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Using a hybrid heterogeneous DEA method to benchmark China’s sustainable urbanization: an empirical study

  • S.I.: DEA in Data Analytics
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Abstract

Due to recent official policy changes, China’s sustainable urbanization has entered a new type of multi-target heterogeneous situation which has never been scientifically researched before. To deal with this new heterogeneous scenario, we introduce a hybrid heterogeneous data envelopment analysis method that contains input segment estimation and efficient frontier construction. We also introduce a bi-level benchmarking method that benchmarks each city’s eco-efficiency and uses those benchmarks to guide sustainable urbanization completion in an empirical study of 206 Chinese prefecture-level cities’ sustainable urbanization. Our main empirical results show that: (1) China’s urbanization is now suffering from serious unsustainability; (2) China’s sustainable urbanization is independent of urban scale; (3) resource over-consumption and pollutant over-emission are the two complementary forces that slow down China’s sustainable urbanization; (4) almost all prefecture-level cities involved in this empirical study should set “Urban–rural integration” as the urbanization development target; and (5) China’s current urbanization has a serious development target mismatch, and this target mismatch is thought to be an important indirect factor that drives China’s urbanization to a low sustainability level. Based on this empirical analysis, we recommend two urbanization policies, “Constructing a distinctive city” and “Constructing hub-and-spoke urban agglomeration”, for Chinese government consideration.

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Notes

  1. http://english.gov.cn/policies/policy_watch/2014/08/23/content_281474983027472.htm.

  2. Total urbanization normally means 100% urban area or all people live in the urban area.

  3. Urban–rural integration means people who live in the rural area and people live in the urban area can have equal social welfare.

  4. A city which selects UR should subsequently determine urban area proportion (equivalently, rural area proportion). For the convenience of description, we refer to a determined urban area proportion as a UR level hereafter. It is trivial to verify that the number of possible UR levels is vast so it can be a challenge for some city’s government to make a proper determination of UR level.

  5. China’s cities can be divided into four types: Provincial-level cities (i.e. municipality), Prefectural-level cities (i.e. prefectural-level city and sub-provincial city), County-level cities (i.e. county-level city, sub-prefectural city, and XPCC city), and Special administrative regions. Considering the availability of national statistical data, we concentrate our research on the Provincial-level cities and Prefectural-level cities. For the convenience of description, we hereafter use “prefecture-level city” to represent all Provincial-level or Prefectural-level cities.

  6. According to Dyson et al. (2001), the traditional homogeneity assumption in classical DEA theory is that organizations use the same range of resources to pursue the same business or non-business goal through the same operational process. Any violation of the above three points results in a heterogeneous situation. In this paper, we do concentrate our research on the heterogeneity caused by the existence of different non-business goals, in particular, the two alternative urbanization targets, TU and UR. For other details, please see Dyson et al. (2001).

  7. In the methodological part, we only consider the situation where rural income is no more than urban income, which is consistent with Chinese cities’ real-world observed data.

  8. For detailed reasons why we do not use the VRS assumption in this research, please see Sect. 3.2.

  9. If \( \sum\limits_{i = 1}^{m} {\frac{{\omega_{i}^{j*} (s_{i}^{1x} )^{*} }}{{\omega_{i1j}^{j*} x_{ij} }}} = \sum\limits_{i = 1}^{m} {\frac{{\omega_{i}^{j*} (s_{i}^{2x} )^{*} }}{{\omega_{i2j}^{j*} x_{ij} }}} \), we record “−” in the tables.

  10. Reference points can be derived by resolving Model (3) for each city respectively.

  11. The proofs of these two lemmas are trivial, thus are omitted here.

  12. Lemma 5.1 would be used in the proof of Lemma 5.2, and Lemma 5.2 would be used to ensure the reasonability of following quantitative benchmark.

  13. \( F_{j}^{ - 1} ( \bullet ) \) is the inverse function of \( F_{j} ( \bullet ) \). In fact, \( F_{0}^{ - 1} \left(\mathop {\hbox{min} }\limits_{{R \in \left\{ {1, \ldots ,k} \right\}}} \left( {\mathop {\hbox{max} }\limits_{{r \in \left\{ {1, \ldots s_{R} } \right\}}} \left( {\frac{{\bar{y}_{R} }}{{y_{Rr0} + s_{r}^{Ry*} }}} \right)} \right)\right) \) may have more than one value. Suppose, without loss of generality, that \( F_{0}^{ - 1} \left(\mathop {\hbox{min} }\limits_{{R \in \left\{ {1, \ldots ,k} \right\}}} \left( {\mathop {\hbox{max} }\limits_{{r \in \left\{ {1, \ldots s_{R} } \right\}}} \left( {\frac{{\bar{y}_{R} }}{{y_{Rr0} + s_{r}^{Ry*} }}} \right)} \right)\right) \) has two values \( X \) and \( Y \). Then city \( {\it DMU}_{0} \) can set either of them as its urbanization target, since it is easy to check that setting target \( X \) and setting target Y would have equal sustainability from the mathematical aspect.

  14. Via Lemma 5.2, it is easy to check that this suggested input variation would keep the sustainability of each city’s urbanization, which is resulted from the first level benchmark, being invariant in the second level benchmark.

  15. Consequent variations of pollutant emission are listed in Tables 22, 23, 24, 25, 26 and 27 as well.

  16. In this paper, a huge city means it has a large urban area rather than a large population.

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Acknowledgements

This research is supported by National Natural Science Foundation of China (No. 71571173), China Postdoctoral Science Foundation (No. 2017M622027), the Fundamental Research Funds for the Central Universities (No. WK2040160029), Top-Notch Young Talents Program of China, and the Research Center of Modern Logistics Engineering of USTC.

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Authors and Affiliations

  1. School of Management, University of Science and Technology of China, 96 Jinzhai Road, Hefei, 230026, Anhui, China

    Xiang Ji, Jie Wu & Qingyuan Zhu

  2. Business School, Soochow University, Suzhou, 215021, China

    Jiasen Sun

Authors
  1. Xiang Ji
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  2. Jie Wu
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  3. Qingyuan Zhu
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Corresponding author

Correspondence to Jie Wu.

Appendices

Appendix A

See Tables 10, 11, 12, 13, 14 and 15.

Table 10 Efficiency scores of East China
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Table 11 Efficiency scores of North China
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Table 12 Efficiency scores of Central China
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Table 13 Efficiency scores of South China
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Table 14 Efficiency scores of Southwest China
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Table 15 Efficiency scores of Northeast China
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Appendix B

See Tables 16, 17, 18, 19, 20, 21.

Table 16 Index-level variations of 1st level benchmark in East China
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Table 17 Index-level variations of 1st level benchmark in North China
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Table 18 Index-level variations of 1st level benchmark in Central China
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Table 19 Index-level variations of 1st level benchmark in South China
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Table 20 Index-level variations of 1st level benchmark in Southwest China
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Table 21 Index-level variations of 1st level benchmark in Northeast China
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Appendix C

See Tables 22, 23, 24, 25, 26, 27.

Table 22 Recommended input variation and consequent emission variation in East China
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Table 23 Recommended input variation and consequent emission variation in North China
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Table 24 Recommended input variation and consequent emission variation in Central China
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Table 25 Recommended input variation and consequent emission variation in South China
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Table 26 Recommended input variation and consequent emission variation in Southwest China
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Table 27 Recommended input variation and consequent emission variation in Northeast China
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Appendix D: Efficiency score radar map of each region

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Appendix E: City urban population proportion radar map of each region

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Ji, X., Wu, J., Zhu, Q. et al. Using a hybrid heterogeneous DEA method to benchmark China’s sustainable urbanization: an empirical study. Ann Oper Res 278, 281–335 (2019). https://doi.org/10.1007/s10479-018-2855-6

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