Carbon emission abatement quota allocation in Chinese manufacturing industries: An integrated cooperative game data envelopment analysis approach

Figures & data

Table 1. The CO₂ emission/GIOV in China from 2004 to 2012.

Year	CO2 emission	Gross industrial output value (GIOV)	CO2 emission/GIOV	CPI
2004	2,322,703.8950	19,396.1056	1.1975	81.8313
2005	2,535,271.3660	21,783.5740	1.1638	85.0227
2006	2,754,416.4470	27,457.1670	1.0032	86.5673
2007	2,932,353.4260	35,363.0840	0.8292	87.8369
2008	3,251,515.2580	44,135.8360	0.7367	92.0238
2009	3,411,188.4130	47,919.9720	0.7119	97.4532
2010	3,700,797.2980	60,955.8500	0.6071	96.7834
2011	3,950,889.9570	73,398.4010	0.5383	100.0000
2012	4,134,711.6380	80,925.5132	0.5109	105.4706

Source: China Statistical Yearbooks 2005–2013, China Energy Statistical Yearbook.

According to OECD statistics, we set CPI Index 2010 = 100.

Table 2. Notation summary.

Notations	Description
$h=1,\dots ,31$	Index of different sub-level industries
$l=1,\dots ,31$	Index of different provinces
$i=1,\dots ,m$	Index of inputs
$r=1,\dots ,s$	Index of desirable outputs
$j,o=1,\dots ,n$	Index of decision making units (DMU)
$x_{\mathit{ij}}$	Value of inputs of ${\mathrm{DMU}}_j$
$y_{\mathit{rj}}$	Value of desirable outputs of ${\mathrm{DMU}}_j$
$b_j$	Value of undesirable output of ${\mathrm{DMU}}_j$
${\lambda }_j,$ ${\xi }_j$	Intensity variables
$\theta$	Expansion proportion of outputs in BCC model
$\eta$	Measure of the directional distance function
$v_i,{\upsilon }_i$	Relative weight of input i
$u_r,{\mu }_r$	Relative weight of desirable output r
${\omega }_1, {\omega }_2,\omega$	Relative weight of the undesirable output
$u_0,{\mu }_0$	Free variable reflecting the RTS property
$g=\left(g_y,g_b\right)$	Direction vector
$E_o^{*}$	Optimal original efficiency of ${\mathrm{DMU}}_o$
$e_o^{*}$	Optimal post-allocation efficiency of ${\mathrm{DMU}}_o$
${\eta }^{*}$	Optimal directional distance function measure
${\mathrm{\psi }}_{\mathrm{o}}^{\mathrm{*}}$	Optimal inefficiency measure
R	Total fixed undesirable output abatement quota
$R_j$	Undesirable output abatement amount of ${\mathrm{DMU}}_j$
${\overline{y}}_{\mathit{rj}},$${\tilde{y}}_{\mathit{rj}}$	The change amount of desirable output r of ${\mathrm{DMU}}_j$
$R_j^{\mathit{max}}$	Maximal undesirable output reduction level of ${\mathrm{DMU}}_j$ with desirable output ${\overline{y}}_{\mathit{rj}}$
$T_{1j},$ $T_{2j},$ $T_j$	The variation of undesirable output reduction amount of ${\mathrm{DMU}}_j$
${\overrightarrow{R}}_j/{\overleftarrow{R}}_j$	Maximal/minimal undesirable output reduction level of ${\mathrm{DMU}}_j$ with the efficient allocation set
$N=\left\{1,\dots ,n\right\}$	Large coalition of all DMU
$K$	Coalition of DMUs
$C_K={\left(c_1,\dots ,c_n\right)}^{\prime }$	Vector used to construct coalition K
${\overrightarrow{R}}_K/{\overleftarrow{R}}_K$	Maximal/minimal quota allocated to coalition K
$V\left(K\right)$	Characteristic function
$Z=\left(z_1,\dots ,z_n\right)$	Pre-nucleolus imputation
$e\left(K,Z\right)$	Excess value of coalition K on imputation Z
$\mathrm{\delta }\left(Z\right)$	Vector of excess values
$\xi$	Least maximal excess value
${\rho }_K$	Dual variable
${\beta }_j$	Dual variable
$\mathrm{\alpha }$	Dual variable
$\mathrm{\tau }$	Dual variable
${\pi }_j$	Dual variable
${\chi }_j$	Dual variable
$O^{\mathit{max}}$	The maximal unsatisfied value
$d_j$	0–1 variable
$f_j$	Instrumental variable depending on $d_j$
M	A large enough positive value

Table 3. A simple example.

DMU	x1	x2	y	b
1	5	9	7	8
2	8	6	7	7
3	9	8	6	8
4	6	10	8	10
5	11	8	7	9

Table 4. Preliminary results.

DMU	Original efficiency Model (4)	Post efficiency Model (10)	Minimal reduction Model (12)	Maximal reduction Model (12)
1	1.0000	1.0000	0	8.0000
2	1.0000	1.0000	0	7.0000
3	0.8571	1.0000	0	8.0000
4	1.0000	1.0000	0	10.0000
5	0.9333	1.0000	0	9.0000

Table 5. The constraint generation process for the minimal excess value.

Iteration no.	${\xi }^{*}$	Solution					$O^{\mathit{max}}$	Constrained coalition
		$z_1^{*}$	$z_2^{*}$	$z_3^{*}$	$z_4^{*}$	$z_5^{*}$
1	1.2000	2.8000	2.3000	2.8000	3.8000	3.3000	2.6000	{1,2,3,5}
2	2.5000	3.0000	1.0000	4.0000	2.5000	4.5000	3.5000	{1,2,4}
3	2.5000	4.0000	3.5000	1.5000	2.5000	4.5000	3.5000	{3,4,5}
4	3.6667	4.0000	1.1667	1.6667	3.6667	1.6667	2.3333	{2,3,4}
5	3.6667	4.0000	1.1667	4.0000	3.6667	3.3333	2.3333	{2,4,5}
6	3.6667	2.8333	2.3333	2.8333	3.6667	3.3333	0.0000	{1,3,4}
7	3.6667	2.8333	2.2333	2.8333	3.6667	3.3333	0.0000	{1,4,5}
8	3.6667	2.8333	2.3333	2.8333	3.6667	3.3333	−0.1667	{1,2,5}

Table 6. Dataset for 31 sub-level manufacturing industries.

DMU	x1	x2	x3	y	u
DMU1	2345.4120	4042.8384	27,505.4652	5268.1562	34,957.9171
DMU2	1000.9680	2017.8770	16,213.1919	1590.2686	26,929.2787
DMU3	1117.6840	1502.0504	11,800.8564	1361.0131	15,294.9203
DMU4	708.4340	214.6285	2474.1824	791.3484	1622.8970
DMU5	2047.9980	5502.0328	63,570.0966	3225.4091	41,235.7124
DMU6	998.5240	4694.9556	8610.8837	1761.7822	4699.3819
DMU7	559.8740	2828.8480	5742.2737	1135.2394	1608.2115
DMU8	444.1300	1377.0669	11,526.3821	1051.5143	8392.0546
DMU9	354.5860	1231.7698	1994.0713	576.6864	821.7364
DMU10	1186.2730	1622.0111	38,461.4019	1284.6778	90,191.8334
DMU11	378.0740	892.9594	4000.2502	461.5240	847.3745
DMU12	508.6820	2247.8443	2804.5532	1025.8159	887.9110
DMU13	2093.8780	813.9607	181,154.4352	3948.9324	2,040,675.7347
DMU14	5338.2090	5070.4290	369,955.4389	6809.4352	499,314.0437
DMU15	1576.8510	2147.7536	16,086.3055	1769.6635	17,149.1155
DMU16	573.7440	498.1379	15,579.9525	677.0168	14,290.6147
DMU17	1615.1240	3436.6337	38,971.3981	2473.5281	16,876.7012
DMU18	3540.7840	5747.2893	294,009.2348	4523.7342	504,976.8358
DMU19	5818.3480	3339.2290	596,681.0204	6951.5540	605,161.6462
DMU20	2810.9660	2201.7215	148,290.1179	3847.8902	132,226.1401
DMU21	1941.0900	3742.9294	38,543.4384	2968.9096	8704.7872
DMU22	3149.3590	4736.7444	34,658.9286	3875.0892	6892.3558
DMU23	2640.3520	3635.8722	17,818.3895	2930.3186	9931.4776
DMU24	4039.9580	4304.9022	27,606.6976	5058.3485	14,469.2241
DMU25	1869.4570	2104.7694	11,495.3636	1644.7536	7011.1171
DMU26	4231.7440	6878.0743	23,290.7460	5549.9724	10,996.4708
DMU27	4642.7820	10,255.5320	26,667.4979	7092.0568	6346.0115
DMU28	584.4970	1155.8961	3112.6044	677.3105	723.7331
DMU29	172.0230	418.9237	16,164.7095	209.0727	10,800.6134
DMU30	141.2020	166.1615	1073.5639	294.5942	328.2493
DMU31	117.0750	149.6450	813.4804	89.8976	347.5371

Figure 1. Normalized carbon emissions and carbon emission intensity.

Figure 2. Relative efficiency of 31 sub-level manufacturing industries.

Table 7. CO₂ abatement quota allocation for 31 sub-level manufacturing industries.

DMUs	Allocation	DMUs	Allocation	DMUs	Allocation
DMU1	2517.0333	DMU11	0	DMU21	8704.7872
DMU2	2961.8097	DMU12	0	DMU22	0
DMU3	2961.8148	DMU13	11,3323.2930	DMU23	0
DMU4	0	DMU14	10,7622.0579	DMU24	0
DMU5	0	DMU15	2961.8123	DMU25	2137.2264
DMU6	0	DMU16	7572.5680	DMU26	0
DMU7	0	DMU17	16,876.7012	DMU27	3184.2017
DMU8	0	DMU18	107,844.4474	DMU28	723.7331
DMU9	0	DMU19	113,323.2930	DMU29	2739.4202
DMU10	2739.4254	DMU20	104,588.3497	DMU30	0
				DMU31	0

Table 8. Relationship associated with the allocation results.

DMU	Emission percentage (%)	Rank	Reduction percentage (%)	Rank	Allocation percentage (%)	Rank
DMU1	0.8574	7	7.2002	15	0.4176	15
DMU2	0.6807	8	10.9985	14	0.4914	12
DMU3	0.3744	9	19.3647	11	0.4914	10
DMU10	2.0804	6	3.0373	17	0.4545	13
DMU13	48.5998	1	5.5532	16	18.8000	1
DMU14	12.9683	3	21.5540	9	17.8542	4
DMU15	0.3623	11	17.2709	13	0.4914	11
DMU16	0.3653	10	52.9898	5	1.2563	8
DMU17	0.3615	12	100.0000	1	2.7998	6
DMU18	12.8063	4	21.3563	10	17.8911	3
DMU19	14.1514	2	18.7261	12	18.8000	1
DMU20	3.1934	5	79.0981	4	17.3509	5
DMU21	0.221	14	100.0000	1	1.4441	7
DMU25	0.1681	15	30.4834	7	0.3546	16
DMU27	0.159	16	50.1764	6	0.5283	9
DMU28	0.0124	17	100.0000	1	0.1201	17
DMU29	0.2273	13	25.3636	8	0.4545	14

Table 9. Summary statistics of 31 provinces for 31 sub-industries.

Statistics	x1	x2	x3	y1	u
Min	0.0000	0.0000	0.0000	0.0000	0.0000
Max	1548.8482	3376.5480	104,242.2540	2286.5395	276,300.7450
Average	60.9982	88.6511	2312.7701	81.2663	4917.0858
Std.ev	116.1812	192.9952	7365.3472	168.0707	116.1812

Table 10. Results of regional CEA allocation scheme (unit: thousand tons).

Regions	I1	I2	I3	I10	I13	I14
Beijing	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000
Tianjin	223.7132	504.0956	0.0000	0.0000	0.0000	0.0000
Hebei	0.0000	0.0000	90.0918	0.0000	0.0000	0.0000
Shanghai	0.0000	0.0000	89.1932	0.0000	0.0000	0.0000
Jiangsu	0.0000	0.0000	230.0905	0.0000	0.0000	0.0000
Zhejiang	0.0000	0.0000	118.9122	0.0000	0.0000	11,687.1846
Fujian	0.0000	0.0000	144.6297	0.0000	0.0000	0.0000
Shandong	0.0000	0.0000	324.8134	0.0000	49,499.2709	0.0000
Guangdong	0.0000	0.0000	94.7229	0.0000	0.0000	16,604.6209
Hainan	0.0000	0.0000	61.5814	0.0000	0.0000	0.0000
Liaoning	628.6325	0.0000	107.5477	1066.2830	0.0000	0.0000
Jilin	0.0000	0.0000	112.9420	0.0000	0.0000	0.0000
Heilongjiang	0.0000	0.0000	0.0000	0.0000	10,990.8629	0.0000
Anhui	322.7990	0.0000	1.1022	0.0000	0.0000	0.0000
Jiangxi	0.0000	0.0000	196.4356	1198.3350	0.0000	0.0000
Henan	0.0000	0.0000	39.1846	0.0000	0.0000	0.0000
Hubei	0.0000	1719.4612	94.7229	474.8074	0.0000	29,510.7443
Hunan	1341.8887	438.4614	23.1890	0.0000	27,667.7339	0.0000
Shanxi	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000
Inner Mongolia	0.0000	0.0000	230.0905	0.0000	0.0000	0.0000
Guangxi	0.0000	0.0000	145.6301	0.0000	0.0000	0.0000
Chongqing	0.0000	0.0000	61.2714	0.0000	0.0000	0.0000
Sichuan	0.0000	0.0000	324.8134	0.0000	0.0000	35,739.9891
Guizhou	0.0000	0.0000	56.6404	0.0000	0.0000	0.0000
Yunnan	0.0000	0.0000	66.0042	0.0000	0.0000	0.0000
Tibet	0.0000	0.0000	23.0872	0.0000	0.0000	0.0000
Shaanxi	0.0000	0.0000	33.4514	0.0000	0.0000	0.0000
Gansu	0.0000	299.7915	126.0718	0.0000	0.0000	0.0000
Qinghai	0.0000	0.0000	41.7131	0.0000	0.0000	0.0000
Ningxia	0.0000	0.0000	85.7997	0.0000	25,165.4252	14,079.5184
Xinjiang	0.0000	0.0000	38.0824	0.0000	0.0000	0.0000

Table 11. Results of regional CEA allocation scheme (unit: thousand tons).

Regions	I15	I16	I17	I18	I19	I20
Beijing	312.2816	0.0000	32.2274	0.0000	0.0000	0.0000
Tianjin	0.0000	3.6336	163.3004	0.0000	0.0000	270.4847
Hebei	0.0000	251.9519	514.2943	924.9577	0.0000	544.0242
Shanghai	0.0000	0.0000	672.0801	14,868.7929	0.0000	1253.9031
Jiangsu	0.0000	920.9691	1780.0800	0.0000	0.0000	8737.7880
Zhejiang	0.0000	966.9343	1982.1896	17,579.1939	0.0000	5521.7351
Fujian	0.0000	177.4540	393.1660	0.0000	0.0000	57.5132
Shandong	0.0000	865.8477	3866.5647	0.0000	0.0000	19,377.8286
Guangdong	0.0000	357.0427	3490.1712	74,471.5030	25,755.3523	7388.6808
Hainan	0.0000	35.8871	40.8632	0.0000	0.0000	0.0000
Liaoning	0.0000	302.5258	533.2964	0.0000	37,107.5793	865.1980
Jilin	1871.7447	574.2076	155.2591	0.0000	0.0000	344.2977
Heilongjiang	0.0000	78.7690	0.0000	0.0000	0.0000	693.9880
Anhui	0.0000	421.8767	187.5374	0.0000	0.0000	423.8788
Jiangxi	0.0000	374.3625	0.0000	0.0000	0.0000	440.9990
Henan	0.0000	354.3782	383.7191	0.0000	0.0000	14,240.5976
Hubei	777.7860	171.5063	38.1489	0.0000	0.0000	732.4983
Hunan	0.0000	67.3061	0.0000	0.0000	0.0000	2330.9355
Shanxi	0.0000	5.9966	0.0000	0.0000	24,785.0413	8069.3588
Inner Mongolia	0.0000	0.0000	148.2670	0.0000	0.0000	1262.4656
Guangxi	0.0000	0.0000	126.4290	0.0000	22,108.4996	9852.1529
Chongqing	0.0000	0.0000	266.5483	0.0000	0.0000	836.7945
Sichuan	0.0000	614.4358	717.0869	0.0000	0.0000	3037.5572
Guizhou	0.0000	0.0000	931.1748	0.0000	0.0000	3454.2565
Yunnan	0.0000	98.6850	80.8533	0.0000	0.0000	2543.6940
Tibet	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000
Shaanxi	0.0000	19.3078	283.3317	0.0000	3566.8206	7095.2553
Gansu	0.0000	46.3543	90.1125	0.0000	0.0000	4736.3018
Qinghai	0.0000	0.0000	0.0000	0.0000	0.0000	118.3759
Ningxia	0.0000	0.0000	0.0000	0.0000	0.0000	157.4397
Xinjiang	0.0000	863.1363	0.0000	0.0000	0.0000	200.3473

Table 12. Results of regional CEA allocation scheme (unit: thousand tons).

Regions	I21	I25	I27	I28	I29
Beijing	37.0665	11.7220	0.0000	1.7815	0.0000
Tianjin	123.1876	33.2374	135.1479	0.0000	4.7496
Hebei	826.7085	55.6882	21.2433	45.9428	11.3411
Shanghai	327.0516	62.4681	601.8260	6.1090	27.3648
Jiangsu	1635.1095	281.8791	601.8260	168.4141	129.1209
Zhejiang	817.5394	109.9419	540.6590	146.6941	224.1699
Fujian	0.0000	0.0000	0.0000	0.0000	48.6643
Shandong	1635.1095	281.8791	601.8260	162.3051	54.0832
Guangdong	1635.1095	244.3248	601.8260	168.4141	662.1570
Hainan	12.0564	0.0000	0.0000	1.0957	0.0000
Liaoning	159.2857	80.0864	0.0000	4.1874	53.7470
Jilin	16.6236	38.8625	0.0000	3.0695	85.4812
Heilongjiang	7.4108	158.6444	0.0000	1.5355	0.5222
Anhui	39.0455	8.9641	0.0000	0.0000	0.0000
Jiangxi	3.8453	8.8393	0.0000	0.0000	0.0000
Henan	181.0752	37.5543	39.9237	3.6403	10.0296
Hubei	123.5324	0.0000	0.0000	0.0000	19.5879
Hunan	133.5340	41.8797	0.0000	3.0158	18.1144
Shanxi	159.0355	13.2928	0.0000	0.0000	1308.2723
Inner Mongolia	45.4263	0.2250	0.0000	0.0000	12.1344
Guangxi	112.2681	29.9922	0.0000	1.6428	3.7036
Chongqing	289.1818	117.9709	0.0000	1.5578	0.0000
Sichuan	224.1255	387.8118	0.0000	2.4687	13.5617
Guizhou	27.7776	2.9274	0.0000	0.4084	2.7338
Yunnan	29.6217	19.5659	0.0000	0.0000	6.9867
Tibet	0.0000	0.0000	0.0000	0.0000	0.0000
Shaanxi	58.3171	89.7181	39.9237	1.4504	15.3631
Gansu	24.0946	19.7510	0.0000	0.0000	27.5315
Qinghai	0.0000	0.0000	0.0000	0.0000	0.0000
Ningxia	0.0000	0.0000	0.0000	0.0000	0.0000
Xinjiang	21.6477	0.0000	0.0000	0.0000	0.0000

Table 13. CO₂ abatement quota allocated to provinces (10 thousand tons).

Provinces	Allocation	Provinces	Allocation
Beijing	395.0790	Hubei	33,662.7956
Tianjin	1461.5499	Hunan	32,066.0585
Hebei	3286.2439	Shanxi	34,340.9973
Shanghai	17,908.7889	Inner Mongolia	1698.6088
Jiangsu	14,485.2774	Guangxi	32,380.3184
Zhejiang	39,695.1540	Chongqing	1573.3246
Fujian	821.4271	Sichuan	41,061.8507
Shandong	76,669.5284	Guizhou	4475.9190
Guangdong	131,473.9251	Yunnan	2845.4106
Hainan	151.4837	Tibet	23.0872
Liaoning	40,908.3691	Shaanxi	11,202.9392
Jilin	3202.4876	Gansu	5370.0089
Heilongjiang	11931.7327	Qinghai	160.0890
Anhui	1405.2036	Ningxia	39,488.1829
Jiangxi	2222.8166	Xinjiang	1123.2137
Henan	15,290.1027

Figure 3. Percentage of carbon emissions and abatement quota for 31 provinces.

Table F1. The codes for two-digit Chinese manufacturing industries

DMUs	Sub-level manufacturing industries
DMU1	Processing of Food from Agricultural Products
DMU2	Manufacture of Foods
DMU3	Manufacture of Liquor, Beverages and Refined Tea
DMU4	Manufacture of Tobacco
DMU5	Manufacture of Textile
DMU6	Manufacture of Textile, Wearing Apparel and Accessories
DMU7	Manufacture of Leather, Fur, Feather and Related Products and Footwear
DMU8	Processing of Timber, Manufacture of Wood, Bamboo, Rattan, Palm and Straw Products
DMU9	Manufacture of Furniture
DMU10	Manufacture of Paper and Paper Products
DMU11	Printing and Reproduction of Recording Media
DMU12	Manufacture of Articles for Culture, Education, Arts and Crafts, Sport and Entertainment Activities
DMU13	Processing of Petroleum, Coking and Processing of Nuclear Fuel
DMU14	Manufacture of Raw Chemical Materials and Chemical Products
DMU15	Manufacture of Medicines
DMU16	Manufacture of Chemical Fibres
DMU17	Manufacture of Rubber and Plastics Products
DMU18	Manufacture of Non-metallic Mineral Products
DMU19	Smelting and Pressing of Ferrous Metals
DMU20	Smelting and Pressing of Non-ferrous Metals
DMU21	Manufacture of Metal Products
DMU22	Manufacture of General Purpose Machinery
DMU23	Manufacture of Special Purpose Machinery
DMU24	Manufacture of Automobiles
DMU25	Manufacture of Railway, Ship, Aerospace and Other Transport Equipment
DMU26	Manufacture of Electrical Machinery and Apparatus
DMU27	Manufacture of Computers, Communication and Other Electronic Equipment
DMU28	Manufacture of Measuring Instruments and Machinery
DMU29	Other Manufacture
DMU30	Utilization of Waste Resources
DMU31	Repair Service of Metal Products, Machinery and Equipment