Exploring shadow prices of carbon emissions at provincial levels in China

Ecological Indicators 46 (2014) 407–414

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Ecological Indicators journal homepage: www.elsevier.com/locate/ecolind

Exploring shadow prices of carbon emissions at provincial levels in China Xingping Zhang ∗ , Qiannan Xu, Fan Zhang, Zhengquan Guo, Rao Rao North China Electric Power University, Box 80, Hui Long Guan, Chang Ping District, Beijing 102206, China

a r t i c l e

i n f o

Article history: Received 9 December 2013 Received in revised form 3 July 2014 Accepted 8 July 2014 Keywords: Carbon dioxide emissions Shadow prices Distance function Abatement cost

a b s t r a c t Since carbon emissions are considered to contribute the lion’s share in global warming, extensive studies have been devoted to measuring the carbon emissions abatement cost in various ways. This paper derives the shadow prices of China’s aggregate carbon emissions at provincial levels by using directional output distance function and Shephard output distance function. The empirical results indicate that the shadow prices estimated by the directional distance function with directional vector of (1,−1) are significantly higher than those estimated by Shephard distance function, which implies that the green production technology is very expensive for the developing country of China. In addition, the shadow prices of carbon emissions present a rising trend during the sample period, which implies that it is increasingly costly for China to regulate CO2 emissions. Moreover, the shadow price is positively correlated with regional economic development levels. Generally, the shadow price of the high income regions is significantly bigger than that of low income regions. Therefore, China should promote regional scheme of carbon emissions reduction, such as regional carbon emissions trading scheme, to fulfill its ambitious target of carbon emissions reductions. © 2014 Elsevier Ltd. All rights reserved.

1. Introduction Since 1970, global ecological footprint has exceeded biocapacity and the discrepancy between the two has increasingly enlarged. Carbon footprint is the largest individual component of global ecological footprint, and carbon emission reduction has been a highlight of the world. China has been the largest carbon emitter in the world since 2007 and the biggest energy consumer since 2010. In 2008, although China’s per person ecological footprint was just 80% of the global average, China has the largest ecological footprint in the world due to its huge population size. Motivated by the fact, this paper estimates the cost of carbon emissions reduction at provincial levels in China since China features a significantly differentiated development mechanism in various regions. Understanding differences across regions can help to identify the factors influencing supply and demand of ecological services in China and allow efficient measures for limiting the growth of China’s carbon footprint to be developed. However, carbon emissions reduction is not free, and it may be expensive for some countries. Extensive studies have been

∗ Corresponding author. Tel.:+86 10 61773096; fax: +86 10 80796904. E-mail address: [email protected] (X. Zhang). http://dx.doi.org/10.1016/j.ecolind.2014.07.007 1470-160X/© 2014 Elsevier Ltd. All rights reserved.

conducted to measure the costs of carbon emissions reduction. Since undesirable outputs like carbon dioxide are non-marketable and cannot be reasonably priced in accordance with general commodities, the costs to reduce carbon emissions have not been included in the accounting system. It is not beneficial to the regulation of factories’ discharges or the implementation of emission-cutting policies. Shadow prices, or the marginal abatement costs of undesirable outputs, which can be interpreted as the opportunity cost of reducing an additional unit of undesirable output in terms of forgoing desirable output, are introduced to price the undesirable outputs properly. Cost function and distance function are the two commonly used methods to estimate the marginal abatement costs of undesirable outputs. Cost function can provide information about the relation between the marginal abatement costs of pollutants and actual emission levels under the assumption concerning cost minimization. However, the assumption of cost-minimizing behavior, which is essential in this method, limits its empirical application since this assumption is improper for the cases where the actions of the parties involved have some public aspects. Distance function, originally introduced by Shephard (1970) and applied by Färe et al. (1993) in empirical fields, has advantages over the cost function method. A distance function requires no behavioral assumptions concerning cost minimization or revenue maximization (Kumbhakar and Lovell, 2000).

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X. Zhang et al. / Ecological Indicators 46 (2014) 407–414

In addition, information on output and input prices or regulatory constraints are not required in a distance function framework (the price data of pollutants are usually unavailable). Therefore, the distance function method has been broadly employed to estimate the shadow prices of undesirable outputs. Generally, a distance function can be estimated in two different ways, i.e., the nonparametric data envelopment analysis (DEA) and parametric approach. The advantage of the DEA is that it does not require the specific functional form for the technology. It has been used in various contexts in which undesirable outputs are present. For example, taking the thermal power sector of China as a case, Kaneko et al. (2010) discussed the marginal abatement costs of SO2 . Choi et al. (2012) employed the slacks-based DEA model to estimate the marginal abatement costs of CO2 emissions for China’s 30 provinces during 2001–2010. However, the DEA is based on a piece-wise linear production frontier that is not differentiable and, hence, its principle disadvantage is that it may be problematic to obtain the relevant abatement costs information. Two primary parametric approaches have been used to estimate the marginal abatement costs in distance function framework. The first parametric approach uses econometric estimation to determine the best-fit distance function (e.g., Lovell et al., 1994; Grosskopf et al., 1997). The principle advantage of this technique is that it is better able to accommodate measurement or other random error and allows for hypothesis testing. However, Coelli and Perelman (1999) indicated that this approach limits the researcher’s ability to apply a priori inequality restrictions on the distance function, a procedure that is easily accomplished with the deterministic approach. As a result, this technique is the most commonly used when all outputs are considered beneficial. The second parametric deterministic approach is originated by Färe et al. (1993) in which the distance function is estimated by using an Aigner and Chu (1968) linear program. Färe and Grosskopf (1998) indicated that this technique is the most common approach of the three primary approaches used to estimate marginal abatement costs in a distance function framework. The advantage of this technique is that the distance function is given a specific differentiable functional form, usually a translog due to its particular flexibility. And it has been widely used in various contexts in which undesirable outputs are present. For example, Lee (2005) estimated shadow prices of SO2 with data from coal-fired US power units operating between 1977 and 1986. Hu et al. (2008) found the marginal abatement cost of SO2 in western areas of China is the highest and that of central areas is the lowest. The directional output distance function appeals to the environmental policies because it allows the expansion of desirable outputs and the reduction of undesirable outputs simultaneously. Correspondingly, the quadratic functional form is usually employed to parameterize the directional output distance function, for the former allows restrictions required by the translation property and experts in the second-order approximation of unknown distance functions. Based on the directional/quadratic method, Matsushita and Yamane (2012) derived shadow prices of CO2 and low-level waste in the case of the electric power sector in Japan. Following this line of research, this paper derives shadow prices of CO2 emissions at China’s provincial levels. China has set an ambitious target of CO2 emission intensity reduction during the 11th Five-Year Plan period (2006–2010), and therefore this period is taken as the sample. Compared with the nonparametric method, the parametric approach has the advantage of providing an estimated parametric representation of the true production technology that is everywhere differentiable. The very feature implies shadow prices can be defined through the assumption the observed price of one desirable output equals its shadow price (Kwon and Yun, 1999). Moreover, we can introduce time trend in parametric approach to capture the effect of neutral technical change. In addition, both

Shephard distance function and the directional distance function are used to explore shadow price of carbon emissions in this paper, which can measure the shadow prices of carbon emissions in different production technologies and provide more insights for policy makers. Shephard output distance function considers the maximal possible proportional expansions onto the boundary of production technology about the observed desirable and undesirable outputs, which is relatively complied with the current production technology. In addition, this paper uses the directional output distance function to estimate shadow prices of pollutants by choosing the directional vector g = (1,−1). This setting will credit the production units for simultaneously expanding good output and contracting bad output production with constant input. Due to this, the results of shadow prices measured by this approach might be respectively high (Vardanyan and Noh, 2006; Choi et al., 2012). To some extent, the shadow price of carbon emissions estimated by directional function may represent the cost of using green production technology which requires reduction in bad outputs. The remainder of this paper is organized as follows. Section 2 mainly introduces the directional output distance function and derives two shadow price models. Section 3 presents the empirical results of shadow prices of CO2 emissions. Section 4 discusses empirical results and provides some policy implications in emissions reductions. The final conclusions are summarized in Section 5.

2. Methods A common feature of Shephard distance function is that they assume the maximal possible proportional expansions onto the boundary of production technology about the observed desirable and undesirable outputs. However, the directional output distance function can expand desirable outputs and contract undesirable outputs simultaneously by choosing a particular direction vector. In fact, the directional output distance function is a generalization of the Shephard output distance function, or the latter is a special case of the former (Färe et al., 2006).

2.1. The directional output distance function In fact, the directional output distance function is a functional representation of the production technology. The production units employ inputs (x) to produce good (desirable) outputs (y) and bad (undesirable) outputs (b). The production technology is expressed as P(x) = {(y, b): x can produce (y, b)}. In line with Chung and Färe (1995) and Färe et al. (2006), we specify the production technology by imposing some assumptions. P(x) is a compact set with P(0) = {0,0} and inputs are strongly or freely disposable. We define g = (gy ,gb ) as the direction vector, and assume g = / 0. The directional output distance function can be described as



→



D0 (x, y, b; gy , gb ) = max ˇ : (y + ˇgy , b − ˇgb ) ∈ P(x) ,

(1)

The function denotes that the simultaneous maximum reduction in bad outputs and expansion in good outputs are feasible in a given production technology. As illustrated in Fig. 1, the production unit A = (b,y) can expand y and contract b along the g1 direction until it reaches the boundary of P(x) at the point A1 = (b − ˇ*gb , y + ˇ*gy ), →

where, ˇ∗ = D0 (x, y, b; g). The distance function takes the value of zero for technically efficient outputs on the boundary of P(x), while positive values suggest inefficient outputs inside the boundary. Corresponding to homogeneity of the standard Shephard output distance function, the

X. Zhang et al. / Ecological Indicators 46 (2014) 407–414

Following Färe et al. (2006) and Yuan et al. (2011), we can recover the directional output distance function given in Eq. (1) from the revenue function as

y=good output

+β * , y -β g b b ( = A1

* g y)

A2

→

D0 (x, y, b; g) = minp {

g2

P(x)

→

∇ y D0 (x, y, b; g) = −

b=bad output

→

o

∇ b D0 (x, y, b; g) = Fig. 1. The directional output distance function.

D0 (x, y + ˛gy , b − ˛gb ; g) = D0 (x, y, b; g) − ˛

qj = −pm

(3)



where D0 (x, y, b) = min  : (y/, b/) ∈ P(x) represents Shephard output distance function. Shephard output distance function is a special case of the directional output distance function. The reciprocal of Shephard output distance function gives the maximum proportional expansion of both desirable and undesirable outputs, which is feasible given the output set P(x). The output distance function measures the maximum potential radial output expansion given observed inputs, shown as (OA/OA2 ) in Fig. 1. Under the technology represented by Shephard output distance function, the production unit A reaches the boundary A2 of P(x) along the g2 direction (see Fig. 1), but not g1 direction.

D0 (xk , yk , bk ; 1, −1) = c0 +

2 + 12 ˇbk

+

N 

N 

dn xnk + c1 yk + c2 bk +

n=1

ın xnk yk +

n=1

N  n=1

The generating units (y,b) either lie on the production frontier, →

or inside the frontier, i.e. D0 (x, y, b; gy , gb )≥0. Based on this point, the revenue function can also  be described as  →

∂D0 (x, y, b)/∂bj

py − qb − lx : D0 (x, y, b; g) ≥0

(10)

∂D0 (x, y, b)/∂ym

2.3.1. The quadratic distance function form In line with Färe et al. (2005) and Fukuyama and Weber (2008), this paper chooses g = (1,−1) as the directional vector, which means the unit expansion of good outputs and the unit reduction of bad outputs in given inputs. The directional vector not only simplifies the estimation of parameters, but satisfies the translation property of the directional output distance function. The specific parametric quadratic function form is defined as

(4)

→k

(9)

→

Generally, the directional output distance function is parameterized by the quadratic functional form, because the latter allows restrictions required by the translation property and experts in the second-order approximation of unknown technology. The flexible translog functional form does not impose strong disposability of outputs and is widely used to estimate Shephard output distance function.

The undesirable outputs are generally non-marketable, whose values can be deduced from the relation between the directional distance function and the revenue function. Let p = (p1 , . . . pM ) represent the price vector of good outputs, and let q = (q1 , . . . qn ) represent the price vector of bad outputs, and also l = (l1 , . . . lN ) is the price vector of inputs. The maximal revenue function is defined as



∂D0 (x, y, b; gy, gb )/∂bj

2.3. The parameter estimation

2.2. The shadow price model



(8)

To compute the price of undesirable outputs, we follow Färe et al. (1993) and Rezek and Blair (2005) in assuming that the shadow price of the desirable output equals its observed price. The frontier shadow price is calculated by substituting the frontier values of y and b when evaluating the derivatives above. Accordingly, the prices of bad outputs can be calculated if one of the prices of good outputs is observable.



R(l, p, q) = maxx,y,b py − qb − lx : (y, b) ∈ P(x)

q ≥0 pgy + qgb

Correspondingly, the shadow price derived by Shephard output distance function is described as

If the directional vector is (y,–b), the relation between the directional distance function and Shephard output distance function is established as follows: 1 D0 (x, y, b; y, −b) = −1 D0 (x, y, b)

(7)

∂D0 (x, y, b; gy, gb )/∂ym

(2)

→

p ≤0 pgy + qgb

→

qj = −pm

→

(5)R (l, p, q) = maxx,y,b

(6)

If the price of one desirable output, say the mth is known, the j = 1, . . ., J nominal undesirable output prices can be recovered as

directional distance function has the following translation property: →

R(l, p, q) − (py − qb − lx) } pg y + qgb

Applying the envelope theorem twice to Eq. (6), we obtain the calculation of shadow price

A=(b,y)

g1=(gy,-gb)

409

1 2

N N   n=1 n=1

n xnk bk + yk bk + v1 t +

1 v t2 2 11

+

cn,n xnk xnk + 12 ˛yk2 N 

(11) n xnk t + ωyk t + bk t

n=1

where, t is the time trend variable and the effect of neutral technical change is captured by v1 and v11 . The extent of biased technical change is estimated by  and the effects of changes in output are estimated by ω and  (Matsushita and Yamane, 2012). We estimate the parameters of Eq. (11) by solving the following minimization problem. The objective minimizes the sum of the

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X. Zhang et al. / Ecological Indicators 46 (2014) 407–414

deviations of the estimated distance functions from the frontier technology in each period. min

K T  

→ [D0t (xkt , ykt , btk ; 1, −1) − 0]

(12)

∂ ln D0 (xk , yk , bk )/ ln y≥0,

k = 1, ..., K

∂ ln D0 (xk , yk , bk )/ ln b ≤ 0, ∂ ln D0 (xk , yk , bk )/ ln xnk ≤ 0,

(ii)

k = 1, ..., K n = 1, ..., N,

(iii) k = 1, ..., K

(iv)

t=1 k=1

c1 + c2 = 1, ˛ +  = 0, ˇ +  = 0, ın + n = 0, ω +  = 0,

subject to →

D0t (xkt , ykt , btk ; 1, −1)≥0,

k = 1, ..., K, t = 1, ..., T

→

∂D0t (xkt , ykt , btk ; 1, −1)/∂y ≤ 0,

k = 1, ..., K,

t = 1, ..., T

n = 1, ..., N cn,n = cn,n ,

n = 1, ..., N

(vi)

(ii) 3. Results

→

∂D0t (xkt , ykt , btk ; 1, −1)/∂b≥0,

k = 1, ..., K, t = 1, ..., T

∂D0t (¯x, ykt , btk ; 1, −1)/∂xn ≥0,

k = 1, ..., K, n = 1, ..., N,

→

t = 1, ..., T

(iii) 3.1. Data and variables (iv)

c1 − c2 = −1, ˛ = ˇ = , ın − n = 0, ω −  = 0, n = 1, ..., N

(v)

cn,n = cn ,n , n = 1, ..., N

(vi)

The restriction given by (i) ensures feasibility of the output–input vector for each observation in each period. The inequality constraints in (ii) and (iii) impose the monotonicity, ensuring that the calculated shadow prices are of the correct sign. We also impose positive monotonicity on the inputs in (iv). That is, at the mean level of inputs, x¯ , an increase in input usage holding good and bad outputs constant, causes the directional output distance function to increase, implying greater inefficiency. The parameter restrictions in (v) are due to the translation property. The form of every restriction will change if a different directional vector is chosen (Färe et al., 2006). Symmetry conditions are imposed in (vi). 2.3.2. The translog distance function form Without imposing strong disposability of outputs, the flexible translog functional form is widely used to estimate Shephard input and output distance function (Lee, 2005; Kwon and Yun, 1999). Specifically, the translog function form is defined as: ln D0 (xk , yk , bk ) = c0 + + 12

(v)

(i)

N N  

N 

N 

+

Kt = Kt−1 (1 − ıt ) + It

n=1

cn,n (ln xnk )(ln xnk )+

n=1 n=1 1 ˛(ln 2

dn ln xnk + c1 ln yk + c2 ln bk

2

yk )2 + 12 ˇ(ln bk ) +

N 

ın ln xnk ln yk

(13)

n=1

n ln xnk ln bk +  ln yk ln bk +

n=1

v1 t + 12 v11 t 2 +

N 

n ln xnk t + ω ln yk t +  ln bk t

n=1

Similarly, the parameters can be estimated by the following linear programming problem:

 K

max

The shadow price of CO2 emissions is estimated by using data of different provinces of mainland China (except Hong Kong and Macao of China) during the 11th Five-Year-Plan (2006–2010). Tibet is excluded for its incomplete data, so the dataset in this paper covers 30 provinces and regions (22 provinces, four municipalities, and four autonomous regions). Specifically, each province or region uses energy consumption (tons of standard coal equivalent, TCE), capital stock(108 Yuan, Yuan represents the monetary unit of China), and labor force (104 person) as inputs and produces one desirable output in the form of GDP (108 Yuan) and one undesirable output in the form of CO2 emissions (104 ton). GDP, energy consumption, and labor are available in the China Statistical Yearbook and China Population Statistical Yearbook. All the monetary variables including GDP and capital stock have been converted into 1995 constant prices with GDP deflectors. As a frequently-used variable in the literature, labor force is represented in terms of total population or labor wages (Soytas et al., 2007). Zhang and Cheng (2009) pointed out that the urban population seemed to share the common change trend with GDP in China, and explained the reason in detail. Following Zhang and Cheng (2009), we choose urban population as the proxy of labor force. To the best of our knowledge, the data on capital stock cannot be obtained from any statistical yearbook or database directly. Following Hu and Kao (2007) and Zhang et al. (2012), we apply the following perpetual inventory method to calculate the capital stock. (15)

where Kt is the gross capital stock in current year; Kt−1 is the gross capital stock in the previous year; ı represents the depreciation rate of capital stock and is set to 6% in accordance with the suggestions of many relevant studies such as Wu (2004) and Zhang et al. (2012); It is the gross fixed capital formation in the current year, which needs to be calculated at 1995 constant prices with GDP deflectors. Chongqing became a municipality out of Sichuan province of China in 1997, and the capital stock of the initiative year (t = 1995) is obtained from Sun and Zhi (2010). China has not promulgated the data of carbon emissions. Following Shu (2012), this paper estimates carbon emissions at China provincial levels by using Eq. (16). CO2 =

8 

Ei × Fi

(16)

i=1

[ln D0 (xk , yk , bk ) − ln 1]

(14)

k=1

subject to ln D0 (xk , yk , bk ) ≤ 0,

k = 1, ..., K

(i)

where CO2 is the total carbon emissions from fossil energy consumption; i indicates the types of fossil fuels, including coal, coke, crude oil, gasoline, kerosene, diesel, fuel oil, and natural gas; Ei is the amount of consumption of fuel i; Fi is the IPCC carbon emission factor of fuel i.

X. Zhang et al. / Ecological Indicators 46 (2014) 407–414

411

Table 1 Descriptive statistics (30 provinces, 5 years, 2006–2010). Variable

Units

Outputs y = GDP b = CO2 emission

Mean

108 Yuan 104 ton

8175.025 32,723.65

Inputs x1 = labor force x2 = capital x3 = energy consumption

104 person 108 Yuan 104 TCE

2056.98 20,005.5 11,293.12

The descriptive statistics for all data used are summarized in Table 1. 3.2. The empirical results In view of the two parametric linear programming models above, we estimate the values of parameters respectively (see Table 2). For the directional distance function, we should test whether the condition of null-jointness between desirable output and undesirable output is satisfied. Recall that (y, b) ∈ P(x) →

if and only if D0 (x, y, b; 1, −1)≥0. Thus, the null-jointness can →

be tested by observing the values of D0 (x, y, 0; 1, −1) for y>0. →

/ P(x), then the property of nullIf D0 (x, y, 0; 1, −1) < 0, (y, 0) ∈ jointness is feasible. Without undesirable outputs, there are no desirable outputs. And the two ones are jointly produced. The test results indicate that the null-jointness condition is satisfied for 90.7% of the observations (136/150), which is an acceptable result to guarantee the following calculation. After obtaining the values of parameters, we can calculate the shadow prices of carbon emissions using Eqs. (9) and (10), which can be interpreted as the opportunity cost of reducing an additional unit of undesirable output (CO2 ) in terms of forgoing desirable output (GDP). The resulting shadow prices are shown in Table 3, in which the last line represents the national average shadow prices weighted by the proportion of provincial CO2 emissions. 4. Discussion and policy implications The empirical results showed in Table 3 indicate that shadow prices estimated by the directional distance function are significantly higher than those estimated by Shephard distance function. This situation is expected since the directional vectors in the two distance functions are different. Shephard distance function assumes the maximal possible proportional expansions onto the boundary of production technology about the observed desirable and undesirable outputs. However, g1 = (1,–1) is chosen as

St. dev.

Min.

Max.

6643.428748 22,683.73

501.257 2458.222

30,219.33 111,400.50

1301.138 15,619.95 7233.38

215.14 1803.83 920.45

6173.20 74,603.55 34,807.77

the directional vector of the directional distance function, which means a unit expansion of GDP accompanied by a unit contraction of carbon emissions given inputs. In doing so, green production technology may be required and the carbon emissions abatement cost must be expensive. The marked high shadow prices estimated by the directional distance function used in this paper imply that the green production technology is very expensive for the developing country of China. Therefore, the developed countries should give the developing countries technical support in order to mitigate the global climate changes. The empirical results intuitively indicate a positive correlation between the shadow prices and the income level. In order to illustrate clearly this situation, we order the provinces in Table 3 by the GDP per capita of 2010. Simply, 30 provinces are classified into three: provinces with high income level (the GDP per capita is more than 19 thousand Yuan), provinces with middle income level (the GDP per capita is less than 19 thousand and more than 10 thousand Yuan), and provinces with low income level (the GDP per capita is less than 10 thousand Yuan). The shadow prices of high income provinces are significantly larger than that of the other provinces. In the high income provinces, Fujian province evidences the averagely highest shadow price of 62.8 Yuan estimated by Shephard distance function, while Guangdong province witnesses the averagely highest shadow price of 176.81 Yuan estimated by the directional distance function. Liaoning province features the averagely lowest shadow price in any case (27.35 Yuan and 103.39 Yuan, respectively). In the middle income provinces, Sichuan has the highest shadow price of 23.66 Yuan estimated by Shephard distance function, while Henan province witnesses the averagely highest shadow price of 95.15 Yuan estimated by the directional distance function. Helongjiang province features the averagely lowest shadow price of 11.1 Yuan and 32.78 Yuan. Shadow prices, estimated by Shephard distance function, of all low income provinces except Jiangxi and Guangxi provinces are less than 10 Yuan. It is worth noting that Shanxi province, a major coal producer, features the averagely lowest shadow price of 3.49 Yuan and 5.57 Yuan estimated by Shephard and directional distance functions, respectively.

Table 2 Parameter values for directional and Shephard model. Parameters

Directional

Shephard

Parameters

Directional

Shephard

c0 d1 d2 d3 c1 c2 c11 c12 c13 c22 c23 c33 ˛ ˇ

−0.06588 0.23246 1.05403 −0.02611 −0.99574 0.00426 −0.10779 −0.55794 1.06385 −0.04207 0.05184 −1.08958 −0.01130 −0.01130

−0.29242 −0.49587 −0.39854 −0.00080 1.00660 −0.00660 0.02937 0.44377 0.00076 −0.60264 0.00016 −0.00015 0.00542 0.00542

ı1 ı2 ı3 1 2 3 

−0.01515 0.07073 0.00020 −0.01515 0.07073 0.00020 −0.01130 0.00890 −0.00170 −0.03370 0.03507 0.00022 −0.00189 −0.00189

−0.01222 0.00334 −0.00011 0.01222 −0.00334 0.00011 −0.00542 −0.00082 −0.00041 0.00652 −0.01632 0.00001 −0.00004 0.00004

v1 v11 1 2 3 ω 

412

Table 3 Shadow prices of different provinces, 2006–2010. Provinces

4.510 3.216 2.774 2.494 2.449 2.073 1.978 1.927 1.906 1.497 1.421 1.413 1.347 1.288 1.280 1.264 1.124 1.061 1.016 1.015 0.986 0.980 0.969 0.915 0.875 0.862 0.790 0.685 0.605 0.461 1.506

Shephard/translog (Yuan/ton)

Directional/quadratic (Yuan/ton)

2006

2007

2008

2009

2010

Average

2006

2007

2008

2009

2010

Average

44.68 42.12 48.43 42.67 38.89 61.14 38.01 32.01 26.22 9.32 10.59 18.89 19.92 15.14 15.66 13.06 19.54 14.78 11.22 21.74 14.06 2.92 24.22 3.80 5.80 22.92 7.13 8.67 4.80 3.46 22.42

50.48 45.48 51.01 39.90 40.83 61.90 35.42 33.42 26.01 9.90 10.49 19.83 20.24 18.65 16.30 16.03 20.03 14.51 10.55 20.16 13.17 3.24 22.45 4.42 6.43 23.09 7.20 8.30 5.42 3.50 23.00

51.74 53.72 53.20 43.87 44.72 67.60 36.34 35.34 28.42 10.23 11.68 17.72 20.82 19.13 16.56 17.47 20.78 13.91 11.63 19.31 11.10 3.02 21.68 4.63 6.53 25.21 7.30 8.87 6.63 3.72 24.04

56.54 58.18 56.08 45.09 46.91 60.91 39.53 38.53 29.37 11.91 13.49 20.91 21.65 18.75 15.84 21.04 21.81 11.88 12.96 20.42 10.32 3.65 24.09 5.22 7.28 26.62 7.43 9.09 6.32 3.57 25.45

56.60 53.80 57.01 45.34 50.35 62.73 47.13 41.13 26.57 13.49 12.22 21.35 23.15 20.04 17.78 22.65 22.94 12.57 12.42 23.23 13.60 4.57 25.55 5.73 7.73 25.56 6.83 9.43 7.27 4.49 26.94

52.22 51.03 53.27 43.46 44.66 62.08 39.65 36.40 27.35 11.10 12.25 19.84 21.26 18.47 23.66 18.41 21.25 13.36 11.79 21.00 12.36 3.49 23.6 4.87 6.81 24.77 7.16 8.87 6.15 3.76 24.37

173.51 118.07 135.92 142.22 105.88 102.36 170.47 104.94 81.88 38.06 31.26 50.63 73.73 79.99 42.13 42.76 45.39 49.89 48.90 91.15 50.13 4.16 73.98 16.52 21.32 49.05 46.59 48.14 11.75 20.65 75.30

176.38 122.76 139.52 145.19 106.16 105.32 181.88 108.17 93.99 40.30 43.19 52.64 78.53 82.68 45.16 57.41 46.95 50.15 49.56 94.67 51.59 5.86 78.15 17.27 21.76 51.37 49.07 53.34 13.68 20.44 80.15

157.58 124.14 119.15 149.20 114.06 107.10 170.55 113.93 108.58 27.28 46.17 43.15 72.68 73.09 29.48 60.06 49.54 33.72 42.21 96.32 37.80 4.76 67.59 14.09 18.08 38.35 40.01 45.31 14.61 20.71 77.67

151.51 126.08 108.59 153.26 117.92 107.19 174.24 117.41 111.58 28.31 53.70 46.98 77.51 69.95 23.78 68.50 51.43 28.18 41.64 95.07 31.78 5.46 59.94 18.43 19.50 34.84 37.91 52.36 15.45 21.10 78.69

162.82 122.14 123.92 158.45 140.10 112.11 184.99 120.02 116.19 31.39 65.91 57.33 86.54 89.78 50.83 81.40 55.48 43.48 65.92 97.77 56.99 7.46 82.01 21.07 15.18 56.05 61.97 54.53 14.69 22.54 89.15

164.07 122.70 125.12 150.09 117.80 107.28 176.81 113.41 103.39 32.78 48.99 50.33 78.14 79.44 72.21 63.36 50.02 40.35 49.95 95.15 45.41 5.57 72.33 17.75 19.02 46.19 47.77 50.74 14.10 21.12 80.19

X. Zhang et al. / Ecological Indicators 46 (2014) 407–414

Shanghai Tianjin Beijing Zhejiang Jiangsu Fujian Guangdong Shandong Liaoning Heilongjiang Inner Mongolia Chongqing Hebei Hubei Sichuan Jilin Hainan Xinjiang Hunan Henan Anhui Shanxi Guangxi Qinghai Ningxia Jiangxi Shaanxi Yunnan Gansu Guizhou National average

Per capita GDP (104 Yuan)

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Therefore, the shadow prices are significantly different across regions. It is worth noting that the provinces are regularly distributed in China. The high-income provinces with high shadow price generally locate in the southeast coast of China and lack primary energy, while the low income provinces with low shadow price generally locate in the west of China and are rich in primary energy (especially the coal). Therefore, those high income provinces have to heavily import energy from other provinces, especially the west provinces. For example, Shanxi province, a low income province with the lowest shadow price, is a dominant electric power supplier to the high income province of Beijing. In China, the high-income provinces feature service and light industry, and the production technical level is relatively high. While the low income provinces feature energy intensive industry and traditional agriculture, and the production technical level is relative low. The shadow prices vary at the provincial levels since there are many differences across provinces, such as the development mechanism, technical level, economic structure, and so on. The empirical results indicate that the shadow prices at provincial levels steadily increased during the sample period (only Xinjiang, Anhui, and Shaanxi province’s shadow prices slightly decreased). The national weighted average shadow prices estimated by Shephard/translog model increased from 22.42 Yuan/ton in 2006 to 26.94 Yuan/ton in 2010, while the ones measured by the directional distance function increased from 75.3 Yuan/ton to 89.15 Yuan/ton in 2010. China has made efforts to build an energyefficient and environmentally friendly society since the beginning of the 11th Five-Year Plan (2006–2010), which means stricter regulations to reduce emissions and increasingly high costs of carbon emissions reduction. The shadow prices estimated by Shephard distance function in this paper are significantly lower than that in Choi et al. (2012), but the shadow prices estimated by the directional distance function in this paper are much higher than that of Choi et al. (2012). Those differences may be incurred by the different methods and data set that the two studies used. However, there are two common conclusions in the two studies. Firstly, there is an intuitively positive correlation between the carbon emissions abatement costs and the income level. It is worth noting that the shadow price of Shanxi province is the lowest in the two studies. Secondly, the average shadow price is increasing during 2006–2010. Since the shadow price is significantly different across provinces, the Chinese government should give impetus to the establishment and implementation of regional scheme of emissions trading. In the 12th Five-Year Plan (2011–2015), China central government has set more ambitious targets of carbon emissions intensity reduction, and assigned it to different provinces. Through the regional emission trading, the provinces whose marginal abatement costs are high can obtain cost savings. Specifically, these provinces with high emission abatement cost can decide at its marginal point whether to implement an abatement strategy or to purchase emission allowances from the provinces with lower marginal abatement cost in CO2 trading market. When the marginal abatement cost is significantly lower than the emission allowance price, the provinces are encouraged to choose the abatement option. Through such a regional emissions trade scheme, a cost saving effect can be realized in regional economies. In addition, promoting clean and renewable energy projects is a suitable alternative, especially for high income regions. Shi et al. (2012) indicated that China still needed to put more efforts into the development and utilization of new energy sources so as to reduce its overdependence on conventional energy resources. Although China central and local governments’ subsidy policy is crucial to the development of clean and renewable energy projects, the cost of clean and renewable energy projects is still expensive. So only these high income regions can afford them. Moreover, the empirical

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results indicate that the carbon emissions abatement cost is expensive for the high income provinces, so the clean and renewable energy projects may be a practical measure for high income regions to fulfill their own target of carbon emissions intensity reduction. Factually, China has chosen 13 pilot cities (high income cities such as Beijing, Shanghai, and so on) to accelerate the development of new energy vehicles through the national and local subsidy support. Meanwhile, the Chinese government has launched a solar rooftop program, especially “The plan to build ten thousand solar roofs in Shanghai”. However, those projects developed slowly, and China must take regional adaptive measures to promote them. 5. Conclusions This paper attempts to simultaneously use the directional output distance function and Shephard output distance function to estimate the shadow price of China’s provincial CO2 emissions. To dig into the differences of shadow prices at the provincial level over time, we choose a sample of 30 provinces during the period of 2006–2010 which spans the 11th Five Year Economic Plan of China. The empirical results indicate the shadow prices estimated by the directional distance function are significantly higher than those estimated by Shephard distance function, which implies that the green production technology is very expensive for a developing country like China. Carbon emissions reduction and climate change are world issues, so the international technical cooperation is very important. In addition, the shadow prices of carbon emissions present a rising trend during the sample period, which implies that it is increasingly costly for China to regulate CO2 emissions. Moreover, the shadow price is positively correlated with regional economic development levels in China. That is, the shadow prices of carbon emissions in high income provinces, such as Shanghai, Beijing, Jiangsu, Zhejiang, Fujian, are significantly higher than those of the other provinces, while the shadow prices of carbon emissions in low income provinces are very low. Therefore, the regional carbon emissions reduction mechanism is required in China, such as the regional carbon emissions trading scheme, promoting clean and renewable energy projects especially in the high income regions. There are several additional avenues of future exploration in estimating the shadow prices of undesirable outputs. The shadow price model developed in this study could also be applied to the analysis of other undesirable outputs in the production process, such as SO2 emissions and industrial wastewater. Due to the inherent disadvantages of methods, future studies can combine the parametric and nonparametric methods, which would yield more valuable suggestions. Acknowledgments The authors would like to thank the anonymous referees and the editor of this journal. The authors also benefit from the discussions with Bin Chen, Myunghun Lee, and Ning Zhang. The authors gratefully acknowledge the financial support by the National Natural Science Foundation of China (Grant nos. 71173075 and 71373077), Beijing Natural Science Foundation of China (Grant no. 9142016), Beijing Planning Project of Philosophy and Social Science (Grant no. 13JGB054), Ministry of Education Doctoral Foundation of China (Grant no. 20110036120013), Program for New Century Excellent Talents in University (Grant no. NCET-12-0850), and the Fundamental Research Funds of the Central Universities of China. References Aigner, D.J., Chu, S.F., 1968. On estimating the industry production function. Am. Econ. Rev. 13, 826–839.

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