Response to editor:

Thank you for your valuable suggestions on our manuscript, "Spatial-Temporal Differences and Convergence Analysis of Residential Building Carbon Emission Efficiency in China ". In response to journal requirements, I have taken the following actions to ensure compliance with PLOS ONE's guidelines:

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(2)Role of Funders: The Liaoning Provincial Social Science Planning Fund (L20BGL029) supported our research, but the funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.

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The revised manuscript, along with the updated cover letter and supporting information files, are attached to this submission. Should you require any further information or clarification, please do not hesitate to contact me. Thank you for considering our revised manuscript for publication.

Thank you in advance for handling the manuscript. We appreciate your time and look forward to your response.

Response to Reviewers:

My manuscript number is PONE-D-24-13372 - Spatial-Temporal Differences and Convergence Analysis of Residential Building Carbon Emission Efficiency in China.

First, I would like to thank all reviewers for their suggestions. They are all very pertinent, which is very useful for me to improve the level of my paper. The answers to the reviewers' questions are as follows, and the points corresponding to the modifications in the revised manuscript are highlighted in the document named 'Revised Manuscript with Track Changes'. For example, mark 'reviewer 1 response 1' to respond to the first question of reviewer 1.

We have revised the relevant content of the manuscript based on the reviewers' comments.

If you have any questions, please point them out directly. Thanks again.

Response to Reviewer 1:

Q1: The article provides a concise overview of the main findings, including the static and dynamic carbon emission efficiencies of residential buildings across different regions in China from 2010 to 2020. However, more detail on the specific results and trends identified would enhance the reader's understanding of the research findings.

R1: According to the reviewer's suggestions, we have added the following sections in the paper to analyze the carbon emission efficiency of residential buildings:

(1)Static Analysis of RBCEE

The efficiency values for each province from 2010 to 2020 were ranked, and the results are shown in Table 4. The data in Table 4 shows that the RBCEE in the eastern coastal is generally higher. Shanghai maintained a leading position from 2010 to 2019, highlighting its advantages in building design, energy-saving technologies, and policy orientation. In contrast, the RBCEE in the northeastern is generally lower and relatively stable overall, with Heilongjiang and Jilin ranking relatively backward, which shows that the region faces a significant challenge in improving building energy efficiency and applying green technology. The northern coastal region, such as Beijing and Tianjin, showed relatively stable performance. Although there was a slight decline in 2018 and 2019, the overall RBCEE remained at a high level, reflecting their efforts in urban planning and green building. However, Hebei's low-carbon development lagged relatively behind with a year-by-year decline in ranking.

Regarding the southern coastal, Hainan consistently maintained a high level. Guangdong shows a fluctuating and then improving trend, while Fujian's RBCEE gradually declined, showing a relatively weak performance. In the Middle Yellow River, provinces like Shaanxi and Shanxi saw a year-by-year decrease in RBCEE. Shaanxi even dropped to the last place in 2020, indicating significant challenges in improving building energy efficiency in this region. However, Inner Mongolia showed a steady improvement trend, especially in the later period, benefiting from policy support and technological advancements, significantly improving its carbon emission efficiency and entering the top ten nationwide. The overall RBCEE in the Middle Yangtze River was relatively low, ranking mainly in the middle to lower ranges. Jiangxi Province showed a significant downward trend, falling from the top ten to the 27th position nationwide, indicating an urgent need to enhance and improve relevant emission reduction technologies. The RBCEE in the southwestern was relatively moderate, with Sichuan and Chongqing showing improvements after 2016, indicating potential for gradual low-carbon transformation.

Conversely, Yunnan and Guizhou performed poorly, especially in 2019 and 2020, which is likely related to the economic development level, building material selection, and residents' environmental awareness in these provinces. The RBCEE in the northwestern varies among provinces. Qinghai and Ningxia maintained high and stable efficiency, while Gansu and Xinjiang showed a downward trend, with Gansu's RBCEE weakening significantly.

Table 4 Efficiency values and ranking of provinces in the eight economic zones for the period 2010-2020

Region Province 2010 Rank 2011 Rank 2012 Rank 2013 Rank 2014 Rank 2015 Rank 2016 Rank 2017 Rank 2018 Rank 2019 Rank 2020 Rank

Northeast Liaoning 0.676 14 0.673 15 0.392 21 0.575 10 0.583 8 0.548 9 0.517 12 0.519 9 0.535 9 0.513 9 0.524 12

Jilin 0.560 22 0.574 21 0.421 17 0.439 17 0.442 13 0.434 14 0.427 19 0.429 17 0.428 16 0.422 15 0.491 14

Heilongjiang 0.548 24 0.545 23 0.300 26 0.427 18 0.432 15 0.420 17 0.454 18 0.442 15 0.441 15 0.441 14 0.470 16

Northern coastal Beijing 1.092 6 1.047 5 0.916 6 1.109 3 1.094 4 1.090 4 1.086 4 1.094 4 1.038 4 1.047 4 1.113 5

Tianjin 1.099 5 1.025 6 0.984 5 0.962 6 0.946 6 1.026 5 0.959 6 0.964 6 0.969 6 0.963 6 0.974 7

Hebei 0.538 26 0.509 27 0.291 28 0.347 23 0.336 22 0.344 23 0.331 25 0.326 22 0.359 20 0.363 20 0.367 24

Shandong 0.619 17 0.613 18 0.355 23 0.401 20 0.397 18 0.421 16 0.406 22 0.407 18 0.458 12 0.456 12 0.430 18

Eastern coastal Shanghai 1.581 2 1.627 2 2.604 1 2.336 1 2.522 1 2.548 1 2.077 1 2.426 1 2.498 1 2.413 1 2.447 1

Jiangsu 0.752 11 0.716 13 0.403 19 0.564 11 0.568 9 0.495 10 0.491 14 0.498 10 0.482 11 0.480 10 0.649 9

Zhejiang 0.885 7 0.829 9 0.456 16 0.638 7 0.642 7 0.705 7 0.661 8 0.768 7 0.608 7 0.609 7 0.721 8

Southern coastal Fujian 0.690 13 0.684 14 0.515 12 0.464 14 0.467 11 0.439 13 0.413 21 0.468 12 0.409 18 0.412 16 0.436 17

Guangdong 0.757 10 0.719 12 0.405 18 0.598 8 0.558 10 0.557 8 0.765 7 0.548 8 0.537 8 0.526 8 1.192 3

Hainan 2.764 1 2.625 1 2.144 2 2.163 2 1.901 2 1.695 2 1.609 2 1.784 2 1.827 2 1.633 2 1.610 2

Middle Yellow River Shaanxi 0.864 9 0.943 7 0.839 7 0.534 12 0.393 19 0.415 18 0.516 13 0.461 13 0.425 17 0.400 18 0.268 30

Shanxi 0.571 21 0.545 24 0.336 24 0.380 22 0.378 20 0.384 20 0.361 24 0.359 20 0.373 19 0.372 19 0.472 15

Henan 0.512 29 0.489 28 0.271 30 0.332 27 0.291 28 0.300 28 0.285 30 0.275 29 0.287 29 0.317 24 0.344 26

Inner Mongolia 0.603 19 0.599 19 0.504 13 0.459 15 0.462 12 0.472 11 0.459 16 0.438 16 0.485 10 0.467 11 0.565 10

Middle Yangtze River Hubei 0.524 27 0.477 29 0.298 27 0.345 24 0.326 24 0.329 25 0.324 26 0.326 22 0.331 22 0.328 22 0.422 19

Hunan 0.489 30 0.438 30 0.397 20 0.326 28 0.333 23 0.335 24 0.318 28 0.308 27 0.298 28 0.299 28 0.416 22

Jiangxi 0.867 8 0.767 11 0.756 9 0.526 13 0.440 14 0.412 19 0.415 20 0.387 19 0.329 24 0.314 25 0.322 27

Anhui 0.523 28 0.524 25 0.368 22 0.341 25 0.347 21 0.362 21 0.305 29 0.303 28 0.318 25 0.272 30 0.370 23

Southwest Yunnan 0.588 20 0.615 17 0.573 11 0.338 26 0.271 29 0.276 29 0.323 27 0.309 26 0.306 26 0.303 26 0.307 29

Guizhou 0.558 23 0.545 22 0.336 24 0.259 30 0.252 30 0.267 30 0.457 17 0.274 30 0.280 30 0.286 29 0.345 25

Sichuan 0.545 25 0.512 26 0.290 29 0.316 29 0.295 27 0.308 27 0.557 10 0.320 25 0.343 21 0.355 21 0.535 11

Chongqing 0.661 15 0.628 16 0.494 14 0.459 16 0.427 16 0.422 15 0.617 9 0.444 14 0.448 13 0.445 13 0.418 20

Guangxi 0.653 16 0.592 20 0.485 15 0.383 21 0.321 25 0.315 26 0.489 15 0.323 24 0.305 27 0.300 27 0.316 28

Northwest Gansu 0.726 12 0.775 10 0.694 10 0.407 19 0.303 26 0.351 22 0.401 23 0.358 21 0.330 23 0.320 23 0.418 21

Qinghai 1.361 3 1.079 4 1.289 3 1.065 4 1.135 3 1.167 3 1.177 3 1.112 3 1.121 3 1.126 3 1.147 4

Ningxia 1.119 4 1.154 3 1.135 4 1.044 5 1.010 5 0.997 6 0.998 5 0.986 5 0.986 5 0.980 5 1.064 6

Xinjiang 0.611 18 0.883 8 0.797 8 0.584 9 0.410 17 0.439 12 0.556 11 0.489 11 0.441 14 0.405 17 0.493 13

(2)Dynamic Analysis of RBCEE

Using the natural breaks method, the ML index of 30 provinces was classified into four categories: Excellent ([1.117, +∞)), Good ([1.084, 1.116]), Moderate ([1.042, 1.083]), and Poor ((-∞, 1.011]). Based on the mean ML index values of the provinces from 2010 to 2020, Fig. 3 was derived. The figure shows that many provinces fall into the "Moderate" category. Specifically, all three provinces in the northeast region are at a moderate level, indicating that factors such as cold climate, ageing buildings, and high energy consumption may impact the RBCEE in this region. In the northern Coastal , performance varies within the region. Thanks to strict environmental policies and advanced technological measures, Beijing (1.0747) and Tianjin (1.0831) are at a moderate level. In contrast, with its traditionally industrial structure that has not fully adapted to energy-saving requirements, Hebei remains at a poor level. This result is consistent with the static analysis findings. The eastern coastal region shows considerable internal differences, with the three provinces falling into good, moderate, and poor levels. The southern coastal region performs excellently overall, mainly Guangdong province (Excellent), which leads in RBCEE, reflecting the technological advantages and policy support in economically developed regions. Hainan (Good) and Fujian (Moderate) show slight lags in efficiency but also demonstrate an improving trend. The Middle Yangtze River region performs relatively poorly, with only Hubei province (1.0554) at a moderate level, while the other three provinces are at poor levels. There is a need to introduce relevant technologies to improve RBCEE in this region.

In the Middle Yellow River region, Henan province (1.1276) stands out with an excellent level, indicating significant achievements in controlling residential building carbon emissions. Shanxi (1.0849) and Inner Mongolia (1.1160) also show good development trends. The southwest region exhibits a complex performance, with Sichuan (1.1709) and Guizhou (1.1350) performing well at excellent levels, reflecting their efforts in promoting green buildings and renewable energy applications. Yunnan (1.1002, Good), Chongqing (1.0601, Moderate), and Guangxi (1.0413, Poor) show varying degrees of improvement potential, especially in Guangxi province. The northwest region remains relatively stable, with no provinces at the poor level, and displays relatively high carbon emission efficiency. Ningxia and Qinghai, both at excellent levels, may benefit from low population density and abundant renewable energy resources.

Fig. 3. Distribution of the Mean ML Index of Provinces from 2010 to 2020

Q2: I recommend adding the given statement after the first line of introduction with the addition of given studies [1,2] as "Crops, livestock, and industrial sectors are the main sources for the carbon emissions [1-3]. The global low-carbon development is closely…"

[1] https://doi.org/10.1016/j.jenvman.2023.119654

[2] https://doi.org/10.47852/bonviewGLCE32021584

[3] https://doi.org/10.1016/B978-0-12-819657-1.00001-3

R2: Following the reviewer's recommendation, we have added the sentence you mentioned immediately after the first line of the introduction and referenced the given literature. To ensure a smooth flow of context, we made some adjustments. The revised sentence is as follows:

China is the world's largest carbon emitter, accounting for about 25% of the world's total carbon emissions. The global low-carbon development is closely related to China's carbon emission reduction efforts [1]. Crops, livestock, and industrial sectors are the main sources of carbon emissions, contributing significantly to the global carbon footprint [2-4]. However, the construction industry, particularly in China, also plays a crucial role in this equation. According to the International Energy Agency (IEA),…

[1]Du, Q., Zhou, J., Pan, T., Sun, Q., and Wu, M. Relationship of carbon emissions and economic growth in China's construction industry. Journal of Cleaner Production.2019;220,99-109. doi:10.1016/j.jclepro.2019.02.123

[2]Elahi, E., Li, G., Han, X., Zhu, W., Liu, Y., Cheng, A.,et al.Decoupling livestock and poultry pollution emissions from industrial development: A step towards reducing environmental emissions. Journal of Environmental Management.2024;350,119654.doi:.10.1016/j. jenvman.2023.119654.

[3]Yin, S., Liu, L., Mahmood, T. New trends in sustainable development for industry 5.0: digital green innovation economy. Green and Low-Carbon Economy.2023. doi:10.47852/bonviewGLCE32021584

[4]Yoro, K. O., Daramola, M. O.CO2 emission sources, greenhouse gases, and the global warming effect. In Advances in carbon capture (pp. 3-28). Woodhead Publishing.2020. doi:10.1016/B978-0-12-819657-1.00001-32

Q3: The paper's analysis of the differences and equity in residential building carbon emission efficiency among regions is an important contribution to the literature. However, the article could provide more detail on the specific equity issues identified and their implications.

R3: Based on the reviewers' suggestions, we have supplemented more descriptions regarding the issue of fairness in the paper, as follows:

Table 6 shows that the Gini coefficient of RBCEE in China showed a fluctuating trend from 2010 to 2020, reflecting changes in the fairness of carbon emission efficiency among different regions. Previous studies have indicated that a Gini coefficient in the range of [0, 0.1] signifies absolute fairness, [0.1, 0.2] indicates relative fairness, [0.2, 0.3] represents reasonable fairness, and [0.3, 1] suggests poor fairness. In 2010, the Gini coefficient was 0.234, which slightly decreased to 0.233 in 2011, indicating a minor improvement in the inequality of RBCEE during this period. However, in 2012, the Gini coefficient significantly increased to 0.356, likely due to uneven policy implementation and unbalanced technological development, which exacerbated regional inequality. In the following years, although the Gini coefficient declined somewhat, it remained at a relatively high level until it dropped to 0.302 in 2016, indicating a mitigation in the inequality of RBCEE. From 2017 to 2019, the Gini coefficient remained relatively stable. By 2020, the Gini coefficient further decreased to 0.325, showing an improvement in the fairness of RBCEE. Overall, during this period, the inequality in carbon emission efficiency experienced significant fluctuations, shifting from a state of reasonable fairness to poor fairness. Still, the later trend showed signs of mitigation. If further emission reduction measures are implemented, it will help to return the RBCEE to a relatively fair state.

Table 6. Overall Theil Index and Gini Coefficient of RBCEE for the Period 2010-2020

Year Theil Index Gini Index Within group contribution Between-group contribution

2010 0.112 0.234 58.24% 41.76%

2011 0.108 0.233 55.77% 44.23%

2012 0.231 0.356 64.19% 35.81%

2013 0.212 0.330 54.77% 45.23%

2014 0.236 0.350 53.57% 46.43%

2015 0.226 0.340 53.14% 46.86%

2016 0.164 0.302 57.14% 42.86%

2017 0.221 0.340 51.35% 48.65%

2018 0.230 0.341 54.90% 45.10%

2019 0.220 0.335 54.31% 45.69%

2020 0.193 0.325 48.38% 51.62%

Q4: The use of σ-convergence, absolute β-convergence, and conditional β-convergence methods to explore the changing trends of residentia

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