## Abstract

China is one of the largest energy consumers and CO_{2} emitters globally. The growth rate of energy consumption in China is about 6 % per year, and it consumed 21 % of the world’s total energy in 2012. In recent years, the Chinese government decided to introduce several energy policy instruments to promote energy efficiency. For instance, the reduction targets for the level of energy intensity have been defined for provinces in China. However, energy intensity is not an accurate proxy for energy efficiency because changes in energy intensity are a function of changes in several socioeconomic factors. In this paper, we present an empirical analysis on the estimation of the persistent and transient energy efficiency of Chinese provinces by employing a log-log aggregate energy demand frontier model. The model is estimated by using data on 29 provinces observed over the period 2003 to 2012. Several econometric model specifications for panel data are used: the random effects model and the true random effects model along with other versions of these models. Our analysis shows that energy intensity cannot measure accurately the level of efficiency in the use of energy in Chinese provinces. Further, our empirical analysis shows that the average value of the *persistent* energy efficiency is around 0.81 whereas the average value of the *transient* energy efficiency is relatively high and shows a value of approximately 0.97. By improving the level of efficiency in the use of energy to 100 %, the total energy consumption in China would decrease by approximately 1000 Mtce, which corresponds to 25 % of total energy consumption in 2012.

### Similar content being viewed by others

## Notes

In the period 1980–2000, China’s energy intensity declined 4.52 % annually. Though experienced a slight increase between 2002 and 2005, it continued with a staggering decline of 18 % between 2005 and 2010. Moreover, we observe heterogeneity in the level and the development of energy intensity across provinces. These differences may be related to variation in the level of central government pressure on provincial government targets to reduce the level of energy intensity.

In previous works (Filippini and Hunt, 2011 and 2012) on the measurement of the level of energy efficiency using aggregate data, the term “underlying energy efficiency” has been used. In this study, following the recent papers by Filippini and Hunt (2015a and 2015b), the general term energy efficiency is used.

For a presentation of parametric and non-parametric methods, see, for instance, Murillo-Zamorano (2004).

In the literature on the estimation of the level of energy efficiency, it is possible to find studies based on non-parametric approaches such as DEA (Hu and Wang (2006), Zhou and Anag (2008)) as well as studies based on SFA (Filippini and Hunt (2011, 2015a, b), Lundgren et al. (2016)). To note, those both approaches have their own advocates. At least in the scientific community, neither one has emerged as dominant. For instance, the Journal of Productivity Analysis, the leading journal in the field of the measurement of productivity and efficiency, regularly publishes contributions based on DEA and contributions based on SFA.

Many papers have also examined the driving forces for energy intensity decline in China using Divisia decomposition method. For instance, Fisher-Vanden et al. (2004) applied the approach using panel data for 2500 industrial enterprises and identified several forces such as research and development expenditures and changes in China’s industrial structure as the principal drivers. Hang and Tu (2007) followed similar approach and showed the asymmetric impacts of energy prices on energy intensity. There are also studies in literature on the structural change effects (Liao et al. 2007; Ma and Stern 2008). Song and Zheng (2012) combined decomposition analysis with econometric model and found the significant impacts of rising income as well as limited effect of energy price on the reduction of energy intensity.

Generally, the empirical literature on the measurement of productive efficiency interprets time-varying and time-invariant inefficiency indicators as alternative measures of productive efficiency. See, for instance, Filippini and Hunt (2012). Only recently, Kumbhakar et al. (2014) introduced a new interpretation of these inefficiency measures based on complementarity. In this paper, we decided to follow this approach.

Generally, the numbers of HDD and CDD are highly correlated. This correlation can create a multicollinearity problem in the econometric estimation. In order to avoid this problem, we use the sum of these two variables. We also tested our results by using dummies to represent different climate zones in Chinese provinces. The regression result shows that the climate variables are still statistically insignificant. Furthermore, the Spearman’s rank correlation coefficient of the estimated efficiencies between model using climate zones dummies and the model using HCDD is very high (around 0.92). Hence, we believe that the variable HCDD that we used in the paper captures the main information of the climate.

As suggested in Filippini and Hunt (2012), time dummies can also be used as an alternative to capture the impacts of UEDT. In a preliminary analysis, we also used time dummies and the results were relatively similar.

The yearbooks of China always have 1-year delay, which means that yearbook in 1997 reports the statistics of 1996.

For a general presentation of these models, see Greene (2008) and Farsi and Filippini (2009). In a preliminary analysis, we also estimate a pooled model as well as a Battese and Coelli model (1992) where the inefficiency varies over time in a fixed way (exponentially). The results of both model specifications were not encouraging.

The TREM is estimated using a simulated maximum likelihood procedure.

To note that in the literature using data for industrialized countries characterized by a relatively small weight of energy to GDP, this potential endogeneity problem is rarely considered.

The instruments considered in our empirical analysis are the ratio of engineers in professional personnel (ENG

_{ it }), the number of secondary schools (SCH_{ it }), and the number of teachers (TEA_{ it }). In order to verify the validity of the instruments, we estimate a classic fixed effects model. To test for weak instruments, we compute the Cragg-Donald Wald*F*test statistic. The value of this statistic (12.21) is larger than the critical value at 10 % level of significance (9.08) suggested by Stock and Yogo (2003). Therefore, we reject the hypothesis that instruments are weak. The Hansen J statistic for testing the overidentification of all instruments does not reject the null hypothesis of valid instruments (chi-sq(2) = 0.50,*P*value = 0.78). All these results show that we are able to find reasonable instruments. Of course, we are aware that this procedure may not be completely satisfactory for the estimation of a SFA.As a robustness check, MREM-2SRI and MTREM-2SRI models are also estimated and presented in the paper.

Lambda (

*λ*) gives information on the relative contribution of*uit*and*vit*on the decomposed error term*εit*and shows that, in this case, the one-sided error component is relatively large.Given the fact that we are using a log-log functional form, the estimated coefficients can be interpreted as elasticities.

In an explorative and preliminary analysis and following the approach suggested by Filippini et al. (2014), we also consider to verify the impact of the change of the energy policy on the level of energy efficiency. In fact, from 2006, the 11th Five-Year Plan and, from 2007, the revised energy conservation law have been implemented. The results show that these changes in the energy policy do not have statistically significant effect on the inefficiency term.

In order to select the variables to consider in the Mundlak adjustment, we estimate a regular fixed and random effects model and we used the Hausman test. The model specification used in the estimation of the Mundlak version of REM and TREM was confirmed by the results of the Hausman test

**.**The Spearman’s rank correlation coefficient between the level of efficiency obtained using MREM and MREM-2SRI is 0.9951. Also, the rank correlation coefficient between the level of efficiency obtained using MTREM and MTREM-2SRI is very high (0.9749).

## References

Aigner, D. J., Lovell, C. A. K., & Schmidt, P. (1977). Formulation and estimation of stochastic frontier production function models.

*Journal of Economics, 6*, 21–37.Battese, G.E., & Coelli, T.J. (1992). Frontier production functions, technical efficiency, and panel data: with application to Paddy farmers in India.

*Journal of Productivity Analysis, 3,*153–169.Bi, G., Song, W., Zhou, P., & Liang, L. (2014). Does environmental regulation affect energy efficiency in China’s thermal power generation? Empirical evidence from a slacks-based DEA model.

*Energy Policy, 66*, 527–546.Butler, J., & Moffitt, R. (1982). A computationally efficient quadrature procedure for the one factor multinomial probit model.

*Econometrica, 50*, 761–764.Chen, G. Q., & Chen, Z. M. (2010). Carbon emissions and resources use by Chinese economy 2007: a 135-sector inventory and input–output embodiment.

*Communications in Nonlinear Science and Numerical Simulation, 15*(11), 3647–3732.Chen, Z. M., & Chen, G. Q. (2011). An overview of energy consumption of the globalized world economy.

*Energy Policy, 39*(10), 5920–5928.Chen, Z. M., Chen, G. Q., Zhou, J. B., Jiang, M. M., & Chen, B. (2010). Ecological input–output modeling for embodied resources and emissions in Chinese economy 2005.

*Communications in Nonlinear Science and Numerical Simulation, 15*(7), 1942–1965.Colombi, R., Kumbhakar, S., Martini, G., & Vittadini, G. (2014). Closed-skew normality in stochastic frontiers with individual effects and long/short-run efficiency. Journal of Productivity Analysis. DOI 10.1007/s11123-014-0386-y

EIA (2013). International Energy Outlook 2013. U.S. Energy Information Administration.

Farsi, M., & Filippini, M. (2009). Efficiency measurement in the electricity and gas distribution sectors. In J. Evans & L. C. Hunt (Eds.),

*International handbook on the economics of energy*(pp. 598–623). Cheltenham: Edward Elgar.Farsi, M., Filippini, M., & Greene, W. (2005a). Efficiency measurement in network industries: application to the Swiss railway companies.

*Journal of Regulatory Economics, 28*, 69–90.Farsi, M., Filippini, M., & Kuenzle, M. (2005b). Unobserved heterogeneity in stochastic frontier models: an application to Swiss nursing homes.

*Applied Economics, 37*, 2127–2141.Filippini, M. and Greene, W. (2015): Persistent and transient productive inefficiency: a maximum simulated likelihood approach. Journal of Productivity Analysis, forthcoming.

Filippini, M., & Hunt, L. (2011). Energy demand and energy efficiency in the OECD countries: a stochastic demand frontier approach.

*The Energy Journal, 32*(2), 59–80.Filippini, M., & Hunt, L. (2012). US residential energy demand and energy efficiency: a stochastic demand frontier approach.

*Energy Economics, 34*, 1484–1491.Filippini, M. and Hunt, L. (2013). ‘Underlying energy efficiency’ in the US. CER-ETH Economics Working Paper Series 13/181.

Filippini, M. and Hunt, L. (2015 a). Measurement of energy efficiency based on economic foundations, Energy Economics (forthcoming).

Filippini, M. and Hunt, L. (2015 b). Measuring persistent and transient energy efficiency in the US, Energy Efficiency, (forthcoming).

Filippini, M., Hunt, L., & Zoric, J. (2014). Impact of energy policy instruments on the estimated level of underlying energy efficiency in the EU residential sector.

*Energy Policy, 69*, 73–81.Fisher-Vanden, K., Jefferson, G., Liu, H., & Tao, Q. (2004). What is driving China’s decline in energy intensity?

*Resource and Energy Economics, 26*, 77–97.Greene, W. (2005a). Reconsidering heterogeneity in panel data estimators of the stochastic frontier model.

*Journal of Economics, 126*, 269–303.Greene, W. (2005b). Fixed and random effects in stochastic frontier models.

*Journal of Productivity Analysis, 23*, 7–32.Greene, W. (2008). The econometric approach to efficiency analysis. Chapter 2. In H. O. Fried, C. A. K. Lovell, & S. S. Schmidt (Eds.),

*The measurement of productive efficiency and productivity growth*(pp. 92–250). Oxford: University Press.Greene, W. (2011).

*Econometric analysis*(7th ed.). Upper Saddle River: Prentice-Hall.Hang, L., & Tu, M. (2007). The impacts of energy prices on energy intensity: evidence from China.

*Energy Policy, 35*, 2978–2988.Hu, J., & Wang, S. (2006). Total-factor energy efficiency of regions in China.

*Energy Policy, 34*, 3206–3217.Hu, J., & Wang, S. (2010). Total-factor energy productivity growth, technical progress, and efficiency change: an empirical study of China.

*Applied Energy, 87*, 3262–3270.IEA (2009). Progress with implementing energy efficiency policies in the G8', International Energy Agency Paper. www.iea.org/publications/free_new_Desc.asp?PUBS_ID=2127

Jaunky, V. C. and Zhang, L. (2016). Convergence of operational efficiency in China’s provincial power sectors. The Energy Journal, forthcoming.

Jondrow, J., Lovell, C. A. K., Materov, I. S., & Schmidt, P. (1982). On the estimation of technical efficiency in the stochastic frontier production function model.

*Journal of Economics, 19*, 233–238.Kumbhakar, S.C. and Lovell, C.A. (2000): Stochastic frontier analysis, Cambridge: Cambridge University Press.

Kumbhahkar, S. C., Lien, G., & Hardaker, J. B. (2014). Technical efficiency in competing panel data models: a study of Norwegian grain farming.

*Journal of Productivity Analysis, 41*, 321–337.Liao, H., Fan, Y., & Wei, Y. (2007). What induced China’s energy intensity to fluctuate: 1997–2006?

*Energy Policy, 35*, 4640–4649.Lundgren, T., Marklund, P., and Zhang, S. (2016). Industrial energy demand and energy efficiency—evidence from Sweden. Resource and Energy Economics, forthcoming. doi:10.1016/j.reseneeco.2016.01.003

Ma, C., & Stern, D. (2008). China’s changing energy intensity trend: a decomposition analysis.

*Energy Economics, 30*, 1037–1053.Mundlak, Y. (1978). On the pooling of time series and cross section data.

*Econometrica, 64*, 69–85.Murillo-Zamorano, L. R. (2004). Economic efficiency and frontier techniques.

*Journal of Economic Surveys, 18*(1), 33–77.Mutter, R. L., Greene, W. H., Spector, W., Rosko, M. D., & Mukamel, D. B. (2013). Investigating the impact of endogeneity on inefficiency estimates in the application of stochastic frontier analysis to nursing homes.

*Journal of Productivity Analysis, 39*, 101–110.NBS, 2004–2013a, China Statistical Yearbooks. Beijing, China.

NBS, 2004–2013b, China urban life and price yearbook. Beijing, China.

Pitt, M., & Lee, L. (1981). The measurement and sources of technical inefficiency in the Indonesian weaving industry.

*Journal of Development Economics, 9*, 43–64.Polachek, S. W., & Yoon, B. J. (1996). Panel estimates of a two-tiered earnings frontier.

*Journal of Applied Econometrics, 11*(2), 169–78.Price, L., Levine, M., Zhou, N., Fridley, D., Aden, N., Lu, H., McNeil, M., Zheng, N., Qin, Y., & Yowargana, P. (2011). Assessment of China’s energy-saving and emission-reduction accomplishments and opportunities during the 11th Five Year Plan.

*Energy Policy, 39*(4), 2165–2168.Song, F., & Zheng, X. (2012). What drives the change in China’s energy intensity: combining decomposition analysis and econometric analysis at the provincial level.

*Energy Policy, 51*, 445–453.Stock, J. and Yogo, M. (2003) Testing for weak instruments in linear IV regression, mimoe, Harvard University.

Terza, J. V., Basu, A., & Rathouz, P. J. (2008). Two-stage residual inclusion estimation: addressing endogeneity in health econometric modeling.

*Journal of Health Economics, 27*(3), 531–543.Tsionas, E. G., & Kumbhakar, S. C. (2014). Firm-heterogeneity, persistent and transient technical inefficiency: a generalized true random-effects model.

*Journal of Applied Econometrics, 29*(1), 110–132.Wei, C., Ni, J., & Shen, M. (2009). Empirical analysis of provincial energy efficiency in China.

*China & World Economy, 17*(5), 88–103.Xia, X. H., Huang, G. T., Chen, G. Q., Zhang, B., Chen, Z. M., & Yang, Q. (2011). Energy security, efficiency and carbon emission of Chinese industry.

*Energy Policy, 39*, 3520–3528.Zhang, L. (2013). Model projections and policy reviews for energy saving in China’s service sector.

*Energy Policy, 59*, 312–320.Zhao, X., Yang, R., & Ma, Q. (2014). China’s total factor energy efficiency of provincial industrial sectors.

*Energy, 65,*52–61.Zhou, P. & Anag, B.W. (2008). Linear programming models for measuring economy-wide energy efficiency performance.

*Energy Policy, 36,*2911–2916.

## Acknowledgments

This paper has been presented at Harvard University (Harvard China Project) and MIT (MIT/Tsinghua China Energy and Climate Project). We are grateful to participants for their comments and suggestions. We also thank the editor and the reviewers for the suggestions. Needless to say, we are responsible for any errors and omissions.

## Author information

### Authors and Affiliations

### Corresponding author

## Rights and permissions

## About this article

### Cite this article

Filippini, M., Zhang, L. Estimation of the energy efficiency in Chinese provinces.
*Energy Efficiency* **9**, 1315–1328 (2016). https://doi.org/10.1007/s12053-016-9425-z

Received:

Accepted:

Published:

Issue Date:

DOI: https://doi.org/10.1007/s12053-016-9425-z