Academic Journal of Science and Technology 
ISSN: 2771-3032 | Vol. 11, No. 2, 2024 

 

196 

Spatial	Analysis	and	Prediction	of	Ecological	Welfare	
Performance:	Evidence	from	284	Prefecture‐level	Cities	
in	China	
Linxinyu Wang 

Anhui University of Finance and Economics, Bengbu, 233030, China 

 

Abstract: The general debate of the 78th session of the United Nations reaffirmed the importance of the Sustainable Urban 
and Community Development Goal (SDG 11), however, the pervasive accounting gaps still lead to significant challenges in the 
monitoring and evaluation of SDG 11 indicators. This paper focuses on ecological welfare performance accounting, aiming to 
assess the weaknesses and internal gaps of regional SDG 11 at the aggregate level, so as to promote eco-city planning and 
management, improve the well-being potential of urban residents, and reduce the adverse impact on the ecological environment. 
Taking China as a developing country as a case, the two-stage DEA model is used to measure the ecological welfare performance 
of 284 cities in China from 2007 to 2022, and the spatiotemporal pattern of efficiency at each stage of the ecological welfare 
transformation process is described, a modified gravitational model is constructed to transform the "attribute data" of ecological 
welfare performance into "relationship data", and the characteristics of network structure are described with the help of social 
network analysis, and the formation mechanism of the spatial correlation network of ecological welfare performance is revealed 
and its dynamic evolution characteristics are revealed through the spatial Markov chain. 

Keywords: Ecological Welfare Performance; Two-stage DEA Model; Social Network Analysis; Space Markov Chain. 
 

1. Background 
Following the Millennium Development Goals, the United 

Nations adopted the 2030 Agenda for Sustainable 
Development in September 2015, which covers 17 
interrelated Sustainable Development Goals (SDGs) and 169 
related targets in three dimensions of economy, society and 
environment, and plans to implement these goals by 2030 by 
UN members[1]. SDG 11 aims to achieve inclusive, resilient 
and sustainable urban development policies and practices that 
prioritize basic services for all, affordable housing, efficient 
transport and green spaces. 

At the same time, the current global environmental 
problems, such as climate change, resource depletion, 
biodiversity reduction, and environmental pollution, pose 
severe challenges to the sustainable development of cities [3]. 
Extreme weather events brought on by climate change 
threaten the resilience of urban infrastructure [4] and can 
cause severe economic losses and social unrest. The over-
exploitation and consumption of resources not only leads to 
the deterioration of the ecological environment, but also 
increases the economic cost of urban operation and affects the 
long-term economic competitiveness of cities [5]. The loss of 
biodiversity weakens the services provided by ecosystems, 
such as air and water purification, climate regulation and soil 
conservation, and reduces the quality of life of residents [6]. 
At the same time, environmental pollution, including air 
pollution, water pollution, and soil pollution, degrades the 
quality of the urban environment, and threatens the health of 
urban residents [7]. Moreover, more than half of the world's 
population lives in urban areas, and this proportion is 
expected to reach 68% by 2050 [8]. In 2015, about 1.2 billion 
people lived in urban slums or slum-like conditions, which is 
expected to increase to 2.5 billion in the next 15 years [9]. 
However, as of 2022, only half of city dwellers have easy 
access to public transport, and problems such as urban sprawl, 

air pollution, and limited public space remain. [10], Cities are 
considered to be the main platforms for the Sustainable 
Development Goals (SDGs) such as poverty eradication, 
healthy living, and quality education [11-13], so "Building 
inclusive, safe, resilient and sustainable cities and human 
settlements" (SDG 11) not only focuses on the sustainability 
of cities per se, but also has an important impact on the 
achievement of all SDGs and is at the heart of achieving the 
SDGs [14], The general debate of the 78th session of the 
United Nations reaffirmed the importance of the Sustainable 
Urban and Community Development Goal (SDG 11). 

At present, most scholars use Ecological Well-being 
Performance (EWP), an important indicator to measure the 
sustainable development capacity of a country or region [27]. 
In the context of global environmental governance and 
sustainable development, China has actively explored the 
path of urban green transformation under the Sustainable 
Development Goals, with significant improvements in urban 
air quality [28], steady increase in carbon emission 
performance [29], and an increase in biodiversity [30], while 
China's smart cities have actively explored renewable energy 
and resources [31], contributing Chinese wisdom and 
solutions to the global urban ecological welfare performance 
and sustainable urban development. 

2. Data Sources, Indicator System and 
Model Construction 

2.1. Data Sources and Processing 
In this paper, 284 cities in China are taken as the research 

unit, and the study period is from 2007 to 2022. The 
evaluation index data are from the China Statistical Yearbook, 
China Energy Statistical Yearbook, China Education 
Statistical Yearbook, China Environment Statistical 
Yearbook and urban statistical yearbooks from 2001 to 2022. 
The data of influencing factor variables are from China 



 

197 

Statistical Yearbook, China Science and Technology 
Statistical Yearbook, China Environment Statistical 
Yearbook and statistical bulletins of various urban areas. The 
original data of the EWP input-output indicators are derived 
from the China Urban Statistical Yearbook and the China 
Urban Construction Statistical Yearbook. 

2.2. Ecological Welfare Performance 
Evaluation Index System 

In this paper, a two-stage DEA method is used to measure 
the ecological welfare performance of 284 cities in China, and 
the premise is to clarify the input and output indicators of each 
stage. In this paper, a two-stage DEA method is used to 
measure the ecological welfare performance of 284 cities in 
China, and the premise is to clarify the input and output 
indicators of each stage. Drawing on the research of [51-52], 
this paper shows that the input indicators are expressed in 
terms of energy consumption and pollution emissions. In this 
paper, a multi-dimensional HDI based on economic welfare, 
social welfare, and environmental welfare is constructed as 
output indicators, including consumption level, education, 
medical and health care, and environmental benefits. The 
comprehensive level of ecological welfare performance is 
evaluated through the first stage input and the second stage 
output. The evaluation index system of each stage in the 
process of ecological welfare transformation was constructed. 

2.3. Two-stage DEA Model 
This paper refers to [53] to decompose the efficiency of 

EWP into two sub-stages, in order to open the "black box" of 
the transformation process of ecological input and welfare 
output. Among them, the first stage is the ecological 
economic transformation stage (L1), that is, the efficiency of 
transforming ecological input into economic output; The 
second stage is the economic welfare transformation stage 
(L2), that is, the efficiency of transforming economic inputs 
into welfare outputs, and the formula is as follows: 

I G I
E

C C G
  

 

 
(1)

In the above formula:  
E – Ecological welfare performance;  
C - ecological consumption, which is the initial input 

indicator;  
G - the level of economic development is the intermediate 

variable in the transformation process of ecological welfare, 
which is not only the output index of the first stage, but also 
the input index of the second stage, and plays a mediating role. 

I – Human Development Index, which indicates the level 
of welfare, is an indicator of final output. 

Compared with other measurement methods, the DEA 
method does not need to pre-set the production function, and 
can handle the input and output of multiple indicators, so it 
can fully reflect the consumption of resources and the 
improvement of economic, social and environmental well-
being in the process of ecosystem operation. However, the 
traditional DEA method ignores the stage efficiency in the 
production process and the impact of each sub-stage on the 
overall efficiency. In view of this shortcoming, some scholars 
[54] have improved the traditional single-stage DEA model 
and constructed a two-stage DEA model, which can 
effectively evaluate the real efficiency of the system in the 
process of operation, fully reflect the effectiveness of input 
and output at each stage and the correlation of sub-stages, and 
is more in line with the actual situation of the transformation 
process of ecological welfare. 

Suppose there are n homogeneous decision units (DMUs) 
and each DMUi (i=1,2,... n) are all broken down into two 
phases. where xij = (xi1, xi2,... xim)T(j=1,2,… m) denotes the 
DMUi input variable at L1; zid=(zi1,zi2,… zir)T(d=1,2,… r) 
denotes the intermediate variable of DMUi, which is both the 
output of L1 and the input of L2; yik=(yi1,yi2,… yip)T 
(k=1,2,… p) denotes the output variable of DMUi at L2. In 
L1, this paper adopts the input-oriented DEA-BCC model, 
and the goal of this stage is to minimize input and maximize 
output, with input/output as the evaluation index, and the 
minimum value of the evaluation index is the optimal value. 

2.3.1. Ecological Economic Transformation Stage 

11
1

1

m

j ijj

r

d idd

w x
minE

z













   (2)

 1

11

. . 1, 1,

r

d idd
m

j ijj

z
s t i n

w x








 





 (3)

1, 0,j dw R   (4)

2.3.2. Transformation Stage of Economic Welfare 
In L2, this paper adopts the output-oriented DEA-BCC 

model, and the goal of this stage is to maximize output and 
minimize input, with output/input as the evaluation index, and 

the maximum value of the evaluation index is the optimal 
value. 

 

21
2

1

p

k ikk
r

d idd

v y
maxE

z









 


     (5)

 21

1

. . 1, 1,

p

k ikk
m

d idd

v y
s t i n

z









 


     (6)



 

198 

2, 0,k dv R        (7)

2.4. Social Network Analysis 
2.4.1. Modified Gravitational Models and Network 

Calculation 
The determination of the spatial correlation of EWP is the 

premise of social network analysis. Drawing on the research 
of [55] et al., this paper uses a modified gravitational model 
to determine the correlation matrix of EWP in prefecture-
level cities in China. The formula is as follows: 

2

2
2

, ,i j yi
y y y y

ij i j i j

EWP EWP disEWP
F K K D

D EWP EWP pgdp pgdp

 
          

(8)

where: is the strength of the ecological welfare 
performance link between urban area and ; It represents the 
contribution rate of urban areas in the relationship with inter-
city ecological welfare performance; Represents the 
ecological welfare performance index; for urban areas and 
"comprehensive economic geography N distance" (km/yuan); 
Represents the spherical distance between cities (km); 
Indicates the per capita GDP of the city (RMB). According to 
equation (1), the gravitational matrix of inter-city ecological 
welfare performance can be calculated, 

The "mean principle method" was used to binarize the 
matrix to obtain the spatial binary matrix of ecological 
welfare performance.  

2.4.2. Characteristics and Evolution Trend of the Overall 
Network Structure 

Data from 2007 to 2022 are selected to plot the overall 
network characteristics of the two phases of EWP, as shown 
in Figures 1 to 4. 

 

 
Figure 1. Network density and relationships in 2007 

 

 
Figure 2. Network densities and relationships in 2022 

 

 
Figure 3. Network level and efficiency in 2007 

 

 
Figure 4. Network level and network efficiency in 2022 

 
According to the results of Figure 6 to Figure 9, the 

network density and correlation coefficient of L1 and L2 
showed a steady increase and then decrease from 2007 to 
2022, and as of 2021, the association coefficient of L1 
decreased from about 8500 at the beginning of the period to 
about 8100, and the association coefficient of L2 decreased 
from about 9000 to about 8200. In contrast, the network 
density and correlation coefficient of L1 decreased slightly, 
while L2 decreased greatly, indicating that the transformation 
of economic welfare is the key link restricting the 
improvement of EWP. From the perspective of dynamic 
evolution trend, the network density and relationship number 
of L1 in the same year are larger than those of L2, as shown 
in Figures 6 and 8. The results of the quantitative analysis are 
consistent with the results of the previous intuitive experience. 
The network rating of L1 increased from 0.0014 in 2007 to 
0.0282 in 2022, and the network rating of L2 increased from 
0.0008 in 2007 to 0.0144 in 2022, as shown in Figures 8 and 
9. The results indicate that there is a certain hierarchical 
structure between the areas with high ecological welfare 
performance and the areas with low ecological welfare 
performance, and the potential of each province in the 



 

199 

network is uneven. Figures 8 and 9 also show the network 
efficiency of two stages: the overall level of network 
efficiency in the two stages is high, which remains above 0.85, 
which is at the upper level, indicating that there are multiple 
superposition phenomena and redundant connections in the 
spatially related network of EWP, and the network stability 
needs to be further improved. 

3. Prediction of the Horizontal 
Transfer Path of Ecological Welfare 
Performance based on Markov 
Chain 

3.1. Research on the Spatiotemporal Transfer 
Path of Ecological Welfare Performance 
Level of Cities in China Based on the 
Traditional Markov Chain 

The traditional Markov chain [57] is based on a stochastic 
process under the condition that both time and state are 
continuous, and no aftereffect is an important feature of it. In 
this model, the transition of state of a system depends only on 
its most recent state, regardless of its earlier state. This 
property makes the Markov chain a powerful tool that can be 
applied in a variety of fields. There are two main reasons for 
using traditional Markov chains: first, Markov chains can 
accurately predict the dynamic changes in the state of a 
system with relatively little computational complexity, which 
is especially important when dealing with large-scale data or 
making long-term predictions; Second, the Markov chain is 
able to describe many real-world processes in a formal way, 
providing them with an efficient way to model them. To use 
a traditional Markov chain, the following requirements need 
to be met: 

(1) The state state of regional economic development level 
at any time series node during the study period is random. 

(2) The type of regional economic development level is 

transferred from this time series node to the next time series 
node according to the path of different probabilities. 

(3) The type of regional economic development level only 
depends on the probability of the transfer path and the state 
under the time series node, and has nothing to do with the 
state before the node, that is, the evolution of the regional 
economic development state has no aftereffect. 

After satisfying the above conditions, we divided the EWP 
from 2007 to 2022 into groups, and then constructed a matrix 
reflecting the probability of state transition, and recorded the 
probability distribution of ecological welfare performance 
from one group to another, so as to describe the process of 
spatiotemporal transfer of EWP. The expression formula is as 
follows: 

ij
ij

i

n
M

n


 

 
(9)

Thereinto: 

11 1

1

j

ij

i ij k k

n n

M

n n


 
   
  


  


 

(10)

where is the state transition probability matrix of , which is 
the sum of the number of spatial units in the study period 
when the level of economic development changes from the 
state of year to the state of j of year. is the sum of the number 
of all spatial units with a state of economic development 
throughout the study period. 

According to the Markov chain principle, the year-by-year 
changes of ecological performance types in cities in China 
from 2007 to 2022 were recorded and analyzed, and the EWP 
and economic development level were set into five groups: 
"low", "low", "medium", "high" and "high", and the 
traditional Markov transfer probability table of the fifth-order 
matrix was obtained, as shown in Table 1. 

 
Table 1. Probability table of traditional Markov chain transfer in fifth-order matrix 

t/t+1 n 1 (Low) 2 (lower) 3 (Medium) 4 (Higher) 5 (High)
1 (Low) 886 0.727 0.221 0.043 0.009 0.000
2 (lower) 869 0.183 0.490 0.251 0.062 0.014

3 (Medium) 840 0.017 0.202 0.452 0.262 0.067
4 (Higher) 829 0.004 0.051 0.221 0.510 0.215
5 (High) 836 0.002 0.008 0.044 0.202 0.743

The diagonal line in Table 9 shows the probability of each 
city maintaining the original economic development level, 
and outside the diagonal is the probability of spatiotemporal 
transfer in each city. According to Table 9, we can know that: 
(1) The stability of EWP in the original state of each city in 
China is strong, the initial category is from low to high, the 
diagonal probability is greater than the non-diagonal 
probability, and the lowest probability of each city to maintain 
the original state is 45.2%, and the highest probability is 
74.3%, indicating that the stability of the economic 
development of each city is strong, but the occurrence of 
spatiotemporal transfer is not excluded. (2) The probability of 
maintaining the original status quo at a low level and a high 
level of ecological efficiency in cities in China is relatively 
low, while the probability of maintaining the original status 
quo at a low, medium and high level is relatively low, ranging 
from [49% to 51%], indicating that there is a polarization of 
EWP in cities in China and a phenomenon of "club 
convergence", indicating that there is a long-term regional 

difference in EWP level among cities. 

3.2. Research on the Spatiotemporal Transfer 
Path of Ecological Performance Level of 
Cities in China based on Spatial Markov 
Chain 

Since economic phenomena are not random, according to 
the first law of geography, everything is related to 
geographical location, so we study the EWP of each city in 
China, which is related to its geographical location, and 
geographical location will affect the distribution, 
development and interaction of things, and this interaction 
will become closer with distance and other factors. However, 
the traditional Markov chain cannot accurately take into 
account the interaction between cities, so the traditional 
Markov chain is combined with local space to introduce the 
concept of "spatial lag" and construct a spatial Markov chain. 

Compared with the traditional Markov chain, the spatial 



 

200 

Markov chain is composed of transition matrices, and the 
spatial weight matrix needs to be introduced to reflect the 
interaction between cities, and the size of the spatial lag value 
determines the spatial lag type to which the spatial unit 
belongs. The expression is: 

1

n

i ij
i

Lag y w



 

 
(11)

 
In the above equation, denotes the spatial lag value, denotes 

the number of spatial units, denotes the attribute value of 
spatial units, and denotes the adjacency space weight matrix 
based on the QueenXX rule. 

In order to test whether the spatial factors have a significant 
impact on the EWP of cities in China, we use the chi-square 
test to verify the situation, and the formula is as follows: 

 

 12

1
1 1 1

2 log ?   
ijn mt tk k

ij

t t
m i j ij

Q
p

Q m




  

    
    


，

，

 

(12)

 
In the above equation, and denotes the sum of the elements 

of the two types of transition matrix and the number of 
regions belonging to this type of transition when the duration 
is , respectively, and the transfer probability value is 
calculated by combining the two types of data, p 
asymptotectively obeys the chi-square distribution, and its 
degrees of freedom are minus the number of transfer 
probabilities of 0. 

In order to take the spatial lag factor of the spatial unit in 
the year as the condition, and the economic development level 
of the year is the type, and the spatial transition probability of 
the year into the type, we consider the spatial effect on the 
basis of the traditional Markov chain, construct the spatial 
Markov chain model, obtain the spatial Markov transfer 
matrix, and further explore the influence and spatial effect 
characteristics of the spatial relationship team in China. 

We set the spatial lag to 5 groups, named none, low-low 
aggregation, low-high aggregation, high-low aggregation, 
and high-high aggregation, and we first set up the spatial 
Markov chain according to the test index p=0.01<0.05, which 
shows that it is meaningful to consider the spillover effect in 
the establishment of spatial Markov chains, and the traditional 
Markov chain cannot well explain the interaction between the 
leading regions, and the results of the path transfer probability 
matrix of spatial Markov chains are shown in Table 2. 

 
Table 2. Spatial Markov chain path transition probability matrix 

Regional context t n 
t+1 

Low Lower Medium Higher High

Gather high 
High and low gathering 
Low and high clusters 

low 0 0.000 0.000 0.000 0.000 0.000
Lower 0 0.000 0.000 0.000 0.000 0.000

medium 0 0.000 0.000 0.000 0.000 0.000
Higher 23 0.000 0.043 0.087 0.478 0.391
high 270 0.000 0.004 0.033 0.115 0.848

Low low aggregation 
Regional context 

low 0 0.000 0.000 0.000 0.000 0.000
Lower 0 0.000 0.000 0.000 0.000 0.000

medium 0 0.000 0.000 0.000 0.000 0.000
Higher 2 0.000 0.500 0.000 0.000 0.500
high 78 0.013 0.013 0.013 0.115 0.846

Gather high 
High and low gathering 

low 129 0.791 0.155 0.047 0.008 0.000
Lower 47 0.234 0.574 0.170 0.021 0.000

medium 5 0.200 0.400 0.400 0.000 0.000
Higher 0 0.000 0.000 0.000 0.000 0.000
high 0 0.000 0.000 0.000 0.000 0.000

Low and high clusters 
Low low aggregation 

low 33 0.939 0.030 0.030 0.000 0.000
Lower 8 0.125 0.625 0.250 0.000 0.000

medium 1 0.000 0.000 1.000 0.000 0.000
Higher 0 0.000 0.000 0.000 0.000 0.000
high 0 0.000 0.000 0.000 0.000 0.000

Regional context 

low 724 0.706 0.242 0.043 0.010 0.000
Lower 814 0.181 0.484 0.256 0.065 0.015

medium 834 0.016 0.201 0.452 0.264 0.067
Higher 804 0.004 0.050 0.225 0.512 0.209
high 488 0.002 0.010 0.055 0.264 0.668

According to Table 10, we can see that: (1) There is a high 
correlation between EWP type transfer and regional 
background, and the probability of spatiotemporal transfer of 
EWP in different regional backgrounds is quite different, and 
the results are quite different from those of the traditional 
Markov chain, so there is a spatial spillover effect of EWP 
transition among cities in China. (2) In the context of most 
regions, the probability of diagonals is greater than that of 
non-diagonals, but in the case of high-high aggregation and 
high-low aggregation, there is a situation where the diagonal 
is equal to the probability of non-diagonal, which indicates 
that most cities in China have the situation of maintaining the 
original state, but there are also some cases of pathway 
transfer, and it is the situation of jump transfer. (3) The 

probability of high EWP level was 84.8% in the regional 
background of high aggregation, which was higher than that 
in the non-regional background (66.8%). The probability of 
low EWP level was 93.9% in the regional context of low and 
low aggregation, which was higher than that in the non-
regional background (70.6%). This suggests that there is a 
"club convergence" phenomenon at the EWP level. (4) The 
change of regional background does not absolutely affect the 
transfer of EWP in each city. (5) Compared with the 
traditional Markov chain, the spatial Markov chain maintains 
the original status quo of the EWP in each city in China 
without setting the regional background, that is, without 
setting the spatial lag, and the path selection will be increased 
and the spatial lock will be reduced. Moreover, the probability 



 

201 

of some transfer paths has been improved, indicating that after 
considering the spatial lag, it can better reflect the EWP 
transfer situation of various cities in China. 

4. Conclusion 
Based on the improved HDI index, economic development 

level and natural consumption index, this paper constructs an 
EWP evaluation index system, decomposes the ecological 
welfare performance into two stages: ecological economic 
transformation and economic welfare transformation, and 
calculates the EWP level of 284 cities in China from 2007 to 
2022 through the two-stage DEA method, and depicts the 
spatiotemporal differentiation characteristics of each stage, 
and then uses social network analysis and Markov chain to 
explore the dynamic evolution trend of EWP from the 
perspective of distribution characteristics and space. The 
main conclusions of the study include: (1) EWP generally 
showed a trend of first increasing and then decreasing during 
the sample period, and its decline in L1 was lower than that 
of L2, which shows that L2 is the key link restricting the 
improvement of EWP. (2) The agglomeration pattern of the 
spatial correlation network of ecological welfare performance 
is characterized by the coexistence of "local agglomeration" 
and "global association", and the network center is 
concentrated in the eastern coastal region, forming a 
significant Matthew effect, while the central and western 
regions and the northeast region mainly play a bridge role. (3) 
The formation and development of the spatial correlation 
network in the two sub-stages of EWP is affected by four 
mechanisms: resource endowment differences, market 
regulation, government macroeconomic regulation and 
control, and science and technology promotion. 

Acknowledgments 
Anhui University of Finance and Economics 

Undergraduate Scientific Research and Innovation 
Foundation Program Grant (XSKY24219). 

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