{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T00:38:21Z","timestamp":1760143101349,"version":"build-2065373602"},"reference-count":52,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2024,1,10]],"date-time":"2024-01-10T00:00:00Z","timestamp":1704844800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["71971163"],"award-info":[{"award-number":["71971163"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Systems"],"abstract":"<jats:p>Due to persistent technological impacts on ecological efficiency (eco-efficiency) and variations in economic power and resource endowments among regions, considering regional and temporal heterogeneity becomes imperative. Ecosystems, often divided into economic production and environmental governance stages, necessitate a holistic assessment incorporating regional, temporal heterogeneity and stage distinctions. To address potential issues of a technology gap ratio (TGR) exceeding 1 within a two-stage network structure with dual heterogeneity, we introduce a segmented projection three-layer meta-frontier analysis method. In empirical study, we systematically examined eco-efficiency, emissions inefficiency and technology gaps across management, regional and temporal dimensions in 30 Chinese provinces from 2016 to 2020. Findings reveal disparities in management eco-efficiency, with the central provinces outperforming the east. Regional differences indicate advanced technology in the east, contributing to superior eco-efficiency. Temporal analysis highlights the positive role of scientific and technological development. Emissions inefficiency improvements are noted, necessitating attention toward management and regional technology levels. Eastern provinces exhibit superior emissions efficiency, emphasizing the role of regional and technological development. Recommendations include prioritizing environmental governance, strengthening regional collaborations and implementing policies to bridge technology gaps.<\/jats:p>","DOI":"10.3390\/systems12010022","type":"journal-article","created":{"date-parts":[[2024,1,11]],"date-time":"2024-01-11T03:21:41Z","timestamp":1704943301000},"page":"22","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Ecological Efficiency Measurement and Technical Heterogeneity Analysis in China: A Two-Stage Three-Level Meta-Frontier Network Model Based on Segmented Projection"],"prefix":"10.3390","volume":"12","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-8068-7716","authenticated-orcid":false,"given":"Ruiyue","family":"Lin","sequence":"first","affiliation":[{"name":"College of Mathematics and Physics, Wenzhou University, Wenzhou 325035, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xinyuan","family":"Wang","sequence":"additional","affiliation":[{"name":"College of Mathematics and Physics, Wenzhou University, Wenzhou 325035, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yu","family":"Jiang","sequence":"additional","affiliation":[{"name":"College of Mathematics and Physics, Wenzhou University, Wenzhou 325035, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2024,1,10]]},"reference":[{"key":"ref_1","first-page":"273","article-title":"\u00d6kologische rationalit\u00e4t: Ansatzpunkte zur ausgestaltung von \u00f6kologieorientierten managementinstrumenten","volume":"44","author":"Schaltegger","year":"1990","journal-title":"Die Unternehm."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"1180","DOI":"10.1016\/j.jclepro.2017.10.204","article-title":"Eco-efficiency assessment of Polish regions: Joint application of life cycle assessment and data envelopment analysis","volume":"172","year":"2018","journal-title":"J. Clean. Prod."},{"key":"ref_3","unstructured":"Lehni, M. (2000). Eco-Efficiency: Creating More Value with Less Impact, World Business Council for Sustainable Development."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"709","DOI":"10.1016\/j.eswa.2013.07.095","article-title":"Measuring energy efficiency performance of China\u2019s transport sector: A data envelopment analysis approach","volume":"41","author":"Zhou","year":"2014","journal-title":"Expert Syst. Appl."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"457","DOI":"10.1007\/s11123-013-0357-8","article-title":"Separating environmental efficiency into production and abatement efficiency: A nonparametric model with application to US power plants","volume":"41","author":"Hampf","year":"2014","journal-title":"J. Prod. Anal."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"118183","DOI":"10.1016\/j.eswa.2022.118183","article-title":"Measuring environmental efficiency of the EU based on a DEA approach with fixed cost allocation under different decision goals","volume":"208","author":"Zhu","year":"2022","journal-title":"Expert Syst. Appl."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"12379","DOI":"10.1016\/j.eswa.2011.04.017","article-title":"Will economic development enhance the energy use efficiency and CO2 emission control efficiency?","volume":"38","author":"Liou","year":"2011","journal-title":"Expert Syst. Appl."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"429","DOI":"10.1016\/0377-2217(78)90138-8","article-title":"Measuring the efficiency of decision making units","volume":"2","author":"Charnes","year":"1978","journal-title":"Eur. J. Oper. Res."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"1613","DOI":"10.1287\/mnsc.32.12.1613","article-title":"Some models for estimating technical and scale inefficiencies in DEA","volume":"32","author":"Banker","year":"1984","journal-title":"Manag. Sci."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"407","DOI":"10.1006\/jeth.1996.0096","article-title":"Benefit and Distance Functions","volume":"70","author":"Chambers","year":"1996","journal-title":"J. Econ. Theory"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"498","DOI":"10.1016\/S0377-2217(99)00407-5","article-title":"A slacks-based measure of efficiency in data envelopment analysis","volume":"130","author":"Tone","year":"2001","journal-title":"Eur. J. Oper. Res."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"1110","DOI":"10.1016\/j.mcm.2011.12.043","article-title":"Environmental efficiency evaluation considering the maximization of desirable outputs and its application","volume":"58","author":"Song","year":"2013","journal-title":"Comput. Math. Model."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"392","DOI":"10.1016\/j.energy.2017.06.040","article-title":"Applying the Dynamic DEA Model to Evaluate the Energy Efficiency of OECD Countries and China","volume":"134","author":"Guo","year":"2017","journal-title":"Energy"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"131","DOI":"10.1016\/j.egypro.2018.09.070","article-title":"Study on Total-Factor Energy Efficiency in Three Provinces of Northeast China Based on SBM Model","volume":"152","author":"Cheng","year":"2018","journal-title":"Energ. Procedia"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"254","DOI":"10.1016\/j.enpol.2019.05.024","article-title":"Carbon Emissions Allocation Based on Satisfaction Perspective and Data Envelopment Analysis","volume":"132","author":"Xie","year":"2019","journal-title":"Energy Policy"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"1925","DOI":"10.1016\/j.jksus.2020.01.033","article-title":"Total factor energy efficiency in regions of China: An empirical analysis on SBM-DEA model with undesired generation","volume":"32","author":"Shang","year":"2020","journal-title":"J. King Saud Univ. Sci."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"123388","DOI":"10.1016\/j.jclepro.2020.123388","article-title":"Assessment of eco-efficiency change considering energy and environment: A study of China\u2019s non-ferrous metals industry","volume":"277","author":"Chen","year":"2020","journal-title":"J. Clean. Prod."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"100652","DOI":"10.1016\/j.envdev.2021.100652","article-title":"Eco-efficiency measurement as an approach to improve the sustainable development of municipalities: A case study in the Midwest of Brazil","volume":"39","author":"Espejo","year":"2021","journal-title":"Environ. Dev."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"119301","DOI":"10.1016\/j.energy.2020.119301","article-title":"The Change in Energy and Carbon Emissions Efficiency after Afforestation in China by Applying a Modified Dynamic SBM Model","volume":"216","author":"Teng","year":"2021","journal-title":"Energy"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"397","DOI":"10.1016\/j.egyr.2021.10.020","article-title":"Energy efficiency evaluation model based on DEA-SBM-Malmquist index","volume":"7","author":"Zheng","year":"2021","journal-title":"Energy Rep."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"108072","DOI":"10.1016\/j.ecolind.2021.108072","article-title":"Industrial eco-efficiency and its determinants in China: A two-stage approach","volume":"130","author":"Matsumoto","year":"2021","journal-title":"Ecol. Indic."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"564","DOI":"10.2307\/1237909","article-title":"Sources of agricultural productivity gap among selected countries","volume":"51","author":"Hayami","year":"1969","journal-title":"Am. J. Agric. Econ."},{"key":"ref_23","unstructured":"Hayami, Y., and Ruttan, V.W. (1985). Agricultural Development; an International Perspective, John Hopkins University Press."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"231","DOI":"10.1007\/s00181-007-0119-4","article-title":"Meta frontier frameworks for the study of firm-level efficiencies and technology ratios","volume":"34","author":"Rao","year":"2008","journal-title":"Empir. Econ."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"283","DOI":"10.1016\/j.econmod.2013.07.017","article-title":"Energy efficiency and production technology heterogeneity in China: A meta-frontier DEA approach","volume":"35","author":"Wang","year":"2013","journal-title":"Econ. Model."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"1054","DOI":"10.1016\/j.jclepro.2017.11.231","article-title":"Decomposition of energy efficiency and energy-saving potential in China: A three-hierarchy meta-frontier approach","volume":"176","author":"Feng","year":"2018","journal-title":"J. Clean. Prod."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"106246","DOI":"10.1016\/j.eneco.2022.106246","article-title":"The internal-structural effects of different types of environmental regulations on China\u2019s green total-factor productivity","volume":"113","author":"Tian","year":"2022","journal-title":"Energy Econ."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"475","DOI":"10.1016\/j.eneco.2016.04.005","article-title":"Measuring total-factor CO2 emission performance and technology gaps using a non-radial directional distance function: A modified approach","volume":"56","author":"Wang","year":"2016","journal-title":"Energy Econ."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"105255","DOI":"10.1016\/j.resconrec.2020.105255","article-title":"Total factor energy efficiency in Chinese manufacturing industry under industry and regional heterogeneities","volume":"168","author":"Chen","year":"2021","journal-title":"Resour. Conserv. Recycl."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"427","DOI":"10.1002\/nav.21815","article-title":"An alternative meta-frontier framework for measuring the heterogeneity of technology","volume":"65","author":"Wang","year":"2018","journal-title":"Nav. Res. Logist. (NRL)"},{"key":"ref_31","doi-asserted-by":"crossref","unstructured":"Chen, Y., Xu, W., Zhou, Q., and Zhou, Z. (2020). Total factor energy efficiency, carbon emission efficiency, and technology gap: Evidence from sub-industries of Anhui province in China. Sustainability, 12.","DOI":"10.3390\/su12041402"},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"219","DOI":"10.1016\/j.ejor.2019.06.053","article-title":"Meta-frontier analysis using cross-efficiency method for performance evaluation","volume":"280","author":"Chen","year":"2020","journal-title":"Eur. J. Oper. Res."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"735","DOI":"10.1016\/j.ejor.2023.10.034","article-title":"A new cross-efficiency meta-frontier analysis method with good ability to identify technology gaps","volume":"314","author":"Lin","year":"2024","journal-title":"Eur. J. Oper. Res."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"102888","DOI":"10.1016\/j.omega.2023.102888","article-title":"Assessing the dynamic efficiency and technology gap of airports under different ownerships: A union dynamic NDEA approach","volume":"119","author":"Yu","year":"2023","journal-title":"Omega"},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"254","DOI":"10.1016\/j.ejor.2021.10.054","article-title":"Integrating group frontier and meta-frontier directional distance functions to evaluate the efficiency of production units","volume":"301","author":"Yu","year":"2022","journal-title":"Eur. J. Oper. Res."},{"key":"ref_36","doi-asserted-by":"crossref","unstructured":"Zhu, J., and Cook, W.D. (2007). Modeling Data Irregularities and Structural Complexities in Data Envelopment Analysis, Springer.","DOI":"10.1007\/978-0-387-71607-7"},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"1047","DOI":"10.1016\/j.ejor.2016.04.034","article-title":"Evaluating the environmental efficiency of a two-stage system with undesired outputs by a DEA approach: An interest preference perspective","volume":"254","author":"Wu","year":"2016","journal-title":"Eur. J. Oper. Res."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"472","DOI":"10.1016\/j.spc.2021.06.010","article-title":"Decomposition of industrial pollution intensity change and reduction potential: A two-stage meta-frontier PDA method","volume":"28","author":"Wang","year":"2021","journal-title":"Sustain. Prod. Consum."},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"495","DOI":"10.1007\/s10479-019-03436-3","article-title":"A meta-frontier network data envelopment analysis approach for the measurement of technological bias with network production structure","volume":"287","author":"Yu","year":"2020","journal-title":"Ann. Oper. Res."},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"146","DOI":"10.1016\/j.eneco.2009.07.006","article-title":"A metafrontier approach for measuring an environmentally sensitive productivity growth index","volume":"32","author":"Oh","year":"2010","journal-title":"Energy Econ."},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"123110","DOI":"10.1016\/j.jclepro.2020.123110","article-title":"Regional Total-Factor Productivity and Environmental Governance Efficiency of China\u2019s Industrial Sectors: A Two-Stage Network-Based Super DEA Approach","volume":"273","author":"Wang","year":"2020","journal-title":"J. Clean. Prod."},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"879","DOI":"10.1016\/j.psep.2021.02.005","article-title":"A Two-Stage Eco-Efficiency Evaluation of China\u2019s Industrial Sectors: A Dynamic Network Data Envelopment Analysis (DNDEA) Approach","volume":"148","author":"Wang","year":"2021","journal-title":"Process Saf. Environ. Prot."},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"74","DOI":"10.1016\/j.omega.2015.03.009","article-title":"Two-stage DEA models with undesirable input-intermediate-outputs","volume":"56","author":"Liu","year":"2015","journal-title":"Omega"},{"key":"ref_44","doi-asserted-by":"crossref","first-page":"243","DOI":"10.1016\/j.ejor.2008.05.027","article-title":"Network DEA: A slacks-based measure approach","volume":"197","author":"Tone","year":"2009","journal-title":"Eur. J. Oper. Res."},{"key":"ref_45","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.omega.2013.12.002","article-title":"Efficiency decomposition in network data envelopment analysis with slacks-based measures","volume":"45","author":"Kao","year":"2014","journal-title":"Omega"},{"key":"ref_46","doi-asserted-by":"crossref","first-page":"418","DOI":"10.1016\/j.ejor.2006.11.041","article-title":"Efficiency decomposition in two-stage data envelopment analysis: An application to non-life insurance companies in Taiwan","volume":"185","author":"Kao","year":"2008","journal-title":"Eur. J. Oper. Res."},{"key":"ref_47","doi-asserted-by":"crossref","first-page":"1170","DOI":"10.1016\/j.ejor.2008.05.011","article-title":"Additive efficiency decomposition in two-stage DEA","volume":"196","author":"Chen","year":"2009","journal-title":"Eur. J. Oper. Res."},{"key":"ref_48","doi-asserted-by":"crossref","first-page":"1247","DOI":"10.1006\/anbe.2001.1691","article-title":"Mann\u2013Whitney U test when variances are unequal","volume":"61","author":"Kasuya","year":"2001","journal-title":"Anim. Behav."},{"key":"ref_49","doi-asserted-by":"crossref","first-page":"567","DOI":"10.1057\/jors.1994.84","article-title":"Efficiency and Cross-efficiency in DEA: Derivations, Meanings and Uses","volume":"45","author":"Doyle","year":"1994","journal-title":"J. Oper. Res. Soc."},{"key":"ref_50","unstructured":"Silkman, R.H. (1986). Measuring Efficiency: An Assessment of Data Envelopment Analysis, Jossey-Bass."},{"key":"ref_51","doi-asserted-by":"crossref","first-page":"1261","DOI":"10.1287\/mnsc.39.10.1261","article-title":"A Procedure for Ranking Efficient Units in Data Envelopment Analysis","volume":"39","author":"Andersen","year":"1993","journal-title":"Manag. Sci."},{"key":"ref_52","doi-asserted-by":"crossref","first-page":"24","DOI":"10.2307\/1907382","article-title":"Estimation of relationships for limited dependent variables","volume":"26","author":"Tobin","year":"1958","journal-title":"Econometrica"}],"container-title":["Systems"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2079-8954\/12\/1\/22\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T13:44:05Z","timestamp":1760103845000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2079-8954\/12\/1\/22"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,1,10]]},"references-count":52,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2024,1]]}},"alternative-id":["systems12010022"],"URL":"https:\/\/doi.org\/10.3390\/systems12010022","relation":{},"ISSN":["2079-8954"],"issn-type":[{"type":"electronic","value":"2079-8954"}],"subject":[],"published":{"date-parts":[[2024,1,10]]}}}