units #1 and #2 is 0.198 dollars per pound, which is less than those between plants. Similarly, the difference between units within P34 is smaller than that between P33 and P34 unit #2 in West Virginia. In Florida, marginal costs for units within P25 differ by 0.01 dollars per pound, while the range of differences between plants is 0.01–0.056 dollars per pound. P37 consists of three units in Philadelphia. 11 According to the American Coal Ash Association (ACAA), coal combustion products that are mainly made of fly ash were widely used to produce road base materials, manufactured aggregates, flowable fills, structural fills and embankments, etc. in the 1980s and 1990s. To a certain extent, then, sales of ash would bring miscellaneous revenues to power plants. 12 This estimate was obtained by taking the arithmetic mean of emissionshare weighted average estimates for four regions; the western area was excluded for comparison with our estimates. 13 Our sulfur-share weighted average estimate for four units in Wisconsin is K0.109 constant 1992 dollars per pound, inflated by the producer price index. 14 Gollop and Roberts (1985) classified plants into five regions, including the West, and calculated the potential cost savings from a system of regional SO2 allowance markets. However, Kolstad and Turnovsky (1998) argued that most plants in the western region were essentially unconstrained by the legal standard due to cheap access to local low-sulfur coal. As a result, they eliminated the western plants from their sample.

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The largest difference in marginal costs between their units is 0.04 dollars per pound; the smallest difference is 0.014. Marginal costs differ by up to 0.062 dollars per pound across plants. In Illinois, the difference within plants is relatively significant but falls short of the maximum difference between plants. Unlike previous states, differences between plants are less than that between units within P13 in Wisconsin. In Iowa, where each individual plant contains only one unit, differences between plants range from 0.015 to 1.306 dollars per pound. In Minnesota, Alabama, Georgia, and Mississippi, only one single plant with two units is reported for each state. Differences between the two units of the same plant across those states vary from 0.003 to 0.469 dollars per pound. Thus, comparisons of unit-specific marginal abatement costs for SO2 enable us to reach the conclusion that differences between plants are generally larger than those between units within the same plant. Much the same result applies to the differences in marginal abatement costs for ash. There are two major types of allowance trading: internal (within a single plant) and external (between plants). Since the 1970 Clean Air Act created a basis for a tradable allowance system, the majority of emissions trading was internal (Hahn and Hester, 1989). Given a wider divergence of SO2 abatement costs between plants than within plants, the potential cost savings would seem to be greater for external trading. A poor record of external trading appears to be attributable to the high transaction costs associated with the acquisition of information on other plants’ willingness to trade. The uncertainty of the system also kept plants from pursuing allowances from outside. Internal trading is more secure regardless of whether or not the system is discontinued. Even after the auctions for Phase I and Phase II allowances were conducted by the EPA in 1993 and the SO2 allowance market became active nationally in 1994, more than two-thirds of the total cumulative allowances transferred through 2001 were traded privately. Of 133 million cumulative private allowances reported to the EPA tracking system, about 57 percent were transferred within companies. Therefore, it might be necessary to lower transaction costs and encourage external trading by improving the system; the effect on social net benefits would depend upon how much further a shift from internal to external trading could reduce abatement costs.

5. Conclusions Faced with restrictions on sulfur dioxide emissions, plants might choose long-run strategies that involve either an investment in improving boiler fuel-efficiency or a shift to a production process that is effective in removing sulfur dioxide. To allow for the possibility of substitution between sulfur and productive capital, we measure the shadow price

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M. Lee / Journal of Environmental Management 77 (2005) 104–110

of sulfur dioxide as the opportunity cost of reducing sulfur emissions in terms of forgone capital. The input distance function is estimated with data from 51 coal-fired units in 38 plants operating between 1977 and 1986. The indirect Morishima elasticities of substitution indicate that the substitutability of capital for sulfur is relatively high. This finding is likely to support the Porter hypothesis in the long run. The overall weighted average shadow price estimate for sulfur is K0.076 dollars per pound in constant 1976 dollars; this is less than the previous estimates of the shadow price of sulfur dioxide obtained by ignoring the substitution possibility between sulfur and capital. It is found that differences in marginal abatement costs for sulfur dioxide between plants are generally larger than those between units in the same plant. In order to maximize the social net benefit from the sulfur dioxide allowance market, it is essential to make system improvements that will lower transaction costs and encourage external trading.

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