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The infeasible problem of Malmquist–Luenberger index and its application on China’s environmental total factor productivity

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Abstract

The Malmquist–Luenberger productivity index would cause infeasible problem when measuring mixed period change of total factor productivity. The former research focuses on the infeasible issue under the hypothesis of constant return to scale (CRS). There are many meaningful solutions which could avoid this infeasible problem of Malmquist–Luenberger productivity index. However, these solutions couldn’t avoid infeasible problem under condition of variable returns to scale (VRS). The new solution is proposed in this paper which could solve this problem under VRS based on super-efficiency issue. The empirical results of environmental total factor productivity (ETFP) change of thirty regions in China indicate that China isn’t efficient from 1997 to 2014. Among eight economic regions northwest and southern coastal decline, the ETFP decrease 15%, 10% respectively. From the perspective of provinces in China, Hainan, Qinghai and Ningxia have the lowest environmental total factor productivity and their environmental technical efficiency is also the lowest. These non-efficient provinces all have lower gross domestic product and they should improve technique change efficiency through adopting advanced technology in the future. The fixed effects regression model illustrates that energy intensity, research and development, foreign direct investment are factors of ETFP in China. Both research and development and foreign direct investment could improve total factor productivity and this indicates that Pollutant Heaven Hypothesis doesn’t exist in China.

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References

  1. Aparicio, J., Pastor, J. T., & Zofio, J. L. (2013). On the inconsistency of the Malmquist–Luenberger index. European Journal of Operational Research, 229(3), 738–742.

  2. Arabi, B., Munisamy, S., & Emrouznejad, A. (2015). A new slacks-based measure of Malmquist–Luenberger index in the presence of undesirable outputs. Omega, 51, 29–37.

  3. Bronzini, R., & Piselli, P. (2009). Determinants of long-run regional productivity with geographical spillovers: The role of R&D, human capital and public infrastructure. Regional Science and Urban Economics, 39(2), 187–199.

  4. Caves, D. W., Christensen, L. R., & Diewert, E. W. (1982). The economic theory of index numbers and the measurement of input, output, and productivity. Econometrica, 50(6), 1393–1414.

  5. Chambers, R. G., Chung, Y., & Färe, R. (1996). Benefit and distance functions. Journal of Economic Theory, 70(2), 407–419.

  6. Chimeli, A., & Braden, J. (2004). Total factor productivity and the environmental Kuznets curve. Journal of Environmental Economics and Management, 49(2), 366–380.

  7. Chung, Y., Färe, R., & Grosskopf, S. (1997). Productivity and undesirable outputs: A directional distance function approach. Journal of Environmental Management, 51(3), 229–240.

  8. Cropper, M. L., & Oates, W. E. (1992). Environmental Economics: A Survey. Journal of Economic Literature, 30(2), 675–740.

  9. Du, M., Wang, B., & Wu, Y. (2014). Sources of China’s economic growth: An empirical analysis based on the BML index with green growth accounting. Sustainability, 6(9), 5983–6004.

  10. Essid, H., Ouellette, P., & Vigeant, S. (2014). Productivity, efficiency, and technical change of Tunisian schools: A bootstrapped Malmquist approach with quasi-fixed inputs. Omega, 42(1), 88–97.

  11. Färe, R., & Grosskopf, S. (2010). Directional distance functions and slacks-based measures of efficiency. European Journal of Operational Research, 200(1), 320–322.

  12. Färe, R., Grosskopf, S., & Lovell, C. A. K. (1994). Production frontiers. Cambridge: Cambridge University Press.

  13. Färe, R., Grosskopf, S., & Pasurka, C. (1986). Effects on relative efficiency in electric power generation due to environmental controls. Resources and Energy, 8, 167–184.

  14. Färe, R., Grosskopf, S., & Pasurka, C. A, Jr. (2001). Accounting for air pollution emissions in measures of state manufacturing productivity growth. Journal of Regional Science, 41(3), 381–409.

  15. Färe, R., Grosskopf, S., & Pasurka, C. A. (2007). Environmental production functions and environmental directional distance functions. Energy, 32(7), 1055–1066.

  16. Färe, R., Grosskopf, S., & Pasurka, C. A. (2014). Potential gains from trading bad outputs: The case of U.S. electric power plants. Resource and Energy Economics, 36(1), 99–112.

  17. Färe, R., Grosskopf, S., Pasurka, C. A., & William, W. (2012). Substitutability among undesirable outputs. Applied Economics, 44(1), 39–47.

  18. Fuentes, R., & Lillo-Banuls, A. (2015). Smoothed bootstrap Malmquist index based on DEA model to compute productivity of tax offices. Expert Systems with Applications, 42(5), 2442–2450.

  19. Gitto, S., & Mancuso, P. (2012). Bootstrapping the Malmquist indexes for Italian airports. International Journal Production Economics, 135(1), 403–411.

  20. He, J. (2006). Pollution haven hypothesis and environmental impacts of foreign direct investment: The case of industrial emission of sulfur dioxide in Chinese provinces. Ecological Economics, 60(1), 228–245.

  21. Horbach, J., Rammer, C., & Rennings, K. (2012). Determinants of eco-innovations by type of environmental impact. Ecological Economics, 78(6), 112–122.

  22. Hu, J. L., & Wang, S. C. (2006). Total-factor energy efficiency of regions in China. Energy Policy, 34(17), 3206–3217.

  23. Kao, C. (2010). Malmquist productivity index based on common-weights DEA: The case of Taiwan forests after reorganization. Omega, 38, 484–491.

  24. Krautzberger, L., & Wetzel, H. (2012). Transport and CO\(_{2}\): Productivity growth and carbon dioxide emissions in the European commercial transport industry. Environmental Resource Economics, 53(3), 435–454.

  25. Kumar, S. (2006). Environmentally sensitive productivity growth: A global analysis using Malmquist–Luenberger index. Ecological Economics, 56(2), 280–293.

  26. Liang, L., Li, Y. J., & Li, S. B. (2009). Increasing the discriminatory power of DEA in the presence of the undesirable outputs and large dimensionality of data sets with PCA. Expert Systems with Applications, 36(3), 5895–5899.

  27. Liu, W., & Tang, D. (2012). Environmental regulation, technological efficiency and total factor productivity growth. Industrial Economics Research, 5, 28–35.

  28. Loko, B., & Diouf, M. (2009). Revisiting the determinants of productivity growth: What’s new? IMF Working Paper; WP/09/225.

  29. Lovell, C., & Rouse, A. (2003). Equivalent standard DEA models to provide super-efficiency scores. Journal of the Operational Research Society, 54(1), 101–108.

  30. Luenberger, D. G. (1992a). Benefit functions and duality. Journal of Mathematical Economics, 21(5), 461–486.

  31. Luenberger, D. G. (1992b). New optimality principles for economic efficiency and equilibrium. Journal of Optimization Theory and Applications, 75(2), 221–264.

  32. Luenberger, D. G. (1994a). Dual Pareto efficiency. Journal of Economic Theory, 62(1), 70–85.

  33. Luenberger, D. G. (1994b). Optimality and the theory of value. Journal of Economic Theory, 63(2), 147–169.

  34. Luenberger, D. G. (1995). Externalities and benefits. Journal of Mathematical Economics, 24(2), 159–177.

  35. Oh, D. H. (2010). A global Malmquist–Luenberger productivity index. Journal of Productivity Analysis, 34(3), 183–197.

  36. Oh, D. H., & Heshmati, A. (2010). A sequential Malmquist–Luenberger productivity index: Environmentally sensitive productivity growth considering the progressive nature of technology. Energy Economics, 32(6), 1345–1355.

  37. Pastor, J. T., Asmild, M., & Lovell, C. A. (2011). The biennial Malmquist productivity change index. Socio-Economic Planning Sciences, 45(1), 10–15.

  38. Reinhard, S. C., Lovell, A. K., & Thijssen, G. (1999). Econometric estimation of technical and environmental efficiency: An application to Dutch dairy farms. American Journal of Agricultural Economics, 81(1), 44–60.

  39. Seiford, L. M., & Zhu, J. (2002). Modeling undesirable factors in efficiency evaluation. European Journal of Operational Research, 142(1), 16–20.

  40. Shephard, R. W. (1953). Cost and production functions. Princeton, NJ: Princeton University Press.

  41. Shestalova, V. (2003). Sequential Malmquist indices of productivity growth: An application to OECD industrial activities. Journal of Productivity Analysis, 19(2/3), 211–226.

  42. Sueyoshi, T., & Goto, M. (2013). DEA environmental assessment in a time horizon: Malmquist index on fuel mix, electricity and \({\rm CO}_{2}\) of industrial nations. Energy Economics, 40, 370–382.

  43. Tang, D., Tang, J., Xiao, Z., Ma, T., & Bethel, B. (2017). Environmental regulation efficiency and total factor productivity-effect analysis based on Chinese data from 2003 to 2013. Ecological Indicators, 73(2), 312–318.

  44. Tone, K. (2010). Variations on the theme of slacks-based measure of efficiency in DEA. European Journal of Operational Research, 200(3), 901–907.

  45. Tulkens, H., & Vanden Eeckaut, P. (1995). Non-parametric efficiency, progress and regress measure for panel data: Methodological aspects. European Journal of Operational Research, 80(3), 474–499.

  46. Wang, B., Wu, Y., & Yan, P. (2010). Environmental efficiency and environmental total factor productivity growth in China’s regional economics. Economic Research Journal, 5, 95–109.

  47. Wheeler, D. (2001). Racing to the bottom? Foreign investment and air pollution in development countries. Journal of Environment and Development, 10(3), 225–245.

  48. Wu, A. H., Cao, Y. Y., & Liu, B. (2013). Energy efficiency evaluation for regions in China: An application of DEA and Malmquist indices. Energy Efficiency, 7(3), 429–439.

  49. Zhang, C., Liu, H., Bressers, H. T., & Buchanan, K. S. (2011). Productivity growth and environmental regulations-accounting for undesirable outputs: Analysis of China’s thirty provincial regions using the Malmquist–Luenberger index. Ecological Economics, 70(12), 2369–2379.

  50. Zhang, Z., & Ye, J. (2015). Decomposition of environmental total factor productivity growth using hyperbolic distance functions: A panel data analysis for China. Energy Economics, 47, 87–97.

  51. Zhang, K., Yi, Y., & Zhang, W. (2014). Environmental total factor productivity and regional disparity in China. Letters in Spatial and Resource Sciences, 7(1), 9–21.

  52. Zhou, P., Ang, B. W., & Han, J. Y. (2010). Total factor carbon emission performance: A Malmquist index analysis. Energy Economics, 32(1), 194–201.

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Acknowledgements

The first author thanks the National Natural Science Foundation of China (Grant Nos. 71471133, 71432007 & 71532015) for funding. This study is partially supported by the Priority Academic Program Development of Jiangsu Higher Education Institutions (China). The corresponding author thanks the 18th Annual Conference of China Management Science for the feedback on an earlier version of the research.

Author information

Correspondence to Jinghua Xu.

Appendix

Appendix

See Appendix Tables 6, 7, 8, 9 and 10.

Table 6 Data set for test
Table 7 Distance value based on the conventional constraint (=) with CRS
Table 8 Distance value based on new constraint (\(<=\)) with CRS
Table 9 Distance value based on the new constraint (\(<=\)) with VRS
Table 10 Distance value based on the new constraint (\(<=\)) of this proposed model with VRS

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Du, J., Duan, Y. & Xu, J. The infeasible problem of Malmquist–Luenberger index and its application on China’s environmental total factor productivity. Ann Oper Res 278, 235–253 (2019). https://doi.org/10.1007/s10479-017-2603-3

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Keywords

  • Infeasible
  • Malmquist–Luenberger index
  • Environmental total factor productivity
  • Variable returns to scale