## Abstract

This paper develops a weighted continuous state space approach to convergence analysis and makes a first empirical attempt at examining the heterogeneity and convergence of China’s marginal abatement cost (MAC) of CO_{2} using a dataset of 286 cities during the years 2002–2013. The results show clear patterns of convergence in China’s MAC but substantial heterogeneity remains in the long run. Both joint and conditional emission-weighted distributions suggest less heterogeneity in abatement cost but greater potential for low-cost abatement opportunities than it appears in the commonly-presented unweighted distributions. The findings provide strong scientific support for China to take more proactive and aggressive measures to mitigate CO_{2} emissions.

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## Notes

- 1.
Early nonparametric models use radial measures, which reflect the necessary proportional improvements of relevant factors (inputs/outputs) for the evaluated decision management unit (DMU) to reach the frontier. Yet radial measures tend to overestimate energy efficiency, because it ignores the non-radial input/output slacks. To overcome this issue, the non-radial SBM was proposed to treat non-proportional improvements (Tone 2001).

- 2.
The approach inevitably underestimates total energy consumption due to notably, the omission of natural gas. The underestimation of energy consumption is likely to generate an upwards bias in the point estimates MAC across the sample. However, as natural gas only accounts for a very small proportion of China’s total energy consumption, we consider the bias to be insignificant. In addition, the bias is to shift the entire MAC distribution upwards while the impact on the dispersion and dynamic convergence or divergence characteristics of MAC distribution (i.e. the focus of the paper) is likely to be even less significant.

- 3.
For simplicity, we are assuming a homogeneous curvature of the MAC curve of PAA cities; however, this may not be true. For a discussion of the implications of heterogeneous curvatures in MAC curves, please refer to Hailu and Ma (2017).

- 4.
The convergence/divergence analysis using the state space approach is a descriptive rather than an inferential model such that it is unable to discern causal effects. Discussion of potential factors that influence heterogeneity and convergence is most likely speculative. Identifying causal effects will have to involve inferential statistics which is beyond the scope of this paper.

## References

Bulli S (2001) distribution dynamics and cross-country convergence: a new approach. Scott J Polit Econ 48:226–243

Chen SY (2010) The shadow price of industrial carbon emissions: parametric and non-parametric approaches. World Econ 8:93–111

Chen SY (2011) Marginal abatement cost and China’s environmental tax reform. China Soc Sci 3:85–100

China’s State Council (2011) Energy conservation and emissions reduction comprehensive work plan for the 12th five-year plan (2011–2015) period, Beijing

China’s State Council (2016) Energy conservation and emissions reduction comprehensive work plan for the 13th five-year plan (2016–2020) period, Beijing

Choi Y, Zhang N, Zhou P (2012) Efficiency and abatement costs of energy-related CO

_{2}emissions in China: a slacks-based efficiency measure. Appl Energy 98:198–208Cooper WW, Seiford LM, Tone K (2007) Data envelopment analysis: a comprehensive text with models, applications, references and DEA-solver software, 2nd edn. Springer Science & Business Media, New York

Du L, Mao J (2015) Estimating the environmental efficiency and marginal CO

_{2}abatement cost of coal-fired power plants in China. Energy Policy 85:347–356Du L, Hanley A, Wei C (2015a) Estimating the marginal abatement cost curve of CO

_{2}emissions in China: provincial panel data analysis. Energy Econ 48:217–229Du L, Hanley A, Wei C (2015b) Marginal abatement costs of carbon dioxide emissions in China: a parametric analysis. Environ Resour Econ 61(2):191–216

General Administration of Quality Supervision, Inspection and Quarantine of the People’s Republic of China (AQSIQ) (2009) GB/T 15317-2009 monitoring and testing for energy saving of coal fired industrial boilers. Standards Press of China, Beijing

Glaeser EL, Kahn ME (2010) The greenness of cities: carbon dioxide emissions and urban development. J Urban Econ 67(3):404–418

Hailu A, Ma C (2017) The efficiency and distributional effects of China’s carbon mitigation policies: a distance function analysis. UWA School of Agricultural and Environment Working Paper

He X (2015) Regional differences in China’s CO

_{2}abatement cost. Energy Policy 80:145–152Herrerias MJ (2012) Weighted convergence and regional growth in China: an alternative approach (1952–2008). Ann Reg Sci 49:685–718

Hong JY (2018) How natural resources affect authoritarian leaders’ provision of public services: evidence from China. J Politics 80(1):178–194

Huang JH, Yu YT, Ma C (2017) Energy efficiency convergence in China: catch-up, lock-in and regulatory uniformity. Environ Resour Econ. https://doi.org/10.1007/s10640-017-0112-0

Intergovernmental Panel on Climate Change (IPCC) (2006) IPCC guidelines for national greenhouse gas inventories

Islam N (2003) What have we learnt from the convergence debate? J Econ Surv 17(3):309–362

Johnson PA (2005) A continuous state space approach to “convergence by parts”. Econ Lett 86(3):317–321

Jones C (1997) On the evolution of the world income distribution. J Econ Perspect 11:19–36

Juessen F (2008) A distribution dynamics approach to regional GDP convergence in unified Germany. Empir Econ 37(3):627–652

Lee M, Zhang N (2012) technical efficiency, shadow price of carbon dioxide emissions, and substitutability for energy in the Chinese manufacturing industries. Energy Econ 34(5):1492–1497

Li S, Cheong TS (2017) Convergence and mobility of rural household income in China: new evidence from a transitional dynamics approach. China Agric Econ Rev 8(3):383–398

Li H, Lu Y, Zhang J, Wang T (2013) Trends in road freight transportation carbon dioxide emissions and policies in China. Energy Policy 57:99–106

List JA (1999) have air pollutant emissions converged among US regions? Evidence from unit root tests. South Econ J 66(1):144–155

Ma C, Hailu A (2016) The marginal abatement cost of carbon emissions in China. Energy J 37(SI1):111–127

Ministry of Environmental Protection (MEP) (2003) Notice on quarterly reporting arrangements for key environmental protection cities. http://www.npc.gov.cn/npc/flsyywd/xingzheng/2002-07/11/content_297385.htm. Accessed 1 Mar 2017. (

**in Chinese**)NBSC (2003–2014b) China urban construction statistical yearbook. China Statistic Press, Beijing

NBSC (2014a) China energy statistical yearbook. China Statistic Press, Beijing

NBSC (2014b) China statistical yearbook. China Statistic Press, Beijing

NBSC (National Bureau of Statistics of China) (2003–2014a) China city statistical yearbook. China Statistic Press, Beijing

NDRC, National Development and Reform Commission (2011) NDRC Circular 2011 No. 9 Attachment—regional achievement of energy reduction targets for the 11th five-year plan (2006–2010) Period. National Development and Reform Commission, Beijing

NDRC, National Development and Reform Commission (2014) Baseline emission factors for regional power grids in China

Newell RG, Stavins RN (2003) Cost heterogeneity and the potential savings from market-based policies. J Regul Econ 23(1):43–59

Nourry M (2009) Re-examining the empirical evidence for stochastic convergence of two air pollutants with a pair-wise approach. Environ Resour Econ 44(4):555–570

Pettersson F, Maddison D, Acar S, Söderholm P (2014) Convergence of carbon dioxide emissions: a review of the literature. Int Rev Environ Resour Econ 7(2):141–178

Quah DT (1993) Empirical cross-section dynamics in economic growth. Eur Econ Rev 37(2):426–434

Quah DT (1996) Twin peaks: growth and convergence in models of distribution dynamics. Econ J 106(437):1045–1055

Quah DT (1997) Empirics for growth and distribution: stratification, polarization, and convergence clubs. J Econ Growth 2(1):27–59

Reichlin L (1999) Discussion of ‘convergence as distribution dynamics’ (by Danny Quah). In: Baldwin R, Cohen D, Sapir A, Venables A (eds) Market integration, regionalism, and the global economy. Cambridge University Press, Cambridge, pp 328–335

Sakamoto H, Islam N (2008) Convergence across Chinese provinces: an analysis using Markov transition matrix. China Econ Rev 19:66–79

Silverman BW (1986) Density estimation for statistics and data analysis, CRC press

Tang K, Yang L, Zhang JW (2016) Estimating the regional total factor efficiency and pollutants’ marginal abatement costs in China: a parametric approach. Appl Energy 184:230–240

Tone K (2001) A slacks-based measure of efficiency in data envelopment analysis. Eur J Oper Res 130(3):498–509

Wang K, Wei Y (2014) China’s regional industrial energy efficiency and carbon emissions abatement costs. Appl Energy 130:617–631

Wang Q, Cui Q, Zhou D, Wang S (2011) Marginal abatement costs of carbon dioxide in China: a nonparametric analysis. Energy Procedia 5:2316–2320

Wang Y, Zhang P, Huang D, Cai C (2014) Convergence behavior of carbon dioxide emissions in China. Econ Model 43:75–80

Wang K, Wei Y, Huang Z (2016a) Potential gains from carbon emissions trading in China: a DEA based estimation on abatement cost savings. Omega 63:48–59

Wang S, Chu C, Chen G, Peng Z, Li F (2016b) Efficiency and reduction cost of carbon emissions in China: a non-radial directional distance function method. J Clean Prod 113:624–634

Wang K, Che LN, Ma C, Wei YM (2017) The shadow price of CO2 emissions in China’s iron and steel industry, UWA School of Agriculture and Environment Working Paper

Wei C, Ni J, Du L (2012) Regional allocation of carbon dioxide abatement in China. China Econ Rev 23(3):552–565

Wei C, Löschel A, Liu B (2013) An empirical analysis of the CO

_{2}shadow price in Chinese thermal power enterprises. Energy Econ 40:22–31Wu Y (2009) China’s capital stock series by region and sector, University of Western Australia. The University of Western Australia Discussion Paper 09.02

Wu JX, Ma C (2017) The heterogeneity and determinants of marginal abatement cost of CO2 emissions in Chinese cities. UWA School of Agricultural and Environment Working Paper

Wu JX, Wu YR, Guo XM, Cheong TS (2016) Convergence of carbon dioxide emissions in Chinese cities: a continuous dynamic distribution approach. Energy Policy 91:207–219

Yuan P, Liang WB, Cheng S (2012) The marginal abatement costs of CO

_{2}in Chinese industrial sectors. Energy Procedia 14:1792–1797Zhan JV (2017) Do natural resources breed corruption? Evidence from China. Environ Resour Econ 66:237–259

Zhang D, Broadstock D (2016) Club convergence in the energy intensity of China. Energy J 37:137–158

Zhang N, Xie H (2015) Toward green IT: modelling sustainable production characteristics for Chinese electronic information industry, 1980–2012. Technol Forecast Soc Change 96:62–70

Zheng S, Wang R, Glaeser EL, Kahn ME (2011) The greenness of China: household carbon dioxide emissions and urban development. J Econ Geogr 11(5):761–792

## Acknowledgements

The research received financial support under a number of funding schemes including the ECR Fellowship Support Award at the University of Western Australia, China National Social Science Foundation (No. 15ZDA054), Humanities and Social Sciences of Ministry of Education Planning Fund (No. 16YJA790050) and the National Natural Science Foundation (No. 71333007).

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## Appendix: Estimating of the MAC of Carbon Dioxide

### Appendix: Estimating of the MAC of Carbon Dioxide

Assuming that there are *I* cities and each city uses *N* inputs \( \varvec{x} = \left( {x_{1} , \ldots ,x_{N} } \right) \in R^{N} \) to produce one good output *y* and one undesirable output *b*, we can then define a production possibility set (PPS) as follows:

where \( \varvec{X} \), \( \varvec{Y} \) and \( \varvec{B} \) are *N* × *I*, 1 × *I* and 1 × *I* matrices of input and output data for all *I* cities. \( \varvec{\lambda}\in R^{I} \) is a non-negative intensity vector, indicating that the above definition corresponds to the constant returns to scale (CRS) technology.

Following Cooper et al. (2007), we can further define the non-radial SBM model:

where \( s_{i,n}^{x} \) and \( s_{i}^{b} \) denote the slack variables of input *n* and the undesirable output, which represent excesses in input *n* and the undesirable output. *s*
_{
i}
^{y}
is a slack variable of the good output which corresponds to shortage in the good output. \( \varvec{X}_{\varvec{n}} \) is the *n*th row of \( \varvec{X} \). The objective value of Eq. (A1) satisfies \( 0 < \rho_{i}^{ *} < 1 \). A DMU (*x*_{i}, *y*_{i}, *b*_{i}) is efficient if and only if \( \rho_{i}^{ *} = 1 \) ,indicating that all slack variables are zero. Since Eq. (A1) is a nonlinear programming model, the dual linear program of Eq. (A1) can be specified as follows:

The dual variables \( \varvec{p}^{\varvec{x}} \in R^{N} , \)*p*^{y} ∊ *R*^{M}, and *p*^{y} ∊ *R*^{K} are the relative shadow prices of input, desirable output and undesirable output, respectively. Assuming that the absolute shadow price of desirable output (gross city product, GCP) equals to its market price (i.e. one), the absolute shadow price of the undesirable output (CO_{2} emissions) can be estimated through:

Therefore, the shadow price of undesirable output can be interpreted as the marginal rate of transformation between undesirable output and desirable output. It shows the tradeoff between desirable and undesirable output. In this paper, we include three inputs (labor, capital, and energy consumption), one desirable output (GCP) and one undesirable output (CO_{2} emissions).

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Wu, J., Ma, C. The Convergence of China’s Marginal Abatement Cost of CO_{2}: An Emission-Weighted Continuous State Space Approach.
*Environ Resource Econ* **72, **1099–1119 (2019) doi:10.1007/s10640-018-0240-1

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### Keywords

- Marginal abatement cost
- Carbon emissions
- Convergence
- State space approach
- Continuous dynamic distribution approach
- China

### JEL Codes

- Q52
- Q53
- Q54
- Q58
- D24
- D61