The Measurement of Satisfaction Degree with Controllable and Uncontrollable Base

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Abstract

Data envelopment analysis （DEA） has gained great popularity in environmental performance measurement because it can provide a synthetic， standardized environmental performance index when pollutants are suitably incorporated into the traditional DEA framework. This paper applies the DEA approaches to evaluate the CO2 emission performance and measure its satisfaction degree of 40 countries and regions from 2008 to 2009. We use the input variables of capital， energy consumption and population and the output variables of gross domestic product （GDP） and the amount of fossilfuel CO2 emissions. Past studies about the application of DEA to environmental performance measurement have not considered uncontrollable factors. In this paper， we present the DEA formulas with controllable and uncontrollable factors to measure environment performance and its satisfaction degree. We first define and construct the environmental production technologies with desirable and undesirable outputs. The degree of environment satisfaction performance based on the DEA approach can be computed by solving a series of data envelopment analysis formulas. A case study of 40 countries and regions applying the DEA approach is also presented.

Key words： DEA； CO2 Emissions； Environment Performance； Controllable； Uncontrollable

INTRODUCTION Carbon dioxide has long been a great problem to the global ecology， and in recent years， the situation has become even worse （Ang et al. 2011）. It is commonly understood that carbon dioxide makes the greatest contribution to greenhouse gas. In the past century， the global climate has undergone significant change， ushering in new issues for leaders and decision makers （Yang and Pollitt， 2009）. The increasing global temperature， the rising sea level， and diminishing grain output， among countless other issues， all contribute to the need for action and counteraction for human perseverance and prosperity. Scientists have documented the increasing global temperature； in the last 30 years， for instance， the average global temperature has risen by .48 degrees C（Yu， 2004； Wei et al， 2004； Tone， 2001）. Humans make a great contribution to the global temperature through the use of fossil fuels （coal， petroleum， etc.） in daily living and industrial production （Zaim， 2004； Scheel， 2001）. The resulting greenhouse gases absorb long-wave radiation in the atmosphere， trapping heat and driving global climate change. Given the current trend of atmospheric change， it is estimated that the global temperature will rise 1.4-5.8 degrees C before the year of 2100. In addition， experts have found that grain reduction also has a positive correlation with the global warming， and they predict this tendency will continue for many years.

Global attention about climate change has increased in recent years， and the need to control and mitigate greenhouse gas emission is likely to be an imminent and integral part of the worldwide policy agenda. Therefore， it is worthwhile to benchmark country by country performance of carbon dioxide output and assess potential for CO2 emission reduction.

Model （1） is constructed based on the assumption of maximizing the output and minimizing the input for each DMUj. This value of f* provides a measure of what is referred to as “technical efficiency” in economics. The minimization identifies a value （1_ f*）xio， which represents the amount by which each input may be reduced without changing the proportions in which these inputs were used. Because f* is minimal， the proportional reduction in all inputs represented by （1_ f*） is maximized.

The variable return to scale （VRS） model based on undesirable outputs proposed by Seiford and Zhu （2002） for any DMUj can be given by model （2）. tj b is the tth undesirable output for DMUj. The other variable is the same with the variable above.

Figure 2 provides some information on the trend of the degree of satisfaction of 40 countries and regions. The ordinate is the value of γ， and the abscissa is number of 40 countries and regions， which can be found in table 2. Interestingly， the results show that the values of DMUs’satisfactions are distributed in the interval between zero and one. Also， we can clearly know the ranking of DMU through the value of satisfaction. Roughly speaking， in the case of γ， it is found that the 34 OECD countries have better CO2 emission performance satisfaction than the other 6 regions.

case of θ the efficiency value is 0.1212 in 2008 and 0.1021 in 2009. It shows that China has a much smaller CO2 emission performance when taking uncontrollable factors into consideration. The results show that in the case of f and θ， the United States， Japan， Iceland， Luxembourg， Norway， and Switzerland are DEA efficient in both 2008 and 2009. It shows in table 2 that the worst performer in the case of f is the Africa region （0.4663） in 2008 and the Africa region （0.4616） 2009. However， in the case ofθ， the worst performer is the “Non-OECD Europe and Eurasia” region （0.0675） in 2008 and the “Non-OECD Europe and Eurasia” region （0.0594） in 2009.

The value of γ for the United States is 0.800017 in 2008 and 0.825015 in 2009， meaning it is the best performing country in both 2008 and 2009. The “Non-OECD Europe and Eurasia” region is 0.0594 in 2008 and 0.0483 in 2009， making it the worst performing region. China’s γ is 0.046071 in 2008 and 0.037453 in 2009. There is a little decline in its degree of satisfaction in 2009 compared to 2008. Interestingly， it is found that the countries with a higher γ are better performers in CO2 emission performance. We can conclude the ranking of countries and regions’ CO2 emission degree of satisfaction based on the result in table 2. The result is presented in table 3.

CONCLUSION

In recent years， data envelopment analysis efficiency approaches that integrate the concept of environmental DEA technology have gained popularity in environmental performance evaluation because they can provide a synthetic， standardized environmental performance index when pollutants are suitably incorporated into the traditional DEA framework. There are no previous studies that evaluate the CO2 emission performance while taking both controllable and uncontrollable factors into consideration. This paper applies the DEA approaches to evaluate the CO2emission performance and measure the degree of satisfaction of 40 countries and regions from

2008 to 2009. Among the countries included in the study，

in the case of φ and θ， the United States， Japan， Iceland， Luxembourg， Norway， and Switzerland are DEA efficient

practitioners in 2008 and 2009. We then applied model 3

to measure the degree of satisfaction. In the case of γ， it shows that the United States is the best performer country in 2008 and 2009. The value of γ＼* MERGEFORMAT for the United States is 0.800017 in 2008 and 0.825015 in 2009. That means the United States makes a great effort to improve economic results and the environment. The“Non-OECD Europe and Eurasia” region is the worst satisfaction performer of all countries and regions in 2008 and 2009.

REFERENCES

[1] Ang， B. W.， Choi， K. H.， （2002）. Boundary problem in carbon emission decomposition. Energy Policy， 20（2）， 1201-1205.

[2] Ang， B. W.， Zhou， P.， Tay， L. P.， （2011）. Potential for reducing global carbon emissions from electricity production- a benchmarking analysis. Energy Policy， 39（3）， 2482-2489.

[3] Banker， R. D.， Charnes， A.， Cooper， W. W.， （1984）. Some models for estimating technical and scale inefficiencies in data envelopment analysis. Management Science， 30（9）， 1078-1092.

[4] Charnes， A.， Cooper， W. W.， Rhodes， E.， （1978）. Measuring the efficiency of decision making units. European Journal of Operational Research， 2（6）， 429-444.

[5] Choi， K. H.， Ang， B. W.， （2001）. A time series analysis of energy related carbon emission in Korea. Energy Policy， 29（7）， 1155-1161.

[6] Chu， W.， Jinlan， N.， Limin， D.， （2012）. Regional allocation of carbon dioxide abatement in China. China Economic Review， 23（7）， 552565.

[7] Cooper， W. W.， Seiford， L. M.， Tone， K.， （2000）. Data envelopment analysis： a comprehensive text with models，

[8] Fare， R.， Grosskopf， S.， Lovell， C. A. K.， Pasurka， C.， （1989）. Multilateral productivity comparisons when some outputs are undesirable： a nonparametric approach. The review of Economics and Statistics， 71（5）， 90-98.

[9] Fare， R.， Grosskopf， S.， Hernandez-Sancho， F.， （2004）. Environmental performance： an index number approach. Resource and Energy Economic， 26（6）， 343-352.

[10] International Energy Agency （IEA）. （2011）. Key world energy statistics. Paris： OECD，

[11] José， .L. Z， Angel， M. P.， （2001）. Environmental efficiency

and regulatory standards： the case of CO2 emissions from OECD industries. Resource and Energy Economics. 23（14）， 6383.

[12] Mielnik， O.， Goldemberg， J.， （1999）. The evolution of the‘‘carbonization index’ in developing countries. Energy Policy， 27（9）， 307308.

[13] Scheel， H.， （2001）. Undesirable outputs in efficiency

valuations. European Journal of Operational Research. 132（5）， 400-410.

[14] Seiford， L. M.， Zhu， J.， （2002）. Modeling undesirable factors

in efficiency evaluation. European Journal of Operational Research. 142（1）， 16-20.

[15] Seiford， L. M.， Zhu， J.， （2005）. A response to comments on modeling undesirable factors in efficiency evaluation. European Journal of Operational Research. 161（4）， 579-581.

[16] Stephan， O.， Ivan， S.， （2006）. Design guideline for maximizing lifetime and avoiding energy holes in sensor networks with uniform distribution and uniform reporting.

[17] Tol， R. S. J.， （2005）. The marginal damage costs of carbon dioxide emissions： an assessment of the uncertainties. Energy Policy， 33（6）， 2064-2074.

[18] Tol， R. S. J.， Pacala， S. W.， Socolow， R. H.， （2009）. Understanding long-term energy use and carbon emissions in the USA. Journal of Policy Modeling， 3（1）， 425445.

[19] Tone， K.， （2001）. A slacks-based measure of efficiency in data envelopment analysis. European Journal of Operational Research， 130（7）， 498-509.

[20] Wang， Q. W.， Zhou， P.， Zhou， D. Q.， （2010）. Research on dynamic carbon dioxide emissions performance， regional disparity and affecting factors in China. China Industrial Economics， 1（1）， 4554.

[21] Wei， Y.， Fan， Y.， Lu， C.， Tsai， H. T.， （2004）. The assessment of vulnerability to natural disasters in China by the DEA method. Environmental Impact Assessment Review， 24（4）， 427-439.

[22] Xiao， D. G.， Zhu， L.， Fan， Y.， （2011）. Evaluation of potential reductions in carbon emissions in Chinese provinces based on environmental DEA. Energy Policy， 39（1）， 23522360.

[23] Yang， H. L.， Pollitt， M.， （2009）. Incorporating both undesirable outputs and uncontrollable variables into DEA： The performance of Chinese coal-fired power plants. European Journal of Operational Research， 197（3）， 1095-1105.

[24] Yu， M.， （2004）. Measuring physical efficiency of domestic airports in Taiwan with undesirable outputs and environmental factors. Journal of Air Transport Management， 10（4）， 295-303.

[25] Zaim， O.， （2004）. Measuring environmental performance of state manufacturing through changes in pollution intensities： a DEA framework. Ecological Economics， 48（1）， 37-47.

[26] Zhou， P， Ang， B.W.， Poh， K.L. （2007）. Measuring environmental performance under different environmental DEA technologies. Energy Economics， 30（5）， 114.

[27] Zhou， P.， Ang， B. W.， Poh， K. L.， （2008）. Measuring environmental performance under different environment DEA technologies. Energy Economics， 30（1）， 1-14.

[28] Zhou， P.， Ang， B. W.， Wang， H.， （2012）. Energy and CO2 emission performance in electricity generation： A non-radial directional distance function approach. European Journal of Operational Research.， 221（3）， 625-635.

[29] Zofio， J. L.， Prieto， A. M.， （2001）. Environmental efficiency and regulatory standards： the case of CO2 emissions from OECD industries. Resource and Energy Economics， 23（1）， 6383.