Correction: Analysis of natural resource total factor productivity in China’s eastern coastal region based on integrating static SBM-DEA with multi-frontier decomposition

There was an inconsistency in the numerical formatting of Table 2 as published. Thousands separators and decimal precision were not standardized across the reported values. The numerical values themselves are unchanged. The corrected Table 2 appears below.

Table 2. Descriptive statistics of the main variables.

There was a mistake in the caption of Figure 2 as published. The capitalization of the subfigure descriptions was inconsistent. The corrected caption of Figure 2 appears below.

“Spatiotemporal characteristics of provincial NTFP (2008–2020). (a) temporal changes in NTFP of coastal provinces during 2008–2020; (b) comparison of NTFP between coastal and non-coastal provinces (2008–2020); (c) rankings of NTFPs by provinces and municipalities in 2020; (d) heat map of NTFP for coastal provinces and municipalities (2008–2020).”

There was a mistake in the caption of Figure 5 as published. The word “and” before subfigure (e) was redundant. The corrected caption of Figure 5 appears below.

“Temporal three-level decomposition of NTFP for the eastern, central, and western regions during 2008–2020: (a) regional disparity index (SI); (b) global efficiency (S^m); (c) provincial heterogeneity index (RI); (d) regional efficiency (S^r); (e) intra-provincial efficiency (MI).”

An incorrect symbol (“p”) was used in the description of the efficiency score. A correction has been made to section 2 Data and method, subsection 2.3.1 Static SBM model specification, Paragraph 6:

“only when ρ = 1 does the DMU lie on the production frontier.”

The citation “An et al. (2022)” has been removed. A correction has been made to section 3 Results and analysis, subsection 3.1 Descriptive statistics, Paragraph 1:

“Specifically, the standard deviation of capital input (553.350) is nearly equal to its mean (475.696), indicating substantial imbalance in fixed-asset investment across regions and industries, consistent with existing findings on China’s regional investment disparities.”

The classification of provinces in the second and third coastal echelons was incorrect. A correction has been made to section 3 Results and analysis, subsection 3.2.1 Regional disparities and the coastal advantage, Paragraph 3:

“The second echelon comprises Shandong and Fujian, representing a catch-up type spanning the Bohai Rim and the southern coast. The third echelon includes Tianjin, Hebei, Liaoning, Guangxi, and Hainan, which have relatively low efficiency and become the weak links in coastal areas.”

The description of the temporal performance of Fujian, Guangxi, Hainan, Tianjin, Hebei, and Liaoning was incorrect. A correction has been made to section 3 Results and analysis, subsection 3.2.2 Multi-year performance of typical coastal provinces, Paragraph 2:

“In contrast, Fujian, Guangxi, and Hainan showed fluctuating upward trends, while Tianjin, Hebei, and Liaoning grew slowly.”

The provincial composition of the second and third echelons was incorrect. A correction has been made to section 3 Results and analysis, subsection 3.2.2 Multi-year performance of typical coastal provinces, Paragraph 3:

“the second echelon (0.3 ≤ NTFP < 0.8) includes Fujian and Shandong; and the third echelon (NTFP < 0.3) includes Guangxi, Hebei, Tianjin, Liaoning, and Hainan.”

The description of the regional MI pattern was overly broad, and the wording describing consistency with previous studies was revised. A correction has been made to section 3 Results and analysis, subsection 3.3.2 Provincial efficiency and intra-provincial temporal variations (S^p and MI), Paragraph 2:

“This contrast underscores that higher MI is closely associated with a more diversified and advanced marine economy. The western region shows relatively lower MI during much of the study period, although it improves markedly after 2016, suggesting a gradual narrowing of intra-provincial efficiency differences across regions. These findings are broadly consistent with the classification of coastal provinces by marine green economy efficiency, which identifies Tianjin, Guangdong, Shandong, Shanghai, and Jiangsu as the highest level, Zhejiang and Fujian as high level, Liaoning and Hebei as median level, and Guangxi and Hainan as low level (Tang et al., 2021).”

The description of RI was revised to clarify the relationship between the regional and provincial frontiers, and a typographical error was corrected. A correction has been made to section 3 Results and analysis, subsection 3.3.3 Decomposition indices and marine economy, Paragraph 3:

“The eastern region has the most moderate and stable RI (RI = S^r/S^*p*), indicating a relatively small gap between the regional and provincial frontiers and, consequently, lower provincial technological heterogeneity. This homogeneity is largely driven by dense marine economic linkages—shipping networks, inter-provincial industrial chains, for example, shipbuilding and marine equipment, and knowledge spillovers from leading ports (Shanghai, Ningbo-Zhoushan, Shenzhen). By contrast, the central region has higher RI, reflecting weaker integration into marine value chains.”

The explanation of low MI was incomplete and did not distinguish the different regional economic characteristics of low-MI coastal provinces. A correction has been made to section 3 Results and analysis, subsection 3.3.3 Decomposition indices and marine economy, Paragraph 4:

“Specifically, we divide provinces with low MI into two groups by regional economic clusters. The results for Hainan and Guangxi may be due to marine economies dominated by low-value-added activities (traditional fisheries and basic tourism) with limited industrial upgrading. Tianjin, Hebei, and Liaoning in the Bohai Rim also show low MI, reflecting heavy-industry dependence and persistent environmental pressure in Bohai Bay.”

The description of the second and third echelons was revised to reflect the corrected classification while retaining the emphasis on Guangxi and Hainan. A correction has been made to section 4 Discussion, subsection 4.2 Intra−coastal heterogeneity, three echelons and marine sector linkages, Paragraph 1:

“Within the coastal region, NTFP exhibits a clear three-echelon structure that closely mirrors the sophistication and diversification of local marine economies. The first echelon (Shanghai, Jiangsu, Zhejiang, Guangdong) consistently operates at the efficiency frontier, driven by high-end marine industries, world-class port clusters (e.g., Shanghai, Ningbo-Zhoushan, Shenzhen), strong marine R&D capacity, and intensive factor allocation. The second echelon (Shandong, Fujian) shows moderate but improving NTFP. Shandong’s rapid catch-up, for instance, is underpinned by its robust marine fisheries and port economy. The third echelon, especially Guangxi and Hainan, lags significantly, with marine economies dominated by low-value-added activities such as traditional fisheries and basic tourism, and with limited industrial upgrading.”

The abbreviation “M-NTFP” was incorrectly used instead of “NTFP”. A correction has been made to section 5 Conclusions, Paragraph 1:

“Using a static SBM-DEA model with undesirable outputs and a three-tier multi-frontier decomposition (global, regional, provincial), we measured and compared NTFP across China’s 31 provinces (2008–2020), focusing on the eastern coastal region.”

The abbreviation “M-NTFP” was incorrectly used instead of “NTFP”. A correction has been made to section 5 Conclusions, Item 1:

“1. NTFP exhibits strong spatial heterogeneity, with coastal provinces maintaining an absolute efficiency advantage 2.3–2.8 times higher than inland areas. This confirms that marine economy factors are critical criteria in MCDM models for national resource allocation.”

The policy recommendation for the third echelon was revised to distinguish different local constraints. A correction has been made to section 5 Conclusions, Item 2:

“2. Coastal regions display a three-echelon structure, with the Yangtze River Delta/Pearl River Delta as the frontier, Shandong and Fujian as catching-up, and Tianjin, Hebei, Liaoning, Guangxi, and Hainan as lagging. This hierarchical pattern provides a basis for echelon-based MCDM policies rather than uniform standards. We propose differentiated marine industry admittance rules, fiscal support schemes and environmental supervision standards matching the three tiers: the first echelon prioritizes marine high-tech innovation, the second promotes transformation of traditional coastal industries, and the third pursues restructuring tailored to local constraints—ecological compensation and green development for Guangxi and Hainan, and decarbonization of heavy industries alongside emerging marine industry cultivation for Tianjin, Hebei, and Liaoning.”

The direction of the SI-based policy recommendation was incorrect. Regions with low, rather than high, SI should focus on cross-regional technological cooperation. A correction has been made to section 5 Conclusions, Item 3:

“3. The multi-frontier decomposition (SI, RI, MI) serves as an analytical MCDM tool that pinpoints the source of inefficiency: regional technology gaps (SI), provincial heterogeneity (RI), or intra-provincial inefficiencies (MI). From the perspective of practical governance, this study recommends taking SI, RI and MI as core evaluation indicators for provincial marine management performance. Regions with low SI should focus on cross-regional technological cooperation; those with prominent RI need deeper inter-provincial coordination of marine industrial chains; areas suffering low MI ought to optimize internal factor allocation. Targeted governance corresponding to each source of inefficiency will effectively cut overall resource efficiency losses.”

The original version of this article has been updated.

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Footnotes

Edited and reviewed by: Karuppiah Koppiahraj, Kalaignarkarunanidhi Institute of Technology (KIT), India