Does ecological poverty trap exist in Chinese cities? Evidence from the distribution dynamics of vegetation coverage

Does ecological poverty trap exist in Chinese cities? 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Evidence from the distribution dynamics of vegetation coverage Di Fan, Qiufeng Chen, Jianxin Wu, Tsun Se Cheong, Ning Ma This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-5794674/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 07 Aug, 2025 Read the published version in Environmental and Ecological Statistics → Version 1 posted 9 You are reading this latest preprint version Abstract This paper is the first to examine the distribution dynamics of vegetation coverage using a dataset of 366 China’s prefecture and above (PAA) cities from 2001 to 2020. The results from the continuous state space approach demonstrate a clear pattern of convergence in China’s vegetation coverage in the long run, proving the effectiveness of government policies in the last two decades. However, catch-up effects in low-vegetation-coverage cities are weak, and an ecological poverty trap exists in Chinese cities. We also find polarization effects in eastern and high-rainfall cities. Some eastern cities with better climate endowments show poor performance in vegetation coverage in the long run, suggesting that ecological damage is caused by overdevelopment rather than natural endowment. Our findings offer robust scientific support for China to take more proactive and aggressive measures to maintain sustainable development. JEL: Q20, Q50, N55 vegetation coverage distribution dynamics ecological poverty continuous state space approach Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 Figure 7 1. Introduction Human activities have triggered unprecedented changes in the social-ecological system in recent decades because of the world’s growing population and resource demand (Odegard et al., 2014). Consequently, environmental stress occurs due to factors like inappropriate land use, deforestation, cropland expansion, and over-exploitation of mining (Lopez, R.,1992; Gray & Moseley, 2005 ; Aksoy & Tumen, 2021 ). In other words, the ecological footprint, which defines resource consumption and water assimilation, rises along with decreasing biocapacity (Wackernagel & Rees, 1998 ). Studies have shown an inverted U-shaped relationship between economic growth and environmental quality, known as the environmental Kuznets curve (EKC) (Barbier, 1997 ; Dinda, 2004 ). The EKC hypothesis suggests that economic growth by itself may be a solution to environmental degradation (Rothman & de Bruyn, 1998 ). However, air quality indexes are frequently used to evaluate environmental quality in existing studies, and other indicators were less considered. Ecological footprint, upon its introduction, was subsequently used to measure environmental degradation and has been promoted as a policy and planning tool for achieving sustainability (Van den Bergh & Verbruggen, 1999 ; Zhao et al., 2005 ). Despite evidence of international inequalities in the ecological footprint (White, 2007 ; Duro & Teixidó-Figueras, 2013 ), few studies have investigated the convergence tendency of vegetation coverage on a national scale. China, the world’s largest developing country, faces severe environmental problems despite its record-breaking growth since the 1980s. To address the accelerating environmental degradation, China has probed ecological improvement through administrative power and gradually developed a discursive policy system with multiple practical approaches, such as green development, ecological public welfare compensation, and ecological relocation. These policies rely on massive resource inputs and strict political regimes, indicating large operation costs. In such a context, the ecological footprint is taken into account when scholars attempt to reassess the effect of a country’s economic policy (Wackernagel et al., 2002 ; Gokmenoglu et al., 2022). In particular, vegetation coverage is commonly used to measure ecological footprint (Lenzen & Murray, 2001 ; Chen et al., 2020 ), and vegetation change in China is also a research focus currently (Du et al., 2019 ; Yang et al., 2021 ; Wang et al., 2022 ). However, the linkage between vegetation change and the long-run evolution of China’s ecological footprint has not been fully investigated in the literature. This study uses a continuous state space approach to analyze the convergence and dynamic change of China’s prefecture and above (PAA) cities from 2001 to 2020, aiming to provide insights for policy evaluation and future adjustments. Using the Normalized Difference Vegetation Index (NDVI) as a proxy for ecological footprint, a remarkable club convergence tendency in vegetation coverage is observed in the entire sample. Since most cities converge to a point higher than the average vegetation coverage level, those cities have notably improved ecological quality during the study period. However, the polarization in the long-run distribution (also called ergodic distribution) suggests that some cities are falling into an ecological poverty trap, where a region runs a biological resources deficit, and the poverty is persistent. In addition to this, some regions have better climate endowments but perform poorly in vegetation, suggesting that ecological damage is caused by overdevelopment rather than natural endowment. Our study contributes to the three strands of literature. First, this study enriches the discussion about the EKC hypothesis. The EKC curve, as described by Panayotou ( 1993 ), was the dominant approach in environmental-related studies, with CO 2 emissions widely used as a proxy for pollution (Lantz & Feng, 2006 ; Kaika & Zervas, 2013 ; Pata, 2018 ). Stern ( 2017 ) pointed out that the EKC is sensitive to sample selection and econometric techniques. In this case, emerging studies employed the ecological footprint as an indicator of environmental quality (Al-Mulali et al., 2015 ; Charfeddine & Mrabet, 2017 ; Destek et al., 2018 ). The EKC was proven to be valid in China using CO2 emissions (Yin et al., 2015 ) and PM2.5 indicators (Hao & Liu., 2016), whereas Yilanci & Pata ( 2020 ) concluded it may be invalid when considering ecological footprint. Different from the research methods in the studies of Al-Mulali et al. ( 2015 ) and Ulucak & Bilgili ( 2018 ), who also took the ecological footprint to extend the EKC discussion, we employ a continuous state space approach in this study. This approach provides a new perspective on understanding the EKC hypothesis by taking China as an example. Second, this study relates to the convergence analyses of economic and environmental variables. The groundbreaking study of Solow ( 1956 ) has stimulated extensive convergence analyses on economic growth (Galor & Tsiddon, 1997 ; Bulli, 2001 ; Maasoumi et al., 2007 ). Whereafter, the robust evidence of Islam ( 2003 ) on income convergence and the EKC hypothesis inspired extensive research in environmental variables (Nourry, 2009 ). Except for the CO 2 emissions, other environmental indicators include NO X (Bulte et al., 2007 ; Criado & Grether, 2011 ; Camarero et al., 2013 ), SO 2 (Bulte et al., 2007 ; Nourry, 2009 ; Payne et al., 2014 ), and PM2.5 (Stern & Zha, 2016 ; Stern & Van Dijk, 2017 ) also have been studied. As for ecological footprint, the majority of convergence analyses were carried out on intergovernmental organizations and geographically close countries, such as members of the OECD (Solarin, 2019 ; Solarin et al., 2019 ), G20 (Bilgili & Ulucak, 2018 ), EU (Ulucak & Apergis, 2018 ), USMCA (Işık et al., 2021 ), African (Bello et al., 2022 ) and Latin American countries (Tillaguango et al., 2021 ). In contrast, this study is the first to analyze the convergence tendency of the ecological footprint of China’s PAA cities, revealing a dynamic evolution process and information about the convergence clubs of a country. Third, this study delves into the ecological impacts of urbanization. Urbanization is the primary determinant and has yielded long-term effects on ecological footprints (Muñiz & Galindo, 2005 ; Zubelzu et al., 2015 ; Al-Mulali & Oztur, 2015; Gassner et al., 2018 ). Ahmed et al. ( 2020 ) proved one-way causality from urbanization to environmental degradation. Further exploration by Ulucak & Khan ( 2020 ) indicated that urbanization decreases the ecological footprint. A similar conclusion also can be seen from Charfeddine ( 2017 ) and Arif et al. ( 2023 ). Different from the above studies, the conditional convergence in our study suggests that urbanization poses varying effects on the vegetation of different cities. While most cities in China have greatly improved their vegetation coverage during the study period, ecological damage was found in some cities despite being endowed with pleasant climates. Methodologically, this study extends previous work using the continuous state space approach (Galor & Tsiddon, 1997 ; Bulli, 2001 ; Maasoumi et al., 2007 ; Burnett, 2016 ; Herrerias et al., 2017 ; Wu & Ma, 2019 ). This approach allows us to highlight the convergence clubs and estimate the transition probability and long-run distribution. As mentioned above, some studies have examined the convergence of ecological footprints across countries. However, they mostly adopted β-convergence (Bilgili & Ulucak, 2018 ) and panel club convergence approaches (also known as the Phillips and Sul approach) (Tillaguango et al., 2021 ; Erdogan & Okumus, 2021 ; Belloc & Molina, 2022 ). The classical β-convergence will yield time- and country-invariant coefficient β because it assumes the technological process is homogeneous (Phillips & Sul, 2007 ). Alternatively, the panel club convergence approach cannot identify all structural parameters and isolate the convergence indicator’s major determinants (Pfaffermayr, 2012 ). Given the weaknesses of these two approaches, the continuous state space approach is superior as it allows us to identify the evolution of environmental indices, including catch-up, stratification, and polarization, and the conditional convergence under this method allows us to examine the potential factors that underlie differences in group convergence tendency. The rest of the paper is organized as follows. Section 2 introduces the state space approach, and Section 3 describes the data. Section 4 presents the static analysis results. Section 5 reports the dynamic analysis results, and Section 6 concludes. 2. Research Methodology Discrete and continuous state space approaches are widely used in distribution dynamics analysis. Although the discrete state space approach is simple in calculation, it suffers from arbitrariness. Morevoer, the discrete state space approach sometimes fails to accurately reflect the probabilistic properties of variables (Quah, 1997 ; Bulli, 2001 ; and Johnson, 2005 ). In comparison, the continuous state space approach can avoid arbitrariness in the discretization process by adopting a nonparametric stochastic kernel approach, allowing for the estimation of distribution with infinite state spaces. Thus, it is regarded as a better alternative to the discrete state space approach. This study employs the continuous state space approach to identify the ecological footprint dynamic changes of 366 Chinese PAA cities between 2001 and 2020. the continuous state space approach was pioneered by Danny Quan in a series of studies on the evolutionary income distribution process among countries (Quan,1996; 1997). After that, this method has been applied to economic growth convergence analysis (Galor & Tsiddon, 1997 ; Bulli, 2001 ; Maassoumi et al., 2007) and environmental studies (Nguyen, 2005; Burnett, 2016 ; Wu et al., 2022 ). It offers two critical advantages ove r conventional convergence approaches (such as σ-convergence, β-convergence, and stochastic convergence). First, it employs a stochastic kernel approach to estimate the transition probability matrix, which enables the examination of long-term trends in convergence and the existence of ecological poverty in Chinese cities. Second, this data-driven method eliminates the model specification errors inherent in traditional parametric approaches since it does not require prior assumptions. The continuous state space approach begins by accessing the transition probability distribution. Suppose that the distribution of Chinese NDVI in PAA-level cities at time t can be expressed by the density function \(\:{\phi\:}_{t}\left(x\right)\) . Because the evolution of the distribution is time-invariant and first-order, we can describe the \(\:\tau\:\) -period-ahead distribution \(\:{\phi\:}_{t+\tau\:}\left(y\right)\) using the base distribution \(\:{\phi\:}_{t}\left(x\right)\) $$\:{\phi\:}_{t+\tau\:}\left(y\right)={\int\:}_{0}^{\infty\:}{{g}_{\tau\:}\left(y\right|x)\phi\:}_{t}\left(x\right)dx$$ 1 , where \(\:{g}_{\tau\:}\left(y\right|x)\) is the conditional probability density that records the transition process of vegetation coverage from time t to t+ \(\:\tau\:\) . Here \(\:\tau\:\) is strictly positive, and for any x , \(\:{\int\:}_{0}^{\infty\:}{g}_{\tau\:}\left(y\right|x)dy=1\) . Keeping the transition probability \(\:{g}_{\tau\:}\left(y\right|x)\) steady, the NDVI distribution will evolve into a long-run equilibrium state \(\:{\phi\:}_{\infty\:}\left(y\right)\) called ergodic distribution. In this case, \(\:{\phi\:}_{\infty\:}\left(y\right)\) can be expressed as $$\:{\phi\:}_{\infty\:}\left(y\right)={\int\:}_{0}^{\infty\:}{{g}_{\tau\:}\left(y\right|x)\phi\:}_{\infty\:}\left(x\right)dx$$ 2 . The continuous state space approach uses a stochastic kernel density method to estimate the transition probability and its ergodic distribution. According to the method’s principle, we can define the joint kernel function \(\:{\phi\:}_{t,t+\tau\:}\left(y,x\right)\) and the marginal kernel function \(\:{\phi\:}_{t}\left(x\right)\) as $$\:{\phi\:}_{t,t+\tau\:}\left(y,x\right)=\frac{1}{n{h}_{x}{h}_{y}}\sum\:_{i=1}^{n}K\left(\frac{x-{x}_{i}}{{h}_{x}},\frac{y-{y}_{i}}{{h}_{y}}\right)\:;{\phi\:}_{t}\left(x\right)=\frac{1}{n{h}_{x}}\sum\:_{i=1}^{n}K\left(\frac{x-{x}_{i}}{{h}_{x}}\right),$$ 3 where \(\:{x}_{i}\) and \(\:{y}_{i}\) stand for the ecological cover level of city i at time t and time t \(\:+\tau\:\) ; \(\:{h}_{x}\) and \(\:{h}_{y}\) denote the bandwidth of x and y , respectively, and can be computed through \(\:h=1.06\sigma\:{n}^{-1/5}\) (Silvierman 1986; Sheather, 2004); and n is the number of cities. \(\:K(\bullet\:)\) represents the relevant kernel density function. Combined with the above definitions of \(\:{\phi\:}_{t,t+\tau\:}\left(y,x\right)\) and \(\:{\phi\:}_{t}\left(x\right)\) , we can further estimate the conditional probability density as $$\:{g}_{\tau\:}\left(y|x\right)=\frac{{\phi\:}_{t,t+\tau\:}\left(y,\:\:x\right)}{{\phi\:}_{t}\left(x\right)}$$ 4 . Unlike the discrete state space approach, which uses a transition probability matrix to depict the results, the continuous state space approach uses a three-dimensional plot or contour map to visually display the transition probability distribution. To gain deeper insight into the convergence trend of vegetation in Chinese cities, we calculate each city’s net transition probability value (NTP) to construct a comprehensive curve that illustrates the overall movement trend. In particular, the NTP can be calculated by the upward transition probability minus the downward transition probability at each point; i.e., the NTP index can be defined as \(\:p\left(x\right)\) in the following equation $$\:p\left(x\right)={\int\:}_{x}^{\infty\:}{g}_{\tau\:}\left(z\right|x)dz-{\int\:}_{0}^{x}{g}_{\tau\:}\left(z\right|x)dz$$ 5 . The NTP serves as a valuable indicator of changing trends at different points. A positive NTP indicates a city’s improvement in the ecological environment. Beyond that, a downward-sloping NTP curve implies a long-term convergence tendency, while an upward slope indicates divergence. 3. Data Description The data used in this paper cover 366 prefectures in China, which include cities, autonomous prefectures, and municipalities). The data contain NDVI values spanning 2001–2020. NDVI is a vegetation index obtained from canopies by applying remote-sensing techniques, and it is the ratio of reflectance from red and near-infrared (NIR) wavebands. NDVI data are from NASA’s EOS/MODIS (TERRA satellite) remote-sensing data product (MOD13A3). After distractions from factors such as cloud cover and atmospheric changes have been eliminated, the maximum value composite (MVC) method is employed to process monthly data and derive annual values. The MVC method selects the pixel with the highest NDVI value for each month and can effectively mitigate any outliers and temporary disturbances in the remote-sensing data. In this way, we obtain a robust and consistent annual NDVI data set for analysis. This study also investigates the long-run distribution of different city groups based on geographic location, income level, and participation, which are believed to influence vegetation. In particular, income levels are measured by the GDP per capita, which istaken from China City Statistical Yearbooks (CCSYs); missing values are derived from provincial statistical yearbooks using the same standard of calculation of CCSYs. As subsequent analyses also divides cities into subgroups based on each city’s average annual precipitation and rainfall, we also obtain data from the China Meteorological Data Service Center. 4. Static Analysis Identifying vegetation changes in Chinese cities over the sample period can provide direct intuition before examing the distribution dynamics of China’s ecological footprint. Figure 1 maps the initial and final spatial distributions of NDVI during the study period, which illustrates a significant increase and deepening in vegetation coverage in central and northwest China. The growth in absolute NDVI values reflects China’s ecological improvement after 20 years of effort. Figure 2 presents the kernel density distributions of the NDVI for PAA cities in three representative years. The sample is equally divided into two periods based the representative years: 2001, 2010, and 2020. Figure 2 (a) depicts the kernel density distribution of absolute NDVI for 366 cities. Overall, the density curves are left-skewed and exhibit asymmetric multimodality. Although most cities converge to the main peak between NDVI values of 7,000 and 8,000, a few cities are spread over the low-NDVI interval and form multiple lower peaks between NDVI values of 1,000 and 3,000. It is worth noting that the NDVI value of the main peak shifted toward the high-NDVI end during the study period, which echoes the evidence from Fig. 1 that the ecological environment improved during the sample period. In this study, the relative position changes of NDVI in each city are our focus rather than the absolute values. Therefore, following a common practice with the continuous state space approach, each city’s NDVI values were divided by its yearly average to obtain the normalized NDVI (RNDVI) for the following analysis. Figure 2 (b) displays the kernel density distribution of the RNDVI. By comparison, the distribution shapes are mostly similar, with a slight difference in the heights of the peaks. But the relative positions between the three curves of the RNDVI are much closer than those of the NDVI. It suggests strong persistence in the relative position change. In addition, the existence of multiple peaks at the low-RNDVI end suggests that some cities have poor and persistent ecological conditions. However, this conclusion is based on static analysis of specific years, whereas dynamic analysis can provide us with a detailed evolution of the ecological footprints of China’s PAA cities over time. 5. Dynamic Analysis 5.1 Distribution Dynamics of the NDVI Figure 3 displays the distribution dynamics of the RNDVI of the 366 PAA cities. Figure 3 (a) is a three-dimensional plot of the transition probability of the RNDVI. To provide direct intuition, for a given RNDVI at time t , we obtain a longitudinal slice along the vertical axis and parallel to the RNDVI t + 1 axis, and the slice yields the distribution probability that this city at time t will transit into a different value at period t + 1 . If the transition probability mass distributed along the 45-degree diagonal, this suggests a strong tendency of persistence in relative position changes. In particular, distribution parallel to the t-axis indicates the tendency of convergence. To visually observe the probability distribution along the main diagonal, this study employs a contour map to provide an aerial view of the three-dimensional diagram. As shown in Fig. 3 (b), the whole sample displays strong persistence in intra-distribution mobility. The net transition probability (NTP) curve in Fig. 3 (c) displays the net evolution trend of cities in terms of the RNDVI and helps identify the convergence tendency. Suppose the NTP curve intersects with the null axis, and the net transition probability is positive on the left side of the intersection point and negative on the right. In that case, the downward-sloping NTP curve indicates that the RNVDI on both sides of the intersection will converge to this point. According to the NTP curve of the whole sample, there is a net convergence tendency in the vegetation coverage of PAA cities during the study period. Figure 3 (d) presents the long-run stationary (ergodic) distribution while keeping the transition probability of the RNDVI constant. Significant left-skewed unimodality can be observed in the ergodic distribution of the sample cities. If current trends continue, most Chinese cities will converge to an RNDVI value that is 1.15 times the average, suggesting that China’s efforts toward ecological improvement have had an effect. China’s ecological protection has changed from key regions’ governance to partitioned and sorted management in the 21st century. The primary strategy is to improve the ecology by distinguishing important ecological functional areas, key resource development zones, and good ecological areas. In 2007, the Chinese government clarified that the ecological function zone was categorized as restricted development zones. Since then, 25 ecological function zones have been identified nationwide, and the ecological conservation redline in ecological function zones has become apparent. After 2012, China embarked the so-called Shan-Shui Initiative, which included a series of projects to conserve and restore natural resources, encompassing mountains, rivers, forests, farmlands, lakes, and grasslands. The initiative was one of the top ten flagship projects for global restoration by United Nations. It demonstrated China’s transition towards emphasizing overall protection, systematic restoration, and comprehensive management in ecological protection. In addition to these efforts, the Chinese government implemented three 5-year plans for ecological protection during the study period, accelerating regional ecosystem protection and helping to extend China’s ecological coverage. To empirically test the robustness of the above results, we examined the distribution dynamics of RNDVI values with an interval of every two years. As shown in Figure A1 , our main empirical results remain robust. 5.2 Conditional Distribution Dynamics 5.2.1 NDVI Groups An important issue in convergence analysis is whether poor ecological cities can catch up with good ecological cities. We divide the 366 PAA cities into three groups for heterogeneity analysis based on RNDVI values in the initial year, 2001. The distribution dynamics of the three groups are shown in Fig. 4 . Unlike the other two groups, the transition probability mass of the low-NDVI group is distributed along the 45-degree diagonal, which suggests strong persistence and immobility in vegetation coverage (Fig. 4 (a)). In contrast, the horizontal transition probability distribution of the medium- and high-NDVI groups implies that there is convergence in vegetation coverage among these cities (see Figs. 4 (d) and 4(g)). Since the NTP curves of the three groups are all downward-sloping, they imply a strong tendency toward convergence on vegetation coverage within the cit y groups. Left-skewed shapes are observed in the long-run stationary distributions of the three NDVI groups. Cities in the low-NDVI group are concentrated on a relatively low point (below average), which suggests less dense vegetation coverage and the existence of ecological poverty (see Fig. 4 (c)). Therefore, we observe no significant catch-up effects in poor ecological cities. Unlike the low-NDVI group, the ergodic distribution of medium- and high-NDVI city groups is slightly bimodal (Figs. 4 (f) and 4(i)). In addition, most cities are clustered to approximately 1.2 times the average NDVI values in these two groups. This implies that these cities became greener through decades of effort. However, the lower peaks of the two groups suggest that ecological poverty also exists in the medium- and high-NDVI city groups. By and large, the remarkable convergence in the three NDVI groups proves the effectiveness of China’s ecological policies. However, low-NDVI cities exhibit significant stickiness in intra-distribution dynamics and have less opportunity to move into the high-NDVI end. This may induce a chronic ecological-poverty trap. 5.2.2 Regional Groups Different regions in China vary in geographic resources, such as climate, soil, and topography. These factors have important impacts on regional ecological coverage (Kogan, 1990 ; Cui, 2013 ). In order to examine the geographic distribution dynamics of China’s vegetation change, we zoned Chinese cities as eastern, central, and western city groups, and presented the results in Fig. 5 . According to the contour map of the eastern city group (Fig. 5 (a)), the above-diagonal transition probability distribution at the lower RNDVI interval suggests significant improvement in vegetation coverage in low-NDVI eastern cities, which can be observed in Fig. 1. The declining NTP curve in Fig. 5 (b) indicates a broad convergence tendency in the eastern city group during the research period. However, the triple intersection points with the horizontal axis suggest the existence of multimodality in the ergodic distribution. The twin peaks in Fig. 5 (c) provide evidence of bimodality club convergence in the long-run distribution. This indicates the existence of polarization in terms of NVDI in eastern cities. Since more than half of the eastern cities are concentrated in the peak with an RNDVI value of 0.6, those cities will have low vegetation coverage even in the long run. By contrast, the contour maps in Fig. 5 (d) and 5(g) show strong persistence. However, the NTP plots in Figs. 5 (e) and 5(h) show clear net convergence trends. The left-skewed unimodality in the ergodic distributions of Figs. 5 (f) and 5(i) show that central and western cities have made progress in vegetation coverage, which also echoes the findings in Fig. 1. However, strong persistence in the transition probability suggests that this process may require a very long time. As shown in Fig. 1, the vegetation coverage in many central and western cities is still poor. More efforts should be dedicated towards enhancing the ecological environments in these regions. 5.2.3 Rainfall Groups Precipitation directly affects soil-water balance, and a soil-moisture regime influences plant growth and crop production. Studies have shown that temporal variation in the NDVI is closely associated with precipitation and demonstrates a strong linear (Nicholson et al., 1990 ) or log-line (Davenport & Nicholson,1993). To examine the role of rainfall in transition probability, we divided these cities into low-, medium-, and high-rainfall groups according to the average rainfall during our sample period. Low-rainfall cities display the most vigorous persistence in transition probability among the three groups, as demonstrated by comparing the three contour maps in Fig. 6 . Meanwhile, the deviation from the diagonal with an RNDVI value below 0.8 in Figs. 6 (d) and 6(g) implies the upward tendency of convergence in medium- and high-rainfall cities. The downward-sloping NTP plots in Figs. 6 (b) and 6(e) reveal the existence of clear net convergence in these two groups. In contrast, high-rainfall cities show no evidence of net convergence (Fig. 6 (h)). As expected, unimodality can be seen in the ergodic distributions of low- and medium-rainfall cities, but bimodality in high-rainfall cities. The polarization of vegetation coverage in high-rainfall cities suggests that those low-NDVI cities had poor performance in sustainable development, even with better natural endowments. 5.2.4 Income Groups Income is another important factor associated with the ecological footprint (Duro & Teixidó-Figueras, 2013 ; Alix-Garcia et al., 2013 ). First, high income is associated with high human activities, which may lead to environmental degradation (Alix-Garcia et al., 2013 ). Second, high-income residents typically have higher requirements for an ecological environment and higher willingness to pay for it (Alix-Garcia et al., 2018 ). To analyze this aspect, we divided sample cities into three groups based on regional income (per capita GDP) in 2020. Figure 7 presents the distribution dynamics of the three income groups. As evident from the contour maps, all three groups exhibit persistence in their transitions. Despite volatility in the net transition probabilities, curves in the middle column, on the whole, show that the vegetation coverage of these groups all converge to intersection points with RNDVI values greater than 1. Left-skewed unimodality is also visible in the long-run stationary distributions of the three groups. The only difference is that low-income and medium-income cities performed better in ecological improvement over the two decades. In China, most high-income cities are either resourced-based (such as Karamay, Ordos, and Haixi) or heavily urbanized (such as Wuxi, Shenzhen, Suizhou, Shanghai, and Zhuhai). Human activities such as resource exploitation and urban construction occupy formerly green spaces and degrade the ecology. Assuming the environmental Kuznets curve exists, Chinese cities are still located on the left side when the environment quality is measured by ecological footprint. Our results alig n with the findings of prior studies (Alix-Garcia et al., 2013 ; Chen et al., 2022 ; Ansari, 2022 ). For instance, Alix-Garcia et al. ( 2013 ) found that income improvement in Mexico led to higher consumption of land-intensive goods, ultimately increasing deforestation. Chen et al. ( 2022 ) demonstrated that the vegetation changes that arise from urbanization have both direct impacts, such as the loss of green land, and indirect impacts from changes in the macro-environment associated with urbanization. 6. Conclusions The Chinese government initially proposed the concept of ecological poverty alleviation to combines poverty alleviation and development into ecological protection. Programs were enacted in ecological function zones such as the Yellow River Basin, Yangtze River Basin, and Qinghai-Tibet Plateau. This is because most ecological function areas are characterized as national-level poverty-stricken regions. Moreover, more fiscal transfer is paid for forestry and grasslands in poor areas to implement several ecological protection and restoration projects like the controlling wind and sand sources in Beijing and Tianjin, the three north shelterbelt programs, and the ecological protection and construction of the three rivers’ sources regions. These projects have greatly improved regional vegetation coverage and preserved China’s ecological diversity. However, as one of the largest countries in the world, China’s vegetation coverage differs greatly across regions. Though examining the distribution dynamics of vegetation coverage across 366 Chinese PAA-level cities using the continuous state space approach, this study provides important implications for improving vegetation coverage in Chinese cities. Our analysis shows a clear convergence tendency in vegetation coverage China’s across 366 cities. Through decades of efforts, most Chinese cities have significantly increased vegetation land and greenness. However, Chinese cities with different initial vegetation coverage exhibit salient heterogeneity in the long-run distribution dynamics of the NDVI. Low-vegetation-coverage cities have fewer opportunities to become high-vegetation-coverage cities, which may form a chronic ecological poverty trap. In addition, polarization in vegetation coverage is present in eastern Chinese cities and high-rainfall cities. Polarization and persistence provide further evidence of the existence of ecological poverty. Furthermore, high-income cities have poorer vegetation coverage performance than low- and medium-income cities. A plausible explanation could be that human production activities associated with urbanization and resource exploitation have led to the destruction of vegetation and occupation of green space, thus deteriorating the urban ecological environment. Our results suggest that policies and laws pertaining to agriculture, forestry, and environmental protection in recent years have been successful with respect to ecological restoration and green area expansion for most Chinese cities. What should not be ignored, however, is the existence of ecological poverty in China. The ecological poverty alleviation program should thus play a more significant role in ecological improvement, especially in Eastern cities. For cities that are endowed with high rainfall but are trapped in ecological-poverty, reducing over-exploitation may be the best way to maintain sustainable development. Meanwhile, we have to admit the existence of limitations in this study. As the convergence analysis is descriptive, the causal effect requires inferential statistics, which is beyond the scope of this paper. Even though the conditional convergence analysis reveals that economic development affects vegetation, the in-depth analysis of the underlying mechanisms deserves further exploration. Additionally, the existence of ecological poverty underscores the need for future studies to uncover more effective ways to relieve such poverty. Declarations Declaration of Interest : This work was supported by the Fundamental Research Funds for the Central Universities (No.23JNLH09), Philosophy and Social Science Planning Projects in Hainan Province (No. HNSK(ZC)23-155), Hainan College of Economics and Business (No. hnjmk2021301). The funding bodies had no involvement in study design, the collection, analysis and interpretation of the data, the writing of the report and the decision to submit the article for publication. Author Contribution All authors involved in study design, the collection, analysis and interpretation of the data, the writing of the manuscript and the decision to submit the article for publication. References Ahmed Z, Zafar MW, Ali S (2020) Linking urbanization, human capital, and the ecological footprint in G7 countries: An empirical analysis. Sustainable Cities Soc 55:102064 Aksoy CG, Tumen S (2021) Local governance quality and the environmental cost of forced migration. J Dev Econ 149:102603 Alix-Garcia JM, Sims KR, Orozco-Olvera VH, Costica LE, Fernández Medina JD, Monroy R (2018) S. Payments for environmental services supported social capital while increasing land management. 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Environ Sci Pollut Res 28(42):59771–59783 Ulucak R, Apergis N (2018) Does convergence really matter for the environment? An application based on club convergence and on the ecological footprint concept for the EU countries. Environ Sci Policy 80:21–27 Ulucak R, Bilgili F (2018) A reinvestigation of EKC model by ecological footprint measurement for high, middle and low income countries. J Clean Prod 188:144–157 Ulucak R, Khan SUD (2020) Determinants of the ecological footprint: Role of renewable energy, natural resources, and urbanization. Sustainable Cities Soc 54:101996 Van den Bergh JC, Verbruggen H (1999) Spatial sustainability, trade and indicators: An evaluation of the ecological footprint. Ecol Econ 29(1):61–72 Wackernagel M, Rees W (1998) Our ecological footprint: Reducing human impact on the earth, vol 9. New Society Wackernagel M, Schulz NB, Deumling D, Linares AC, Jenkins M, Kapos V, Randers J (2002) Tracking the ecological overshoot of the human economy. Proceedings of the National Academy of Sciences , 99(14), 9266–9271 Wang N, Du Y, Liang F, Wang H, Yi J (2022) The spatiotemporal response of China's vegetation greenness to human socio-economic activities. J Environ Manage 305:114304 White TJ (2007) Sharing resources: The global distribution of the Ecological Footprint. Ecol Econ 64(2):402–410 Wu J, Ma C (2019) The convergence of China’s marginal abatement cost of CO 2: an emission-weighted continuous state space approach. Environ resource Econ 72:1099–1119 Wu JX, He LY, Zhang Z (2022) On the co-evolution of PM2. 5 concentrations and income in China: A joint distribution dynamics approach. Energy Econ 105:105706 Yang K, Sun W, Luo Y, Zhao L (2021) Impact of urban expansion on vegetation: The case of China (2000–2018). J Environ Manage 291:112598 Yilanci V, Pata UK (2020) Investigating the EKC hypothesis for China: the role of economic complexity on ecological footprint. Environ Sci Pollut Res 27(26):32683–32694 Yin J, Zheng M, Chen J (2015) The effects of environmental regulation and technical progress on CO2 Kuznets curve: An evidence from China. Energy Policy 77:97–108 Zhao S, Li Z, Li W (2005) A modified method of ecological footprint calculation and its application. Ecol Model 185(1):65–75 Zubelzu S, Álvarez R, Hernández A (2015) Methodology to calculate the carbon footprint of household land use in the urban planning stage. Land Use Policy 48:223–235 Additional Declarations No competing interests reported. Supplementary Files Appendix.docx Cite Share Download PDF Status: Published Journal Publication published 07 Aug, 2025 Read the published version in Environmental and Ecological Statistics → Version 1 posted Editorial decision: Revision requested 05 Mar, 2025 Reviews received at journal 16 Feb, 2025 Reviews received at journal 12 Jan, 2025 Reviewers agreed at journal 11 Jan, 2025 Reviewers agreed at journal 09 Jan, 2025 Reviewers invited by journal 09 Jan, 2025 Editor assigned by journal 09 Jan, 2025 Submission checks completed at journal 09 Jan, 2025 First submitted to journal 09 Jan, 2025 You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. 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Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-5794674","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":401117755,"identity":"cf243a43-b599-410f-99f4-92fa34395dc2","order_by":0,"name":"Di Fan","email":"","orcid":"","institution":"Jinan University","correspondingAuthor":false,"prefix":"","firstName":"Di","middleName":"","lastName":"Fan","suffix":""},{"id":401117756,"identity":"a34239a5-43e3-4e0c-a499-b7e6a3ce5e0c","order_by":1,"name":"Qiufeng Chen","email":"","orcid":"","institution":"Huizhou University","correspondingAuthor":false,"prefix":"","firstName":"Qiufeng","middleName":"","lastName":"Chen","suffix":""},{"id":401117757,"identity":"c8b3778e-e5ff-4068-ab10-0bb633910d2f","order_by":2,"name":"Jianxin Wu","email":"","orcid":"","institution":"Jinan University","correspondingAuthor":false,"prefix":"","firstName":"Jianxin","middleName":"","lastName":"Wu","suffix":""},{"id":401117758,"identity":"473b7571-8438-4bbc-85c2-47c2b6d7690c","order_by":3,"name":"Tsun Se Cheong","email":"","orcid":"","institution":"The Hang Seng University of Hong Kong","correspondingAuthor":false,"prefix":"","firstName":"Tsun","middleName":"Se","lastName":"Cheong","suffix":""},{"id":401117759,"identity":"14663f25-ef00-4c1f-af97-20e3a38f5c8f","order_by":4,"name":"Ning Ma","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA/ElEQVRIiWNgGAWjYDACCcYGKAvEqDgAZh54QLyWMwcYeEBaEvBqQeYwtkG0MODTwj+7ue3BD4Zt8gzSzW0Pv867I2cvdvgh0BY7Od0G7Fok7hxsN+xhuG3YIHOw3Vh22zNjHuk0A6CWZGOzA9i1GEgktknwMNxmbAAypCW3HU7skU4AaTmQuA2PFsk/DLftIVrmgLSkfyCoRRpoSyJIi+THBpCWHPy2SNwAapFhuJ0MtoXh2GFjnts5BQcSDHD7hX9G+jPJNwy3bRskgIwfNYfl2Genb/7wocJODpcWMGD8x8BgD1TAzINwMB7lKFp/EKlwFIyCUTAKRhYAAAh7YT+NG5dcAAAAAElFTkSuQmCC","orcid":"","institution":"Hainan College of Economics and Business","correspondingAuthor":true,"prefix":"","firstName":"Ning","middleName":"","lastName":"Ma","suffix":""}],"badges":[],"createdAt":"2025-01-09 08:38:18","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-5794674/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-5794674/v1","draftVersion":[],"editorialEvents":[{"content":"https://doi.org/10.1007/s10651-025-00671-9","type":"published","date":"2025-08-07T15:57:28+00:00"}],"editorialNote":"","failedWorkflow":false,"files":[{"id":73653746,"identity":"ad04fd2f-fa27-42db-b4c5-a8adc45f9e85","added_by":"auto","created_at":"2025-01-13 09:59:06","extension":"png","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":558668,"visible":true,"origin":"","legend":"\u003cp\u003eMap of the spatial distribution of NDVI in 2001(a) and 2020 (b)\u003c/p\u003e","description":"","filename":"1.png","url":"https://assets-eu.researchsquare.com/files/rs-5794674/v1/0b048f7a57075672b58331a0.png"},{"id":73652094,"identity":"22ec0146-cdc2-4569-a2ac-4bd525ce87d4","added_by":"auto","created_at":"2025-01-13 09:51:06","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":123699,"visible":true,"origin":"","legend":"\u003cp\u003eDistribution of NDVI and RNDVI in representative years\u003c/p\u003e\n\u003cp\u003e\u003cem\u003eNote: The horizontal axis represents the NDVI and RNDVI values, respectively. The vertical axis denotes the kernel density of the sample cities in specific years.\u003c/em\u003e\u003c/p\u003e","description":"","filename":"2.png","url":"https://assets-eu.researchsquare.com/files/rs-5794674/v1/303a2e08863efd522dc5ae83.png"},{"id":73651787,"identity":"2d86feab-5067-48ce-aaca-4c616ee9c5c1","added_by":"auto","created_at":"2025-01-13 09:43:06","extension":"png","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":82312,"visible":true,"origin":"","legend":"\u003cp\u003eTransition probabilities and ergodic distributions using annual transitions\u003c/p\u003e","description":"","filename":"3.png","url":"https://assets-eu.researchsquare.com/files/rs-5794674/v1/45e23ed4041b48916d08add1.png"},{"id":73652097,"identity":"0d2129b9-8340-43b7-8461-0569d4e356ce","added_by":"auto","created_at":"2025-01-13 09:51:06","extension":"png","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":69898,"visible":true,"origin":"","legend":"\u003cp\u003eTransition probabilities and ergodic distributions by NDVI groups\u003c/p\u003e\n\u003cp\u003e\u003cem\u003eNote: Panels (a), (b), and (c) are for low-NDVI cities; panels (d), (e), and (f) are for medium-NDVI cities; and panels (g), (h), and (i) are for high-NDVI cities.\u003c/em\u003e\u003c/p\u003e\n\u003cp\u003e\u003cem\u003eRNDVI ranges for the three city groups are low RNDVI, [0.117–0.959], 122 cities; middle RNDVI, [0.959–1.146], 122 cities; and high RNDVI, [1.146–1.392], 122 cities. RNDVI values here are for 2001.\u003c/em\u003e\u003c/p\u003e","description":"","filename":"4.png","url":"https://assets-eu.researchsquare.com/files/rs-5794674/v1/e5e982366ca85504ab56e1ee.png"},{"id":73651797,"identity":"25b89704-0960-4677-b11d-0ce337048fe9","added_by":"auto","created_at":"2025-01-13 09:43:06","extension":"png","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":80893,"visible":true,"origin":"","legend":"\u003cp\u003eTransition probabilities and ergodic distributions by region\u003c/p\u003e\n\u003cp\u003e\u003cem\u003eNote: Panels (a), (b), and (c) are for eastern cities; panels (d), (e), and (f) are for central cities; and panels (g), (h), and (i) are for western cities.\u003c/em\u003e\u003c/p\u003e\n\u003cp\u003e\u003cem\u003eEast City group consists 127 cities from Beijing, Tianjin, Shanghai and cities in Hebei, Shanxi, Liaoning, Jiangsu, Zhejiang, Fujian, Shandong, Guangdong, and Hainan provinces; Central City group comprises 111 cities in Anhui, Henan, Heilongjiang, Hubei, Hunan, Jilin, Jiangxi, Inner Mongolia, and Chongqing provinces; West city group includes 128 cities in Gansu, Guangxi, Guizhou, Ningxia, Qinghai, Shanxi, Sichuan, Xizang, Xinjiang, and Yunnan provinces\u003c/em\u003e.\u003c/p\u003e","description":"","filename":"5.png","url":"https://assets-eu.researchsquare.com/files/rs-5794674/v1/0826673d4ba58c3786057c29.png"},{"id":73651813,"identity":"3f1a1b24-99e1-4a50-ac8d-388fe6c13d76","added_by":"auto","created_at":"2025-01-13 09:43:07","extension":"png","order_by":6,"title":"Figure 6","display":"","copyAsset":false,"role":"figure","size":75391,"visible":true,"origin":"","legend":"\u003cp\u003eTransition probabilities and ergodic distributions by rainfall\u003c/p\u003e\n\u003cp\u003e\u003cem\u003eNote: Panels (a), (b), and (c) are for low-rainfall cities; panels (d), (e), and (f) are for medium-rainfall cities; and panels (g), (h), and (i) are for high-rainfall cities.\u003c/em\u003e\u003c/p\u003e\n\u003cp\u003e\u003cem\u003eThe average annual rainfall of 122 low-rainfall cities is between 125.48mm and 663.17mm; the average annual rainfall of 122 medium-rainfall cities ranges from 665.88mm to 1206.69mm; the average yearly rainfall of 122 high-rainfall cities is from 1211.06mm to 1222111.58mm.\u003c/em\u003e\u003c/p\u003e","description":"","filename":"6.png","url":"https://assets-eu.researchsquare.com/files/rs-5794674/v1/b62e4ec5af4c0079dd144a39.png"},{"id":73651794,"identity":"cbadf667-ae8b-4405-a9d8-f362a4ba76f8","added_by":"auto","created_at":"2025-01-13 09:43:06","extension":"png","order_by":7,"title":"Figure 7","display":"","copyAsset":false,"role":"figure","size":78298,"visible":true,"origin":"","legend":"\u003cp\u003eTransition probabilities and ergodic distributions by income\u003c/p\u003e\n\u003cp\u003e\u003cem\u003eNote: Panels (a), (b), and (c) are for low-income cities; panels (d), (e), and (f) are for medium-income cities; and panels (g), (h), and (i) are for high-income cities.\u003c/em\u003e\u003c/p\u003e\n\u003cp\u003e\u003cem\u003eThe per capita GDP of 122 low-income cities in 2020 is between 14958 and 22122 yuan; The per capita GDP of 122 medium-income cities in 2020 is from 22251 to 44021 yuan; The per capita GDP of 122 high-income cities in 2020 ranged from 44137 to 96134 yuan.\u003c/em\u003e\u003c/p\u003e","description":"","filename":"7.png","url":"https://assets-eu.researchsquare.com/files/rs-5794674/v1/898dcace79e6ef43295ebf9e.png"},{"id":88814144,"identity":"fb2b347e-628f-4da4-955c-8d3fefe5326a","added_by":"auto","created_at":"2025-08-11 16:07:31","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":1695386,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-5794674/v1/59dc6b31-7483-4312-9875-08b879e18aee.pdf"},{"id":73652095,"identity":"61f2b2ab-eff1-4baa-99ff-55206101a354","added_by":"auto","created_at":"2025-01-13 09:51:06","extension":"docx","order_by":1,"title":"","display":"","copyAsset":false,"role":"supplement","size":125047,"visible":true,"origin":"","legend":"","description":"","filename":"Appendix.docx","url":"https://assets-eu.researchsquare.com/files/rs-5794674/v1/939a88ca4505f423386f470f.docx"}],"financialInterests":"No competing interests reported.","formattedTitle":"Does ecological poverty trap exist in Chinese cities? Evidence from the distribution dynamics of vegetation coverage","fulltext":[{"header":"1. Introduction","content":"\u003cp\u003eHuman activities have triggered unprecedented changes in the social-ecological system in recent decades because of the world\u0026rsquo;s growing population and resource demand (Odegard et al., 2014). Consequently, environmental stress occurs due to factors like inappropriate land use, deforestation, cropland expansion, and over-exploitation of mining (Lopez, R.,1992; Gray \u0026amp; Moseley, \u003cspan citationid=\"CR32\" class=\"CitationRef\"\u003e2005\u003c/span\u003e; Aksoy \u0026amp; Tumen, \u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2021\u003c/span\u003e). In other words, the ecological footprint, which defines resource consumption and water assimilation, rises along with decreasing biocapacity (Wackernagel \u0026amp; Rees, \u003cspan citationid=\"CR68\" class=\"CitationRef\"\u003e1998\u003c/span\u003e). Studies have shown an inverted U-shaped relationship between economic growth and environmental quality, known as the environmental Kuznets curve (EKC) (Barbier, \u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e1997\u003c/span\u003e; Dinda, \u003cspan citationid=\"CR25\" class=\"CitationRef\"\u003e2004\u003c/span\u003e). The EKC hypothesis suggests that economic growth by itself may be a solution to environmental degradation (Rothman \u0026amp; de Bruyn, \u003cspan citationid=\"CR56\" class=\"CitationRef\"\u003e1998\u003c/span\u003e). However, air quality indexes are frequently used to evaluate environmental quality in existing studies, and other indicators were less considered. Ecological footprint, upon its introduction, was subsequently used to measure environmental degradation and has been promoted as a policy and planning tool for achieving sustainability (Van den Bergh \u0026amp; Verbruggen, \u003cspan citationid=\"CR67\" class=\"CitationRef\"\u003e1999\u003c/span\u003e; Zhao et al., \u003cspan citationid=\"CR77\" class=\"CitationRef\"\u003e2005\u003c/span\u003e). Despite evidence of international inequalities in the ecological footprint (White, \u003cspan citationid=\"CR71\" class=\"CitationRef\"\u003e2007\u003c/span\u003e; Duro \u0026amp; Teixid\u0026oacute;-Figueras, \u003cspan citationid=\"CR27\" class=\"CitationRef\"\u003e2013\u003c/span\u003e), few studies have investigated the convergence tendency of vegetation coverage on a national scale.\u003c/p\u003e \u003cp\u003eChina, the world\u0026rsquo;s largest developing country, faces severe environmental problems despite its record-breaking growth since the 1980s. To address the accelerating environmental degradation, China has probed ecological improvement through administrative power and gradually developed a discursive policy system with multiple practical approaches, such as green development, ecological public welfare compensation, and ecological relocation. These policies rely on massive resource inputs and strict political regimes, indicating large operation costs. In such a context, the ecological footprint is taken into account when scholars attempt to reassess the effect of a country\u0026rsquo;s economic policy (Wackernagel et al., \u003cspan citationid=\"CR69\" class=\"CitationRef\"\u003e2002\u003c/span\u003e; Gokmenoglu et al., 2022). In particular, vegetation coverage is commonly used to measure ecological footprint (Lenzen \u0026amp; Murray, \u003cspan citationid=\"CR41\" class=\"CitationRef\"\u003e2001\u003c/span\u003e; Chen et al., \u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e2020\u003c/span\u003e), and vegetation change in China is also a research focus currently (Du et al., \u003cspan citationid=\"CR26\" class=\"CitationRef\"\u003e2019\u003c/span\u003e; Yang et al., \u003cspan citationid=\"CR74\" class=\"CitationRef\"\u003e2021\u003c/span\u003e; Wang et al., \u003cspan citationid=\"CR70\" class=\"CitationRef\"\u003e2022\u003c/span\u003e). However, the linkage between vegetation change and the long-run evolution of China\u0026rsquo;s ecological footprint has not been fully investigated in the literature.\u003c/p\u003e \u003cp\u003eThis study uses a continuous state space approach to analyze the convergence and dynamic change of China\u0026rsquo;s prefecture and above (PAA) cities from 2001 to 2020, aiming to provide insights for policy evaluation and future adjustments. Using the Normalized Difference Vegetation Index (NDVI) as a proxy for ecological footprint, a remarkable club convergence tendency in vegetation coverage is observed in the entire sample. Since most cities converge to a point higher than the average vegetation coverage level, those cities have notably improved ecological quality during the study period. However, the polarization in the long-run distribution (also called ergodic distribution) suggests that some cities are falling into an ecological poverty trap, where a region runs a biological resources deficit, and the poverty is persistent. In addition to this, some regions have better climate endowments but perform poorly in vegetation, suggesting that ecological damage is caused by overdevelopment rather than natural endowment.\u003c/p\u003e \u003cp\u003eOur study contributes to the three strands of literature. \u003cb\u003eFirst, this study enriches the discussion about the EKC hypothesis.\u003c/b\u003e The EKC curve, as described by Panayotou (\u003cspan citationid=\"CR49\" class=\"CitationRef\"\u003e1993\u003c/span\u003e), was the dominant approach in environmental-related studies, with CO\u003csub\u003e2\u003c/sub\u003e emissions widely used as a proxy for pollution (Lantz \u0026amp; Feng, \u003cspan citationid=\"CR40\" class=\"CitationRef\"\u003e2006\u003c/span\u003e; Kaika \u0026amp; Zervas, \u003cspan citationid=\"CR38\" class=\"CitationRef\"\u003e2013\u003c/span\u003e; Pata, \u003cspan citationid=\"CR50\" class=\"CitationRef\"\u003e2018\u003c/span\u003e). Stern (\u003cspan citationid=\"CR61\" class=\"CitationRef\"\u003e2017\u003c/span\u003e) pointed out that the EKC is sensitive to sample selection and econometric techniques. In this case, emerging studies employed the ecological footprint as an indicator of environmental quality (Al-Mulali et al., \u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e2015\u003c/span\u003e; Charfeddine \u0026amp; Mrabet, \u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e2017\u003c/span\u003e; Destek et al., \u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e2018\u003c/span\u003e). The EKC was proven to be valid in China using CO2 emissions (Yin et al., \u003cspan citationid=\"CR76\" class=\"CitationRef\"\u003e2015\u003c/span\u003e) and PM2.5 indicators (Hao \u0026amp; Liu., 2016), whereas Yilanci \u0026amp; Pata (\u003cspan citationid=\"CR75\" class=\"CitationRef\"\u003e2020\u003c/span\u003e) concluded it may be invalid when considering ecological footprint. Different from the research methods in the studies of Al-Mulali et al. (\u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e2015\u003c/span\u003e) and Ulucak \u0026amp; Bilgili (\u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e2018\u003c/span\u003e), who also took the ecological footprint to extend the EKC discussion, we employ a continuous state space approach in this study. This approach provides a new perspective on understanding the EKC hypothesis by taking China as an example.\u003c/p\u003e \u003cp\u003e \u003cb\u003eSecond, this study relates to the convergence analyses of economic and environmental variables.\u003c/b\u003e The groundbreaking study of Solow (\u003cspan citationid=\"CR59\" class=\"CitationRef\"\u003e1956\u003c/span\u003e) has stimulated extensive convergence analyses on economic growth (Galor \u0026amp; Tsiddon, \u003cspan citationid=\"CR29\" class=\"CitationRef\"\u003e1997\u003c/span\u003e; Bulli, \u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e2001\u003c/span\u003e; Maasoumi et al., \u003cspan citationid=\"CR43\" class=\"CitationRef\"\u003e2007\u003c/span\u003e). Whereafter, the robust evidence of Islam (\u003cspan citationid=\"CR36\" class=\"CitationRef\"\u003e2003\u003c/span\u003e) on income convergence and the EKC hypothesis inspired extensive research in environmental variables (Nourry, \u003cspan citationid=\"CR47\" class=\"CitationRef\"\u003e2009\u003c/span\u003e). Except for the CO\u003csub\u003e2\u003c/sub\u003e emissions, other environmental indicators include NO\u003csub\u003eX\u003c/sub\u003e (Bulte et al., \u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e2007\u003c/span\u003e; Criado \u0026amp; Grether, \u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e2011\u003c/span\u003e; Camarero et al., \u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e2013\u003c/span\u003e), SO\u003csub\u003e2\u003c/sub\u003e (Bulte et al., \u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e2007\u003c/span\u003e; Nourry, \u003cspan citationid=\"CR47\" class=\"CitationRef\"\u003e2009\u003c/span\u003e; Payne et al., \u003cspan citationid=\"CR51\" class=\"CitationRef\"\u003e2014\u003c/span\u003e), and PM2.5 (Stern \u0026amp; Zha, \u003cspan citationid=\"CR62\" class=\"CitationRef\"\u003e2016\u003c/span\u003e; Stern \u0026amp; Van Dijk, \u003cspan citationid=\"CR61\" class=\"CitationRef\"\u003e2017\u003c/span\u003e) also have been studied. As for ecological footprint, the majority of convergence analyses were carried out on intergovernmental organizations and geographically close countries, such as members of the OECD (Solarin, \u003cspan citationid=\"CR57\" class=\"CitationRef\"\u003e2019\u003c/span\u003e; Solarin et al., \u003cspan citationid=\"CR58\" class=\"CitationRef\"\u003e2019\u003c/span\u003e), G20 (Bilgili \u0026amp; Ulucak, \u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e2018\u003c/span\u003e), EU (Ulucak \u0026amp; Apergis, \u003cspan citationid=\"CR64\" class=\"CitationRef\"\u003e2018\u003c/span\u003e), USMCA (Işık et al., \u003cspan citationid=\"CR35\" class=\"CitationRef\"\u003e2021\u003c/span\u003e), African (Bello et al., \u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e2022\u003c/span\u003e) and Latin American countries (Tillaguango et al., \u003cspan citationid=\"CR63\" class=\"CitationRef\"\u003e2021\u003c/span\u003e). In contrast, this study is the first to analyze the convergence tendency of the ecological footprint of China\u0026rsquo;s PAA cities, revealing a dynamic evolution process and information about the convergence clubs of a country.\u003c/p\u003e \u003cp\u003e \u003cb\u003eThird, this study delves into the ecological impacts of urbanization.\u003c/b\u003e Urbanization is the primary determinant and has yielded long-term effects on ecological footprints (Mu\u0026ntilde;iz \u0026amp; Galindo, \u003cspan citationid=\"CR44\" class=\"CitationRef\"\u003e2005\u003c/span\u003e; Zubelzu et al., \u003cspan citationid=\"CR78\" class=\"CitationRef\"\u003e2015\u003c/span\u003e; Al-Mulali \u0026amp; Oztur, 2015; Gassner et al., \u003cspan citationid=\"CR30\" class=\"CitationRef\"\u003e2018\u003c/span\u003e). Ahmed et al. (\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e2020\u003c/span\u003e) proved one-way causality from urbanization to environmental degradation. Further exploration by Ulucak \u0026amp; Khan (\u003cspan citationid=\"CR66\" class=\"CitationRef\"\u003e2020\u003c/span\u003e) indicated that urbanization decreases the ecological footprint. A similar conclusion also can be seen from Charfeddine (\u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e2017\u003c/span\u003e) and Arif et al. (\u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e2023\u003c/span\u003e). Different from the above studies, the conditional convergence in our study suggests that urbanization poses varying effects on the vegetation of different cities. While most cities in China have greatly improved their vegetation coverage during the study period, ecological damage was found in some cities despite being endowed with pleasant climates.\u003c/p\u003e \u003cp\u003eMethodologically, this study extends previous work using the continuous state space approach (Galor \u0026amp; Tsiddon, \u003cspan citationid=\"CR29\" class=\"CitationRef\"\u003e1997\u003c/span\u003e; Bulli, \u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e2001\u003c/span\u003e; Maasoumi et al., \u003cspan citationid=\"CR43\" class=\"CitationRef\"\u003e2007\u003c/span\u003e; Burnett, \u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e2016\u003c/span\u003e; Herrerias et al., \u003cspan citationid=\"CR34\" class=\"CitationRef\"\u003e2017\u003c/span\u003e; Wu \u0026amp; Ma, \u003cspan citationid=\"CR72\" class=\"CitationRef\"\u003e2019\u003c/span\u003e). This approach allows us to highlight the convergence clubs and estimate the transition probability and long-run distribution. As mentioned above, some studies have examined the convergence of ecological footprints across countries. However, they mostly adopted β-convergence (Bilgili \u0026amp; Ulucak, \u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e2018\u003c/span\u003e) and panel club convergence approaches (also known as the Phillips and Sul approach) (Tillaguango et al., \u003cspan citationid=\"CR63\" class=\"CitationRef\"\u003e2021\u003c/span\u003e; Erdogan \u0026amp; Okumus, \u003cspan citationid=\"CR28\" class=\"CitationRef\"\u003e2021\u003c/span\u003e; Belloc \u0026amp; Molina, \u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e2022\u003c/span\u003e). The classical β-convergence will yield time- and country-invariant coefficient β because it assumes the technological process is homogeneous (Phillips \u0026amp; Sul, \u003cspan citationid=\"CR53\" class=\"CitationRef\"\u003e2007\u003c/span\u003e). Alternatively, the panel club convergence approach cannot identify all structural parameters and isolate the convergence indicator\u0026rsquo;s major determinants (Pfaffermayr, \u003cspan citationid=\"CR52\" class=\"CitationRef\"\u003e2012\u003c/span\u003e). Given the weaknesses of these two approaches, the continuous state space approach is superior as it allows us to identify the evolution of environmental indices, including catch-up, stratification, and polarization, and the conditional convergence under this method allows us to examine the potential factors that underlie differences in group convergence tendency.\u003c/p\u003e \u003cp\u003eThe rest of the paper is organized as follows. Section \u003cspan refid=\"Sec2\" class=\"InternalRef\"\u003e2\u003c/span\u003e introduces the state space approach, and Section 3 describes the data. Section \u003cspan refid=\"Sec4\" class=\"InternalRef\"\u003e4\u003c/span\u003e presents the static analysis results. Section \u003cspan refid=\"Sec5\" class=\"InternalRef\"\u003e5\u003c/span\u003e reports the dynamic analysis results, and Section 6 concludes.\u003c/p\u003e"},{"header":"2. Research Methodology","content":"\u003cp\u003eDiscrete and continuous state space approaches are widely used in distribution dynamics analysis. Although the discrete state space approach is simple in calculation, it suffers from arbitrariness. Morevoer, the discrete state space approach sometimes fails to accurately reflect the probabilistic properties of variables (Quah, \u003cspan citationid=\"CR55\" class=\"CitationRef\"\u003e1997\u003c/span\u003e; Bulli, \u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e2001\u003c/span\u003e; and Johnson, \u003cspan citationid=\"CR37\" class=\"CitationRef\"\u003e2005\u003c/span\u003e). In comparison, the continuous state space approach can avoid arbitrariness in the discretization process by adopting a nonparametric stochastic kernel approach, allowing for the estimation of distribution with infinite state spaces. Thus, it is regarded as a better alternative to the discrete state space approach.\u003c/p\u003e \u003cp\u003eThis study employs the continuous state space approach to identify the ecological footprint dynamic changes of 366 Chinese PAA cities between 2001 and 2020. the continuous state space approach was pioneered by Danny Quan in a series of studies on the evolutionary income distribution process among countries (Quan,1996; 1997). After that, this method has been applied to economic growth convergence analysis (Galor \u0026amp; Tsiddon, \u003cspan citationid=\"CR29\" class=\"CitationRef\"\u003e1997\u003c/span\u003e; Bulli, \u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e2001\u003c/span\u003e; Maassoumi et al., 2007) and environmental studies (Nguyen, 2005; Burnett, \u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e2016\u003c/span\u003e; Wu et al., \u003cspan citationid=\"CR73\" class=\"CitationRef\"\u003e2022\u003c/span\u003e). It offers two critical advantages ove\u003cspan type=\"Underline\" class=\"Underline\" name=\"Emphasis\"\u003er\u003c/span\u003e conventional convergence approaches (such as σ-convergence, β-convergence, and stochastic convergence). First, it employs a stochastic kernel approach to estimate the transition probability matrix, which enables the examination of long-term trends in convergence and the existence of ecological poverty in Chinese cities. Second, this data-driven method eliminates the model specification errors inherent in traditional parametric approaches since it does not require prior assumptions.\u003c/p\u003e \u003cp\u003eThe continuous state space approach begins by accessing the transition probability distribution. Suppose that the distribution of Chinese NDVI in PAA-level cities at time \u003cem\u003et\u003c/em\u003e can be expressed by the density function \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\phi\\:}_{t}\\left(x\\right)\\)\u003c/span\u003e\u003c/span\u003e. Because the evolution of the distribution is time-invariant and first-order, we can describe the \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\tau\\:\\)\u003c/span\u003e\u003c/span\u003e-period-ahead distribution \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\phi\\:}_{t+\\tau\\:}\\left(y\\right)\\)\u003c/span\u003e\u003c/span\u003e using the base distribution \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\phi\\:}_{t}\\left(x\\right)\\)\u003c/span\u003e\u003c/span\u003e\u003cdiv id=\"Equ1\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ1\" name=\"EquationSource\"\u003e\n$$\\:{\\phi\\:}_{t+\\tau\\:}\\left(y\\right)={\\int\\:}_{0}^{\\infty\\:}{{g}_{\\tau\\:}\\left(y\\right|x)\\phi\\:}_{t}\\left(x\\right)dx$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e1\u003c/div\u003e\u003c/div\u003e,\u003c/p\u003e \u003cp\u003ewhere \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{g}_{\\tau\\:}\\left(y\\right|x)\\)\u003c/span\u003e\u003c/span\u003e is the conditional probability density that records the transition process of vegetation coverage from time \u003cem\u003et\u003c/em\u003e to \u003cem\u003et+\u003c/em\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\tau\\:\\)\u003c/span\u003e\u003c/span\u003e. Here \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\tau\\:\\)\u003c/span\u003e\u003c/span\u003e is strictly positive, and for any \u003cem\u003ex\u003c/em\u003e, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\int\\:}_{0}^{\\infty\\:}{g}_{\\tau\\:}\\left(y\\right|x)dy=1\\)\u003c/span\u003e\u003c/span\u003e.\u003c/p\u003e \u003cp\u003eKeeping the transition probability \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{g}_{\\tau\\:}\\left(y\\right|x)\\)\u003c/span\u003e\u003c/span\u003e steady, the NDVI distribution will evolve into a long-run equilibrium state \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\phi\\:}_{\\infty\\:}\\left(y\\right)\\)\u003c/span\u003e\u003c/span\u003e called ergodic distribution. In this case, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\phi\\:}_{\\infty\\:}\\left(y\\right)\\)\u003c/span\u003e\u003c/span\u003e can be expressed as\u003cdiv id=\"Equ2\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ2\" name=\"EquationSource\"\u003e\n$$\\:{\\phi\\:}_{\\infty\\:}\\left(y\\right)={\\int\\:}_{0}^{\\infty\\:}{{g}_{\\tau\\:}\\left(y\\right|x)\\phi\\:}_{\\infty\\:}\\left(x\\right)dx$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e2\u003c/div\u003e\u003c/div\u003e.\u003c/p\u003e \u003cp\u003eThe continuous state space approach uses a stochastic kernel density method to estimate the transition probability and its ergodic distribution. According to the method\u0026rsquo;s principle, we can define the joint kernel function \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\phi\\:}_{t,t+\\tau\\:}\\left(y,x\\right)\\)\u003c/span\u003e\u003c/span\u003e and the marginal kernel function \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\phi\\:}_{t}\\left(x\\right)\\)\u003c/span\u003e\u003c/span\u003e as\u003cdiv id=\"Equ3\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ3\" name=\"EquationSource\"\u003e\n$$\\:{\\phi\\:}_{t,t+\\tau\\:}\\left(y,x\\right)=\\frac{1}{n{h}_{x}{h}_{y}}\\sum\\:_{i=1}^{n}K\\left(\\frac{x-{x}_{i}}{{h}_{x}},\\frac{y-{y}_{i}}{{h}_{y}}\\right)\\:;{\\phi\\:}_{t}\\left(x\\right)=\\frac{1}{n{h}_{x}}\\sum\\:_{i=1}^{n}K\\left(\\frac{x-{x}_{i}}{{h}_{x}}\\right),$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e3\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003ewhere \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{x}_{i}\\)\u003c/span\u003e\u003c/span\u003e and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{y}_{i}\\)\u003c/span\u003e\u003c/span\u003e stand for the ecological cover level of city \u003cem\u003ei\u003c/em\u003e at time \u003cem\u003et\u003c/em\u003e and time \u003cem\u003et\u003c/em\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:+\\tau\\:\\)\u003c/span\u003e\u003c/span\u003e; \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{h}_{x}\\)\u003c/span\u003e\u003c/span\u003eand \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{h}_{y}\\)\u003c/span\u003e\u003c/span\u003edenote the bandwidth of \u003cem\u003ex\u003c/em\u003e and \u003cem\u003ey\u003c/em\u003e, respectively, and can be computed through \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:h=1.06\\sigma\\:{n}^{-1/5}\\)\u003c/span\u003e\u003c/span\u003e (Silvierman 1986; Sheather, 2004); and \u003cem\u003en\u003c/em\u003e is the number of cities. \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:K(\\bullet\\:)\\)\u003c/span\u003e\u003c/span\u003e represents the relevant kernel density function. Combined with the above definitions of \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\phi\\:}_{t,t+\\tau\\:}\\left(y,x\\right)\\)\u003c/span\u003e\u003c/span\u003eand \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\phi\\:}_{t}\\left(x\\right)\\)\u003c/span\u003e\u003c/span\u003e, we can further estimate the conditional probability density as\u003cdiv id=\"Equ4\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ4\" name=\"EquationSource\"\u003e\n$$\\:{g}_{\\tau\\:}\\left(y|x\\right)=\\frac{{\\phi\\:}_{t,t+\\tau\\:}\\left(y,\\:\\:x\\right)}{{\\phi\\:}_{t}\\left(x\\right)}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e4\u003c/div\u003e\u003c/div\u003e.\u003c/p\u003e \u003cp\u003eUnlike the discrete state space approach, which uses a transition probability matrix to depict the results, the continuous state space approach uses a three-dimensional plot or contour map to visually display the transition probability distribution. To gain deeper insight into the convergence trend of vegetation in Chinese cities, we calculate each city\u0026rsquo;s net transition probability value (NTP) to construct a comprehensive curve that illustrates the overall movement trend. In particular, the NTP can be calculated by the upward transition probability minus the downward transition probability at each point; i.e., the NTP index can be defined as \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:p\\left(x\\right)\\)\u003c/span\u003e\u003c/span\u003e in the following equation\u003cdiv id=\"Equ5\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ5\" name=\"EquationSource\"\u003e\n$$\\:p\\left(x\\right)={\\int\\:}_{x}^{\\infty\\:}{g}_{\\tau\\:}\\left(z\\right|x)dz-{\\int\\:}_{0}^{x}{g}_{\\tau\\:}\\left(z\\right|x)dz$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e5\u003c/div\u003e\u003c/div\u003e.\u003c/p\u003e \u003cp\u003eThe NTP serves as a valuable indicator of changing trends at different points. A positive NTP indicates a city\u0026rsquo;s improvement in the ecological environment. Beyond that, a downward-sloping NTP curve implies a long-term convergence tendency, while an upward slope indicates divergence.\u003c/p\u003e"},{"header":"3. Data Description","content":"\u003cp\u003eThe data used in this paper cover 366 prefectures in China, which include cities, autonomous prefectures, and municipalities). The data contain NDVI values spanning 2001\u0026ndash;2020. NDVI is a vegetation index obtained from canopies by applying remote-sensing techniques, and it is the ratio of reflectance from red and near-infrared (NIR) wavebands. NDVI data are from NASA\u0026rsquo;s EOS/MODIS (TERRA satellite) remote-sensing data product (MOD13A3). After distractions from factors such as cloud cover and atmospheric changes have been eliminated, the maximum value composite (MVC) method is employed to process monthly data and derive annual values. The MVC method selects the pixel with the highest NDVI value for each month and can effectively mitigate any outliers and temporary disturbances in the remote-sensing data. In this way, we obtain a robust and consistent annual NDVI data set for analysis.\u003c/p\u003e \u003cp\u003eThis study also investigates the long-run distribution of different city groups based on geographic location, income level, and participation, which are believed to influence vegetation. In particular, income levels are measured by the GDP per capita, which istaken from China City Statistical Yearbooks (CCSYs); missing values are derived from provincial statistical yearbooks using the same standard of calculation of CCSYs. As subsequent analyses also divides cities into subgroups based on each city\u0026rsquo;s average annual precipitation and rainfall, we also obtain data from the China Meteorological Data Service Center.\u003c/p\u003e"},{"header":"4. Static Analysis","content":"\u003cp\u003eIdentifying vegetation changes in Chinese cities over the sample period can provide direct intuition before examing the distribution dynamics of China\u0026rsquo;s ecological footprint. Figure\u0026nbsp;1 maps the initial and final spatial distributions of NDVI during the study period, which illustrates a significant increase and deepening in vegetation coverage in central and northwest China. The growth in absolute NDVI values reflects China\u0026rsquo;s ecological improvement after 20 years of effort.\u003c/p\u003e\n\u003cp\u003eFigure \u003cspan class=\"InternalRef\"\u003e2\u003c/span\u003e presents the kernel density distributions of the NDVI for PAA cities in three representative years. The sample is equally divided into two periods based the representative years: 2001, 2010, and 2020. Figure \u003cspan class=\"InternalRef\"\u003e2\u003c/span\u003e(a) depicts the kernel density distribution of absolute NDVI for 366 cities. Overall, the density curves are left-skewed and exhibit asymmetric multimodality. Although most cities converge to the main peak between NDVI values of 7,000 and 8,000, a few cities are spread over the low-NDVI interval and form multiple lower peaks between NDVI values of 1,000 and 3,000. It is worth noting that the NDVI value of the main peak shifted toward the high-NDVI end during the study period, which echoes the evidence from Fig.\u0026nbsp;1 that the ecological environment improved during the sample period.\u003c/p\u003e\n\u003cp\u003eIn this study, the relative position changes of NDVI in each city are our focus rather than the absolute values. Therefore, following a common practice with the continuous state space approach, each city\u0026rsquo;s NDVI values were divided by its yearly average to obtain the normalized NDVI (RNDVI) for the following analysis. Figure \u003cspan class=\"InternalRef\"\u003e2\u003c/span\u003e(b) displays the kernel density distribution of the RNDVI. By comparison, the distribution shapes are mostly similar, with a slight difference in the heights of the peaks. But the relative positions between the three curves of the RNDVI are much closer than those of the NDVI. It suggests strong persistence in the relative position change. In addition, the existence of multiple peaks at the low-RNDVI end suggests that some cities have poor and persistent ecological conditions. However, this conclusion is based on static analysis of specific years, whereas dynamic analysis can provide us with a detailed evolution of the ecological footprints of China\u0026rsquo;s PAA cities over time.\u003c/p\u003e"},{"header":"5. Dynamic Analysis","content":"\u003cdiv id=\"Sec6\" class=\"Section2\"\u003e\n \u003ch2\u003e5.1 Distribution Dynamics of the NDVI\u003c/h2\u003e\n \u003cp\u003eFigure \u003cspan class=\"InternalRef\"\u003e3\u003c/span\u003e displays the distribution dynamics of the RNDVI of the 366 PAA cities. Figure \u003cspan class=\"InternalRef\"\u003e3\u003c/span\u003e(a) is a three-dimensional plot of the transition probability of the RNDVI. To provide direct intuition, for a given RNDVI at time \u003cem\u003et\u003c/em\u003e, we obtain a longitudinal slice along the vertical axis and parallel to the RNDVI \u003cem\u003et\u0026thinsp;+\u0026thinsp;1\u003c/em\u003e axis, and the slice yields the distribution probability that this city at time \u003cem\u003et\u003c/em\u003e will transit into a different value at period \u003cem\u003et\u0026thinsp;+\u0026thinsp;1\u003c/em\u003e. If the transition probability mass distributed along the 45-degree diagonal, this suggests a strong tendency of persistence in relative position changes. In particular, distribution parallel to the t-axis indicates the tendency of convergence. To visually observe the probability distribution along the main diagonal, this study employs a contour map to provide an aerial view of the three-dimensional diagram. As shown in Fig. \u003cspan class=\"InternalRef\"\u003e3\u003c/span\u003e(b), the whole sample displays strong persistence in intra-distribution mobility.\u003c/p\u003e\n \u003cp\u003eThe net transition probability (NTP) curve in Fig. \u003cspan class=\"InternalRef\"\u003e3\u003c/span\u003e(c) displays the net evolution trend of cities in terms of the RNDVI and helps identify the convergence tendency. Suppose the NTP curve intersects with the null axis, and the net transition probability is positive on the left side of the intersection point and negative on the right. In that case, the downward-sloping NTP curve indicates that the RNVDI on both sides of the intersection will converge to this point. According to the NTP curve of the whole sample, there is a net convergence tendency in the vegetation coverage of PAA cities during the study period.\u003c/p\u003e\n \u003cp\u003eFigure \u003cspan class=\"InternalRef\"\u003e3\u003c/span\u003e(d) presents the long-run stationary (ergodic) distribution while keeping the transition probability of the RNDVI constant. Significant left-skewed unimodality can be observed in the ergodic distribution of the sample cities. If current trends continue, most Chinese cities will converge to an RNDVI value that is 1.15 times the average, suggesting that China\u0026rsquo;s efforts toward ecological improvement have had an effect. China\u0026rsquo;s ecological protection has changed from key regions\u0026rsquo; governance to partitioned and sorted management in the 21st century. The primary strategy is to improve the ecology by distinguishing important ecological functional areas, key resource development zones, and good ecological areas. In 2007, the Chinese government clarified that the ecological function zone was categorized as restricted development zones. Since then, 25 ecological function zones have been identified nationwide, and the ecological conservation redline in ecological function zones has become apparent. After 2012, China embarked the so-called Shan-Shui Initiative, which included a series of projects to conserve and restore natural resources, encompassing mountains, rivers, forests, farmlands, lakes, and grasslands. The initiative was one of the top ten flagship projects for global restoration by United Nations. It demonstrated China\u0026rsquo;s transition towards emphasizing overall protection, systematic restoration, and comprehensive management in ecological protection. In addition to these efforts, the Chinese government implemented three 5-year plans for ecological protection during the study period, accelerating regional ecosystem protection and helping to extend China\u0026rsquo;s ecological coverage.\u003c/p\u003e\n \u003cp\u003eTo empirically test the robustness of the above results, we examined the distribution dynamics of RNDVI values with an interval of every two years. As shown in Figure \u003cspan class=\"InternalRef\"\u003eA1\u003c/span\u003e, our main empirical results remain robust.\u003c/p\u003e\n \u003cp\u003e\u003cbr\u003e\u003c/p\u003e\n\u003c/div\u003e\n\u003cdiv id=\"Sec7\" class=\"Section2\"\u003e\n \u003ch2\u003e5.2 Conditional Distribution Dynamics\u003c/h2\u003e\n \u003cdiv id=\"Sec8\" class=\"Section3\"\u003e\n \u003ch2\u003e5.2.1 NDVI Groups\u003c/h2\u003e\n \u003cp\u003eAn important issue in convergence analysis is whether poor ecological cities can catch up with good ecological cities. We divide the 366 PAA cities into three groups for heterogeneity analysis based on RNDVI values in the initial year, 2001. The distribution dynamics of the three groups are shown in Fig. \u003cspan class=\"InternalRef\"\u003e4\u003c/span\u003e. Unlike the other two groups, the transition probability mass of the low-NDVI group is distributed along the 45-degree diagonal, which suggests strong persistence and immobility in vegetation coverage (Fig. \u003cspan class=\"InternalRef\"\u003e4\u003c/span\u003e(a)). In contrast, the horizontal transition probability distribution of the medium- and high-NDVI groups implies that there is convergence in vegetation coverage among these cities (see Figs. \u003cspan class=\"InternalRef\"\u003e4\u003c/span\u003e(d) and 4(g)). Since the NTP curves of the three groups are all downward-sloping, they imply a strong tendency toward convergence on vegetation coverage within the cit\u003cspan type=\"Underline\" class=\"Underline\" name=\"Emphasis\"\u003ey\u003c/span\u003e groups.\u003c/p\u003e\n \u003cp\u003eLeft-skewed shapes are observed in the long-run stationary distributions of the three NDVI groups. Cities in the low-NDVI group are concentrated on a relatively low point (below average), which suggests less dense vegetation coverage and the existence of ecological poverty (see Fig. \u003cspan class=\"InternalRef\"\u003e4\u003c/span\u003e(c)). Therefore, we observe no significant catch-up effects in poor ecological cities. Unlike the low-NDVI group, the ergodic distribution of medium- and high-NDVI city groups is slightly bimodal (Figs. \u003cspan class=\"InternalRef\"\u003e4\u003c/span\u003e(f) and 4(i)). In addition, most cities are clustered to approximately 1.2 times the average NDVI values in these two groups. This implies that these cities became greener through decades of effort. However, the lower peaks of the two groups suggest that ecological poverty also exists in the medium- and high-NDVI city groups. By and large, the remarkable convergence in the three NDVI groups proves the effectiveness of China\u0026rsquo;s ecological policies. However, low-NDVI cities exhibit significant stickiness in intra-distribution dynamics and have less opportunity to move into the high-NDVI end. This may induce a chronic ecological-poverty trap.\u003c/p\u003e\n \u003c/div\u003e\n \u003cdiv id=\"Sec9\" class=\"Section3\"\u003e\n \u003ch2\u003e5.2.2 Regional Groups\u003c/h2\u003e\n \u003cp\u003eDifferent regions in China vary in geographic resources, such as climate, soil, and topography. These factors have important impacts on regional ecological coverage (Kogan, \u003cspan class=\"CitationRef\"\u003e1990\u003c/span\u003e; Cui, \u003cspan class=\"CitationRef\"\u003e2013\u003c/span\u003e). In order to examine the geographic distribution dynamics of China\u0026rsquo;s vegetation change, we zoned Chinese cities as eastern, central, and western city groups, and presented the results in Fig. \u003cspan class=\"InternalRef\"\u003e5\u003c/span\u003e.\u003c/p\u003e\n \u003cp\u003eAccording to the contour map of the eastern city group (Fig. \u003cspan class=\"InternalRef\"\u003e5\u003c/span\u003e(a)), the above-diagonal transition probability distribution at the lower RNDVI interval suggests significant improvement in vegetation coverage in low-NDVI eastern cities, which can be observed in Fig. 1. The declining NTP curve in Fig. \u003cspan class=\"InternalRef\"\u003e5\u003c/span\u003e(b) indicates a broad convergence tendency in the eastern city group during the research period. However, the triple intersection points with the horizontal axis suggest the existence of multimodality in the ergodic distribution. The twin peaks in Fig. \u003cspan class=\"InternalRef\"\u003e5\u003c/span\u003e(c) provide evidence of bimodality club convergence in the long-run distribution. This indicates the existence of polarization in terms of NVDI in eastern cities. Since more than half of the eastern cities are concentrated in the peak with an RNDVI value of 0.6, those cities will have low vegetation coverage even in the long run. By contrast, the contour maps in Fig. \u003cspan class=\"InternalRef\"\u003e5\u003c/span\u003e(d) and 5(g) show strong persistence. However, the NTP plots in Figs. \u003cspan class=\"InternalRef\"\u003e5\u003c/span\u003e(e) and 5(h) show clear net convergence trends. The left-skewed unimodality in the ergodic distributions of Figs. \u003cspan class=\"InternalRef\"\u003e5\u003c/span\u003e(f) and 5(i) show that central and western cities have made progress in vegetation coverage, which also echoes the findings in Fig.\u0026nbsp;1. However, strong persistence in the transition probability suggests that this process may require a very long time. As shown in Fig.\u0026nbsp;1, the vegetation coverage in many central and western cities is still poor. More efforts should be dedicated towards enhancing the ecological environments in these regions.\u003c/p\u003e\n \u003c/div\u003e\n \u003cdiv id=\"Sec10\" class=\"Section3\"\u003e\n \u003ch2\u003e5.2.3 Rainfall Groups\u003c/h2\u003e\n \u003cp\u003ePrecipitation directly affects soil-water balance, and a soil-moisture regime influences plant growth and crop production. Studies have shown that temporal variation in the NDVI is closely associated with precipitation and demonstrates a strong linear (Nicholson et al., \u003cspan class=\"CitationRef\"\u003e1990\u003c/span\u003e) or log-line (Davenport \u0026amp; Nicholson,1993). To examine the role of rainfall in transition probability, we divided these cities into low-, medium-, and high-rainfall groups according to the average rainfall during our sample period.\u003c/p\u003e\n \u003cp\u003eLow-rainfall cities display the most vigorous persistence in transition probability among the three groups, as demonstrated by comparing the three contour maps in Fig. \u003cspan class=\"InternalRef\"\u003e6\u003c/span\u003e. Meanwhile, the deviation from the diagonal with an RNDVI value below 0.8 in Figs. \u003cspan class=\"InternalRef\"\u003e6\u003c/span\u003e(d) and 6(g) implies the upward tendency of convergence in medium- and high-rainfall cities. The downward-sloping NTP plots in Figs. \u003cspan class=\"InternalRef\"\u003e6\u003c/span\u003e(b) and 6(e) reveal the existence of clear net convergence in these two groups. In contrast, high-rainfall cities show no evidence of net convergence (Fig. \u003cspan class=\"InternalRef\"\u003e6\u003c/span\u003e(h)). As expected, unimodality can be seen in the ergodic distributions of low- and medium-rainfall cities, but bimodality in high-rainfall cities. The polarization of vegetation coverage in high-rainfall cities suggests that those low-NDVI cities had poor performance in sustainable development, even with better natural endowments.\u003c/p\u003e\n \u003c/div\u003e\n \u003cdiv id=\"Sec11\" class=\"Section3\"\u003e\n \u003ch2\u003e5.2.4 Income Groups\u003c/h2\u003e\n \u003cp\u003eIncome is another important factor associated with the ecological footprint (Duro \u0026amp; Teixid\u0026oacute;-Figueras, \u003cspan class=\"CitationRef\"\u003e2013\u003c/span\u003e; Alix-Garcia et al., \u003cspan class=\"CitationRef\"\u003e2013\u003c/span\u003e). First, high income is associated with high human activities, which may lead to environmental degradation (Alix-Garcia et al., \u003cspan class=\"CitationRef\"\u003e2013\u003c/span\u003e). Second, high-income residents typically have higher requirements for an ecological environment and higher willingness to pay for it (Alix-Garcia et al., \u003cspan class=\"CitationRef\"\u003e2018\u003c/span\u003e). To analyze this aspect, we divided sample cities into three groups based on regional income (per capita GDP) in 2020.\u003c/p\u003e\n \u003cp\u003eFigure \u003cspan class=\"InternalRef\"\u003e7\u003c/span\u003e presents the distribution dynamics of the three income groups. As evident from the contour maps, all three groups exhibit persistence in their transitions. Despite volatility in the net transition probabilities, curves in the middle column, on the whole, show that the vegetation coverage of these groups all converge to intersection points with RNDVI values greater than 1. Left-skewed unimodality is also visible in the long-run stationary distributions of the three groups. The only difference is that low-income and medium-income cities performed better in ecological improvement over the two decades. In China, most high-income cities are either resourced-based (such as Karamay, Ordos, and Haixi) or heavily urbanized (such as Wuxi, Shenzhen, Suizhou, Shanghai, and Zhuhai). Human activities such as resource exploitation and urban construction occupy formerly green spaces and degrade the ecology. Assuming the environmental Kuznets curve exists, Chinese cities are still located on the left side when the environment quality is measured by ecological footprint. Our results alig\u003cspan type=\"Underline\" class=\"Underline\" name=\"Emphasis\"\u003en\u003c/span\u003e with the findings of prior studies (Alix-Garcia et al., \u003cspan class=\"CitationRef\"\u003e2013\u003c/span\u003e; Chen et al., \u003cspan class=\"CitationRef\"\u003e2022\u003c/span\u003e; Ansari, \u003cspan class=\"CitationRef\"\u003e2022\u003c/span\u003e). For instance, Alix-Garcia et al. (\u003cspan class=\"CitationRef\"\u003e2013\u003c/span\u003e) found that income improvement in Mexico led to higher consumption of land-intensive goods, ultimately increasing deforestation. Chen et al. (\u003cspan class=\"CitationRef\"\u003e2022\u003c/span\u003e) demonstrated that the vegetation changes that arise from urbanization have both direct impacts, such as the loss of green land, and indirect impacts from changes in the macro-environment associated with urbanization.\u003c/p\u003e\n \u003c/div\u003e\n\u003c/div\u003e"},{"header":"6. Conclusions","content":"\u003cp\u003eThe Chinese government initially proposed the concept of ecological poverty alleviation to combines poverty alleviation and development into ecological protection. Programs were enacted in ecological function zones such as the Yellow River Basin, Yangtze River Basin, and Qinghai-Tibet Plateau. This is because most ecological function areas are characterized as national-level poverty-stricken regions. Moreover, more fiscal transfer is paid for forestry and grasslands in poor areas to implement several ecological protection and restoration projects like the controlling wind and sand sources in Beijing and Tianjin, the three north shelterbelt programs, and the ecological protection and construction of the three rivers\u0026rsquo; sources regions. These projects have greatly improved regional vegetation coverage and preserved China\u0026rsquo;s ecological diversity. However, as one of the largest countries in the world, China\u0026rsquo;s vegetation coverage differs greatly across regions. Though examining the distribution dynamics of vegetation coverage across 366 Chinese PAA-level cities using the continuous state space approach, this study provides important implications for improving vegetation coverage in Chinese cities.\u003c/p\u003e \u003cp\u003eOur analysis shows a clear convergence tendency in vegetation coverage China\u0026rsquo;s across 366 cities. Through decades of efforts, most Chinese cities have significantly increased vegetation land and greenness. However, Chinese cities with different initial vegetation coverage exhibit salient heterogeneity in the long-run distribution dynamics of the NDVI. Low-vegetation-coverage cities have fewer opportunities to become high-vegetation-coverage cities, which may form a chronic ecological poverty trap. In addition, polarization in vegetation coverage is present in eastern Chinese cities and high-rainfall cities. Polarization and persistence provide further evidence of the existence of ecological poverty. Furthermore, high-income cities have poorer vegetation coverage performance than low- and medium-income cities. A plausible explanation could be that human production activities associated with urbanization and resource exploitation have led to the destruction of vegetation and occupation of green space, thus deteriorating the urban ecological environment.\u003c/p\u003e \u003cp\u003eOur results suggest that policies and laws pertaining to agriculture, forestry, and environmental protection in recent years have been successful with respect to ecological restoration and green area expansion for most Chinese cities. What should not be ignored, however, is the existence of ecological poverty in China. The ecological poverty alleviation program should thus play a more significant role in ecological improvement, especially in Eastern cities. For cities that are endowed with high rainfall but are trapped in ecological-poverty, reducing over-exploitation may be the best way to maintain sustainable development.\u003c/p\u003e \u003cp\u003eMeanwhile, we have to admit the existence of limitations in this study. As the convergence analysis is descriptive, the causal effect requires inferential statistics, which is beyond the scope of this paper. Even though the conditional convergence analysis reveals that economic development affects vegetation, the in-depth analysis of the underlying mechanisms deserves further exploration. Additionally, the existence of ecological poverty underscores the need for future studies to uncover more effective ways to relieve such poverty.\u003c/p\u003e"},{"header":"Declarations","content":"\u003cp\u003e\u003cem\u003eDeclaration of Interest\u003c/em\u003e: This work was supported by the Fundamental Research Funds for the Central Universities (No.23JNLH09), Philosophy and Social Science Planning Projects in Hainan Province (No. HNSK(ZC)23-155), Hainan College of Economics and Business (No. hnjmk2021301).\u003c/p\u003e\n\u003cp\u003eThe funding bodies had no involvement in study design, the collection, analysis and interpretation of the data, the writing of the report and the decision to submit the article for publication.\u003c/p\u003e\u003ch2\u003eAuthor Contribution\u003c/h2\u003e\u003cp\u003eAll authors involved in study design, the collection, analysis and interpretation of the data, the writing of the manuscript and the decision to submit the article for publication.\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\u003cli\u003e\u003cspan\u003eAhmed Z, Zafar MW, Ali S (2020) Linking urbanization, human capital, and the ecological footprint in G7 countries: An empirical analysis. 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Land Use Policy 48:223\u0026ndash;235\u003c/span\u003e\u003c/li\u003e\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":true,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"environmental-and-ecological-statistics","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"eest","sideBox":"Learn more about [Environmental and Ecological Statistics](http://link.springer.com/journal/10651)","snPcode":"10651","submissionUrl":"https://submission.nature.com/new-submission/10651/3","title":"Environmental and Ecological Statistics","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"em","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false},"keywords":"vegetation coverage, distribution dynamics, ecological poverty, continuous state space approach","lastPublishedDoi":"10.21203/rs.3.rs-5794674/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-5794674/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eThis paper is the first to examine the distribution dynamics of vegetation coverage using a dataset of 366 China’s prefecture and above (PAA) cities from 2001 to 2020. The results from the continuous state space approach demonstrate a clear pattern of convergence in China’s vegetation coverage in the long run, proving the effectiveness of government policies in the last two decades. However, catch-up effects in low-vegetation-coverage cities are weak, and an ecological poverty trap exists in Chinese cities. We also find polarization effects in eastern and high-rainfall cities. Some eastern cities with better climate endowments show poor performance in vegetation coverage in the long run, suggesting that ecological damage is caused by overdevelopment rather than natural endowment. Our findings offer robust scientific support for China to take more proactive and aggressive measures to maintain sustainable development.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eJEL: \u003c/strong\u003e\u0026nbsp;Q20, Q50, N55\u003c/p\u003e","manuscriptTitle":"Does ecological poverty trap exist in Chinese cities? 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