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Citation: Cong, X.; Wang, S.; Wang,
L.; Šaparauskas, J.; Górecki, J.;
Skibniewski, M.J. Allocation
Efficiency Measurement and
Spatio-Temporal Differences Analysis
of Digital Infrastructure: The Case of
China’s Shandong Province. Systems
2022,10, 205. https://doi.org/
10.3390/systems10060205
Academic Editor: William T. Scherer
Received: 11 October 2022
Accepted: 1 November 2022
Published: 3 November 2022
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systems
Article
Allocation Efficiency Measurement and Spatio-Temporal
Differences Analysis of Digital Infrastructure: The Case of
China’s Shandong Province
Xuhui Cong 1, Sai Wang 1, Liang Wang 2,*, Jonas Šaparauskas 3, Jarosław Górecki 4
and Miroslaw J. Skibniewski 5,6,7,8
1Business School, Shandong University of Technology, Zibo 255049, China
2Management School, Hainan University, Haikou 570228, China
3Department of Construction Management and Real Estate, Faculty of Civil Engineering, Vilnius Gediminas
Technical University, Saul ˙
etekio Al. 11, LT-10223 Vilnius, Lithuania
4Faculty of Civil and Environmental Engineering and Architecture, Bydgoszcz University of Science and
Technology, 85-796 Bydgoszcz, Poland
5Department of Civil & Environmental Engineering, University of Maryland, College Park, MD 20742, USA
6Institute for Theoretical and Applied Informatics, Polish Academy of Sciences, 5, 44-100 Gliwice, Poland
7Department of Construction Engineering, ChaoYang University of Technology, 168, Jifong E. Rd.,
Wufong District, Taichung City 41349, Taiwan
8Vilnius Gediminas Technical University, Vilnius 10223, Lithuania
*Correspondence: liangwang@hainanu.edu.cn
Abstract:
After Shandong Province started the construction about digital infrastructure, the con-
struction of digital infrastructure reached social consensus, promoting digital development of the
province. However, it inevitably exposed problems such as non-targeted policies and uneven devel-
opment levels. This study uses the non-expectation super-efficiency SBM model and kernel density
estimation method to compare the digital infrastructure allocation efficiency of 16 prefecture-level
cities in Shandong Province and analyzes the spatial and temporal differences. Results show that
the overall level of digital infrastructure allocation efficiency in Shandong Province shows a steady
and policy-stimulated growth, but no high-value aggregation area has been formed and regional
synergistic development remains to be strengthened. Recommendations are provided on four as-
pects: increased government expenditure, policy heterogeneity, attention to low-level construction
areas, and promotion of regional synergistic development to improve the construction of digital
infrastructure in Shandong and sustain its strong digital thrust.
Keywords: digital infrastructure; allocation efficiency; spatio-temporal differences
1. Introduction
China’s 14th Five-Year Plan forwards the strategic goal of “accelerating digital develop-
ment and building a digital China”. This means an efficient and stable digital infrastructure
is considered key to the construction of said digital China. Shandong Province closely
followed this national development strategy and pushed for strong provincial construction
needs, issued a guiding document on the “digital infrastructure construction in Shandong
Province”, and created a forward-looking layout for emerging infrastructure.
To properly execute this important strategic goal layout, Shandong Province formu-
lated the 14th Five-Year Development Plan, and forwarded a grand blueprint to “increase
the construction of digital infrastructure, strengthen the provincial capital economic circle,
enhance the Jiaodong economic circle, revitalize the Lunan economic circle, and promote
high-quality economic development, and build a strong digital province”. This blueprint
indicated the direction and specific goals. The 16 cities in Shandong Province have dif-
ferences in economic and social development, resource endowment and other aspects,
Systems 2022,10, 205. https://doi.org/10.3390/systems10060205 https://www.mdpi.com/journal/systems
Systems 2022,10, 205 2 of 22
and allocation of digital infrastructure needs which have obvious differences. Hence, it is
now important to measure the efficiency of digital infrastructure allocation in Shandong
Province, clarify its spatial and temporal differences, and formulate a synergistic linkage
mechanism for digital infrastructure allocation, considering the goal of building an efficient
and synergistic digital infrastructure system in the province.
Existing studies on digital infrastructure mainly focus on the connotation and exten-
sion of digital infrastructure, its driving effects, and the construction models and paths.
First, in terms of connotation and extension, the existing studies introduce digital infrastruc-
ture systematically and elaborate the beneficial effects of digital infrastructure construction
on society and economy on the macro and micro levels [
1
–
3
]. Second, the literature on
driving effects usually unites digital infrastructure and digital economy to advance the
development of the digital economy through digital infrastructure construction, while the
digital economy also promotes digital infrastructure construction [4,5].
Simultaneously, the construction of digital infrastructure also promotes industrial
development, enhances employment, and produces a multiplier effect on total economic
volume [
6
,
7
]. Last, digital technology innovation should be promoted according to the
characteristics of digital infrastructure, government support should likewise be increased,
and timely responses to difficulties such as high costs and lack of talent should be developed
to facilitate the rapid formation of digital cities and societies [1,2,8].
However, limited studies explore the allocation efficiency of digital infrastructure, with
indicators and methods for measuring allocation efficiency needing further exploration to
investigate potential problems and improve the allocation efficiency of digital infrastructure.
Hence, this study examines the measurement perspective, method, and index system.
First, it establishes a digital infrastructure allocation efficiency measurement index
system key dimension, namely staff and financial inputs, digital infrastructure, society, econ-
omy, and technology. Then, using non-expectation super-efficiency Slacks-based measure
model (SBM) and kernel density estimation methods, we analyze the digital infrastructure
allocation efficiency and spatial and temporal differences. This comprehensively measures
the digital infrastructure allocation efficiency of the entire Shandong Province along with
its three economic circles and prefecture-level cities, deeply analyzes the problems and
shortcomings in the digital infrastructure construction process, and puts forward targeted
policy recommendations.
This study analyzes the digital infrastructure allocation efficiency and spatial–temporal
differences in Shandong Province under a strong digital province. It also proposes targeted
policy recommendations based on the results to aid in realizing a strong digital province in
Shandong Province.
The rest of this study is as follows: the second chapter provides a comprehensive liter-
ature review on the status of digital infrastructure research. The third chapter introduces
the research object and research methodology, including the specific steps and formulas
of the methodology. The fourth focuses on the principles of the construction of the digital
infrastructure allocation efficiency measurement index system in Shandong Province and
the indicators included. The fifth measures the allocation efficiency of digital infrastructure
in Shandong province and analyzes the spatial and temporal differences in the allocation
efficiency, as well as potential problems and shortcomings. The sixth part proposes cor-
responding policy recommendations based on the results of the analysis. The last part
summarizes the study and outlines its shortcomings for future research directions.
2. Literature Review
Since the concept of digital infrastructure was proposed, various in-depth studies on
digital infrastructure from multiple perspectives in multiple fields have been forwarded.
Currently, research on the measurement of digital infrastructure construction efficiency
mainly focuses on three areas: the connotation and extension of digital infrastructure, the
driving effect, and the mode and path of construction.
Systems 2022,10, 205 3 of 22
The first area explores the connotation and extension of digital infrastructure. Digital
infrastructure mainly refers to the new infrastructure based on an information network, and
it is driven by the integration and innovation of new generation information technology
and various fields of economy and society. This provides the digital capability for social
production and life, and digitally empowers various industries [
9
]. In 2021, Hustad argues
that at the micro level, digital infrastructure development is an important guarantee for
governments, enterprises, and other organizations to enhance digital technologies and
organize digital transformation [2].
Digital infrastructure development has been increasingly involved in a variety of
areas and industries. At the macro level, new digital infrastructure breaks down data silos,
enhances services, helps modernize urban governance systems and governance capabilities,
and promotes high-quality economic development [
3
]. The successful construction of
digital infrastructure opens new economies and societies, creates jobs, and improves the
quality of life. Countries also receive a variety of benefits from digital infrastructure, such as
capacity expansion, time savings, streamlined operations, cost savings, increased efficiency,
and enhanced security [1].
Most extant studies likewise explore the driving effect of digital infrastructure con-
struction. In the development process of the digital economy, digital technologies related
to artificial intelligence and big data should be introduced and applied scientifically and
reasonably in economic development to enhance the development of the digital economy.
Here, it is necessary to have a comprehensive understanding of the development of the
digital economy from the perspective of digital infrastructure, identify the existing prob-
lems, and develop a high-quality development path based on the actual problems. This
effectively promotes the development of the digital economy [4,5].
Digital infrastructure construction on the one hand directly drives economic growth
through investment. On the other hand, it attracts the inflow of capital through environmen-
tal improvement while driving the development of upstream and downstream industries
and producing a multiplier effect on the total economic volume [
6
,
10
]. Technology diffusion
and knowledge spillover from digital infrastructure during research and development
(R&D) and construction positively contribute to services employment. Moreover, the posi-
tive effect of digital infrastructure on services employment is stronger for countries with
the relatively high institutional quality yet relatively low education levels [7].
Last are extant studies’ exploration on the patterns and paths of digital infrastructure
construction. Currently, the physical infrastructure construction has become saturated,
the promotion kinetic energy of the industry has weakened, and digital infrastructure
construction has become the new kinetic energy of regional economic growth. It is therefore
necessary to further analyze the mode and path of digital infrastructure construction
according to the characteristics of digital infrastructure.
To effectively promote the construction of new digital infrastructure, diversified invest-
ment entities should be attracted, the leading role of the government should be strength-
ened, top-level design should be enhanced, and supporting policy and financial support
should be increased [
8
]. While building digital infrastructure, various obstacles and difficul-
ties exist. These include high costs, lack of public investment funds, lack of Information and
Communications Technology (ICT) talents, and concerns about the privacy and security of
information data. Hence, government and relevant departments should develop timely,
comprehensive, and detailed response plans to ensure the smooth construction of digital
infrastructure and promote the rapid formation of digital cities and societies [
1
]. In 2021,
Hustad argues that during this process, there is a need to focus on sustainable develop-
ment by promoting technological advances and innovations that change the way digital
infrastructure is involved and used, thereby finding sustainable responses to economic and
environmental challenges for both economic growth and global development [2].
Despite these previous explorations, it remains difficult to give clear direction and
reference on the main bottlenecks, allocation level, and future trends of digital infrastructure
construction in Shandong Province. Hence, this study considers the requirements and
Systems 2022,10, 205 4 of 22
characteristics of digital infrastructure construction, constructs a suitable measurement
index system, focuses on measuring the level of digital infrastructure allocation, and
analyzes the development relationship within and among the three major economic circles
of Shandong Province, Jiaodong, and Lunan. This allows the study to better forward
suggestions that make the balanced and linked development of digital infrastructure
allocation in the three major economic circles of Shandong.
3. Research Objectives and Methods
3.1. Research Objectives
This study takes the 16 prefecture-level cities included in the provincial capital,
Jiaodong, and Lunan economic circles proposed in the 14th Five-Year Plan of Shandong
Province as the research objects, explores the digital infrastructure allocation efficiency
and spatial and temporal differences in the province, and proposes responsive policy
recommendations following local conditions and study results.
3.2. Research Methods
The non-expectation super-efficiency SBM model was used to calculate the efficiency of
digital infrastructure allocation after combining the requirements and objectives of a “strong
digital province” with 16 prefecture-level cities in Shandong Province. Subsequently, kernel
density estimation was used to analyze the efficiency of digital infrastructure allocation
and spatial and temporal differences in the province.
Introduction to the Research Methods and Feasibility Analysis
(1)
Non-expectation super-efficiency SBM model
Data envelopment analysis (DEA) is a nonparametric method for calculating the
efficiency of multiple decision units. Jointly proposed by Charnes, Cooper, and Rhodes
in 1978 [
11
], the model compares the efficiency among multiple service units providing
similar services by explicitly considering the use of multiple inputs and the generation of
multiple outputs. This had led to the model’s wide use in performance evaluation.
The shortcomings of traditional DEA models, such as radial DEA’s overestimation
of the efficiency value of decision-making units (DMUs) when it is over-input and/or
under-output and angle DEA’s ignorance of the variation of inputs or outputs, often
lead to the mismatch between calculated results and objective facts. To overcome these
problems, Tone created an efficiency measure based on slack variables (the SBM model) in
2001 and continuously improved it by proposing the super-efficient SBM model and the
non-expectation SBM model variants [12].
Following Tone’s research, Cheng-Gang combined the super-efficient SBM model in
2014 and the non-expectation SBM model and proposed the non-expectation super-efficient
SBM model to evaluate the efficiency value of DMUs. This method has been applied to
assess the efficiency of the green economy in China [
13
], assess the energy efficiency of
the inter-provincial service industries [
14
], and assess the eco-efficiency of coal mining
areas [15], among other areas.
When measuring the efficiency of digital infrastructure allocation in Shandong Province,
some slack variables were selected to make the assessment scope more comprehensive, and
the SBM model considered slack variables in the objective function to solve the problem of
slackness of input–output variables. The efficiency values of the effective decision units
measured by the traditional SBM model were all 1, which made it difficult to distinguish
the efficiency differences among the effective decision units and leads to bias in the final
decision. The super-efficient SBM model decomposed the effective units with the efficiency
value of 1, thereby comparing the effective decision units and improving the accuracy of
the comparison results.
Additionally, while building digital infrastructure, it is inevitable to produce unde-
sired output and the most efficient production method as of current must be the green
production method, i.e., producing more desired output and less undesired output with
Systems 2022,10, 205 5 of 22
less input. Therefore, this study selected the non-expectation super-efficiency SBM model
to measure the level of digital infrastructure allocation in each prefecture-level city in
Shandong Province.
(2)
Kernel density estimation method
The kernel density estimation method, as proposed by Rosenblatt and Parzen, is based
on a nonparametric fitting method to achieve an optimal fit of the parametric distribution
and construct a model of the data distribution when the prior knowledge based on the
data distribution is unknown [
16
]. It is one of the most studied methods in nonparametric
inspection and is commonly used to estimate an unknown probability density function,
which is a natural extension of the histogram. This improves the problem of discontinuity
that exists in the histogram using higher analytical accuracy.
Since the kernel density estimation method does not utilize a priori knowledge on
the data distribution and does not attach any assumptions to it, the method studies the
characteristics of data distribution from the data sample itself, and is therefore widely
used in contexts such as wind power penetration dynamic economic dispatch [
17
], an-
alyzing the spatial and temporal changes of arable land use efficiency in the Yangtze
River economic zone [
18
], exploring 6G multi-source information fusion indoor position-
ing [
19
], and analyzing the impact of traffic infrastructure on NO
2
concentration levels [
20
],
among others.
In measuring the allocation efficiency of digital infrastructure in Shandong Province,
the method was highly adaptable and flexible because it was not limited by the data
and did not require the prior assumption of the probability distribution pattern of the
data, but dealt with the probability distribution through the characteristics of the data
itself. The kernel density estimation was fitted to all sample observations using a smooth
peak function to describe the location, shape, and extension of the distribution of digital
infrastructure allocation efficiency along with continuous density curves, revealing the
time-series dynamic change pattern of digital infrastructure allocation efficiency in each
prefecture-level city in Shandong.
The specific formula of the research methodology is shown in Appendix A.
4. The Measurement Index System of Digital Infrastructure Allocation Efficiency
To scientifically measure the efficiency of digital infrastructure allocation, this study
considered the characteristics of digital infrastructure, and constructed a digital infrastruc-
ture allocation efficiency measurement index system in Shandong based on the principles
of scientificity, systematization, and independence and operability, which was combined
with the actual situation in Shandong Province, as shown in Table 1.
4.1. Input Indicators
The allocation of digital infrastructure requires both relevant digital infrastructure as
the basis and human and financial support. Hence, this study divided the input indicators
into two dimensions: personnel and financial input and digital infrastructure input [
21
,
22
].
Staff and financial inputs (X
1
)—the construction of digital infrastructure requires
science and technology innovation. R&D resources are important indicators of the country’s
science and technology activities and its level of science and technology investment are a
reflection of China’s independent innovation capabilities in building an innovative country.
Hence, this study used the proportion of R&D personnel to employees (X
11
) and the
proportion of R&D expenditure to Gross Domestic Product (GDP) (X
12
) the number of R&D
resources [23–25].
Systems 2022,10, 205 6 of 22
Table 1.
Digital infrastructure allocation efficiency measurement index system in Shandong Province.
Target Layer Guideline Layer Indicator Layer
Inputs
Staff and financial inputs X1
R&D personnel as a proportion of
employed persons X11
R&D expenditure as a percentage of GDP X12
Science and education expenditure as a
proportion of general public expenditure X13
The proportion of fixed asset investment in
information and soft technology to the total
social fixed asset investment X14
Number of college students per
10,000 people X15
Digital infrastructure inputs X2
Number of cell phone subscribers
per 10,000 households X21
Number of Internet broadband access
subscribers per 10,000 households X22
Number of computers per 100 people X23
Number of websites per 100 companies X24
Expected output
Social Y1
Inclusive Digital Finance Y11
The proportion of employed persons in
information and software technology Y12
Economy Y2
Total Telecommunications Business Y21
E-commerce sales Y22
Total Factor Productivity Y23
The proportion of tertiary industry output value
and secondary industry output value Y24
Technology Y3Number of Invention Patents Y31
Non-desired outputs Social Injustice Z1
Income gap between urban and
rural residents Z11
Consumption gap between urban and
rural residents Z12
Digital infrastructure construction requires government and social support, along
with a good development environment and material security. Thus, the proportion of
science and education expenditure to general public expenditure (X
13
) and the proportion
of investment in information and software technology fixed assets to the total social fixed
asset investment (X
14
) were used to reflect the importance of digital infrastructure by local
governments and relevant departments [26,27].
Human capital is also an important support for scientific and technological innovation,
a cornerstone of digital infrastructure construction, and a new driving force for a strong
digital province. Hence, the number of university students per 10,000 people (X
15
) was
used to characterize human capital [28,29].
Digital infrastructure inputs (X
2
)—mobile communication and the Internet assume an
important supporting role in many sectors. Therefore, the number of cell phone subscribers
per 10,000 households (X
21
) and the number of Internet broadband access subscribers per
10,000 households (X
22
) were used to reflect the level of digital infrastructure construc-
tion [
30
,
31
]. The digitalization and informatization of enterprises effectively contribute to a
strong digital province, hence the number of computers used per 100 people (X
23
) and the
number of websites per 100 enterprises (X
24
) characterize the investment of enterprises in
digital construction in each region [32,33].
4.2. Output Indicators
The construction of digital infrastructure has improved economic productivity and
people’s living standards. However, it has also brought a negative impact in the construc-
Systems 2022,10, 205 7 of 22
tion process. Therefore, this study considered expected and unexpected output in the
output indicators.
Expected output indicators—digital infrastructure construction promotes strong digi-
talization and science and technology innovation. Thus, this study divided the expected
output into three dimensions: social, economic, and technological.
Society (Y
1
): Digital infrastructure construction enhances public daily work efficiency
and improves the quality of life. It also creates more employment opportunities, affecting
the employment rate. This study used the Digital Inclusion Index (Y
11
) to reflect the im-
provement of residents’ daily life and work from multiple perspectives, such as depth of use,
breadth of coverage, and degree of digitization. The proportion of employed people in in-
formation and technology employment (Y
12
) was used to reflect the change in employment
rate and labor income of the population by digital infrastructure development [34,35].
Economy (Y
2
): digital infrastructure construction promotes the economic development
of related industries; hence the total telecommunication business (Y21) was used to reflect
the economic power provided by digital infrastructure [
36
,
37
]. E-commerce, as an important
driver of economic development in China, helps clear the obstacles to the development
of various industries, hence the use of e-commerce sales (Y
22
) to characterize the role of
digitalization in the process of the strong digital province [
38
–
40
]. Total factor productivity
includes economic policies, the role of government in the economy, work attitudes, positive
externalities caused by an educated workforce, technological learning, among others,
explaining the use of total factor productivity (Y
23
) to reflect the extent of effective economic
growth in each location [41–43].
During digital infrastructure construction, the realization of economic and social
benefits that the positive environmental benefits generated should be considered. The
industrial structure, which is associated with issues such as energy consumption and
pollution emission, is key to accelerating the transformation of old and new dynamics.
Therefore, the proportion of tertiary industry output value and secondary industry output
value (Y24) is used to characterize the industrial structure [44,45].
Technology (Y
3
): digital infrastructure construction improves independent innovation
capacity and breakthrough key technological issues, injecting new vitality into economic
development. This explains the study’s use of number of invention patents (Y
31
) to charac-
terize the scientific research output [46,47].
Non-expected output indicators—currently, digital infrastructure construction mainly
focuses on urban areas, increasing an already existing urban–rural divide. Therefore, this
study considered the social balance in terms of unexpected output, mainly divided into
two dimensions: income and consumption. Since digital infrastructure is mainly carried
out in cities, the income gap between urban and rural residents (Z
11
) and the consumption
gap between urban and rural residents (Z
12
) were used to characterize social injustice
(Z1) [48,49].
5. Empirical Analysis
5.1. Measurement of Digital Infrastructure Allocation Efficiency in Shandong Province
Based on the digital infrastructure allocation efficiency measurement index system
and index data of Shandong Province, the non-expectation super-efficiency SBM model was
used to obtain the digital infrastructure allocation efficiency values of each prefecture-level
city in Shandong Province from 2014 to 2020. To better analyze the allocation efficiency
of each prefecture-level city in Shandong Province, the cities in Shandong Province were
divided based on three abovementioned economic circles. We then took the average value
of the allocation efficiency of the cities included in each economic circle and all cities in
Shandong Province as the allocation efficiency value of digital infrastructure at the level of
each economic circle and Shandong Province as a whole, and subsequently analyzed the
potential problems existing in them. The specific allocation efficiency values are shown
in Table 2.
Systems 2022,10, 205 8 of 22
Table 2. Efficiency values of digital infrastructure allocation in Shandong Province.
Region Prefecture
Level City 2014 2015 2016 2017 2018 2019 2020
Provincial
Capital
Economic
Circle
Jinan 1.307 1.226 1.194 1.193 1.188 1.182 1.207
Zibo 1.039 1.012 1.070 1.060 1.017 1.067 1.061
Dongying 1.145 1.174 1.165 1.150 1.169 1.210 1.529
Tai’an 1.094 1.076 1.057 1.035 1.046 1.015 1.050
Dezhou 1.067 1.042 1.066 1.072 1.049 1.037 1.070
Liaocheng 1.139 1.406 1.192 1.142 1.018 1.111 1.106
Binzhou 2.178 1.118 1.023 1.016 1.025 1.038 1.025
Average value 1.281 1.151 1.110 1.095 1.073 1.094 1.150
Jiaodong
Economic
Circle
Qingdao 1.193 1.217 1.299 1.278 1.269 1.256 1.223
Yantai 1.068 1.029 1.006 1.009 1.719 1.156 1.142
Weifang 1.161 1.042 1.010 1.009 1.035 1.151 1.053
Weihai 1.095 1.051 1.076 1.071 1.062 1.046 1.033
Rizhao 1.086 1.113 1.137 1.130 1.153 1.058 1.055
Average value 1.121 1.090 1.106 1.100 1.247 1.134 1.101
Lunan
Economic
Circle
Zaozhuang 1.078 1.066 1.030 1.090 1.130 1.088 1.141
Jining 1.064 1.051 1.015 1.000 1.007 1.045 1.012
Linyi 1.191 1.145 1.181 1.148 1.267 1.128 1.146
Heze 1.069 1.144 1.080 1.150 1.247 1.284 1.355
Average value 1.100 1.102 1.077 1.097 1.163 1.136 1.163
Shandong
Province Average value 1.186 1.120 1.100 1.097 1.150 1.117 1.138
The provincial capital economic circle included the seven cities of Jinan, Zibo, Dongy-
ing, Tai’an, Dezhou, Liaocheng, and Binzhou. The Jiaodong economic circle included
the five cities of Qingdao, Yantai, Weifang, Weihai, and Rizhao. The Lunan economic
circle included the four cities of Zaozhuang, Jining, Linyi, and Heze. The data used was
obtained from the China City Statistical Yearbook, the Shandong Statistical Yearbook, the
bulletin of the Department of Industry, and Information Technology of Shandong Province,
and the statistical bulletin and statistical yearbook of the National Economic and Social
Development Bureau of each prefecture-level city in Shandong Province.
To better observe the digital infrastructure allocation efficiency values of each economic
circle and each prefecture-level city, this study used a line graph for analysis [
50
]. The
details are shown in Figure 1.
Systems 2022, 10, x FOR PEER REVIEW 9 of 23
Figure 1. Line graph of digital infrastructure allocation efficiency for Shandong Province as a whole,
the three economic circles and prefecture-level cities.
5.1.1. Overall and Inter-Economic Circle Measurement
From the perspective of Shandong Province as a whole, the specific values and dy-
namic change process of its allocation efficiency values are analyzed in conjunction with
Table 2 and Figure 1. During the study period, the overall digital infrastructure allocation
efficiency of Shandong Province first decreased and then increased. The average efficiency
of Shandong Province decreased from 1.186 in 2014 to 1.097 in 2017. With the promulga-
tion of the Digital Shandong Development Plan in 2018, the average efficiency increased
to 1.138 in 2020.
This guiding document forwards the requirements and goals for the construction of
digital infrastructure in Shandong Province, which provides a good construction environ-
ment for the construction of digital infrastructure and encourages all regions in Shandong
to further regard digital infrastructure. This efficiency of digital infrastructure allocation
gradually improves and tends to stabilize.
By comparing the three major economic circles, the digital infrastructure allocation
efficiency of the provincial capital economic circle has drastically changed during the
study period. The Jiaodong and Lunan economic circles were at 1.281 in 2014, and then
experienced a yearly decline until they fell to the same level as their 2017 numbers. In
2018, these economic circles were influenced by the policies of Shandong Province, hence
the increase in their digital infrastructure allocation efficiency.
In contrast, the allocation efficiency of the provincial capital economic circle contin-
ues to decline to 1.073, widening its gap with the Jiaodong and Lunan economic circles. It
only started to rebound in 2019 and improved to 1.150 in 2020, which is higher than the
average level of the province. The quantified range of digital infrastructure allocation ef-
ficiency of the provincial capital economic circle during the study period is 1.073~1.281.
The digital infrastructure allocation efficiency of the Jiaodong economic circle performed
better during the study period, which was higher than the provincial average during
2016–2019 and increased significantly in 2018 with an allocation efficiency of 1.247, far
ahead of the provincial capital and Lunan economic circles.
However, this also led to a yearly decline in the allocation efficiency of the Jiaodong
economic circle in the two succeeding years which was lower than the 2020 provincial
average. The quantified range of digital infrastructure allocation efficiency in the Jiaodong
economic circle during the study period was at 1.090~1.247. The digital infrastructure
Figure 1.
Line graph of digital infrastructure allocation efficiency for Shandong Province as a whole,
the three economic circles and prefecture-level cities.
Systems 2022,10, 205 9 of 22
5.1.1. Overall and Inter-Economic Circle Measurement
From the perspective of Shandong Province as a whole, the specific values and dy-
namic change process of its allocation efficiency values are analyzed in conjunction with
Table 2and Figure 1. During the study period, the overall digital infrastructure allocation
efficiency of Shandong Province first decreased and then increased. The average efficiency
of Shandong Province decreased from 1.186 in 2014 to 1.097 in 2017. With the promulgation
of the Digital Shandong Development Plan in 2018, the average efficiency increased to
1.138 in 2020.
This guiding document forwards the requirements and goals for the construction of
digital infrastructure in Shandong Province, which provides a good construction environ-
ment for the construction of digital infrastructure and encourages all regions in Shandong
to further regard digital infrastructure. This efficiency of digital infrastructure allocation
gradually improves and tends to stabilize.
By comparing the three major economic circles, the digital infrastructure allocation
efficiency of the provincial capital economic circle has drastically changed during the
study period. The Jiaodong and Lunan economic circles were at 1.281 in 2014, and then
experienced a yearly decline until they fell to the same level as their 2017 numbers. In 2018,
these economic circles were influenced by the policies of Shandong Province, hence the
increase in their digital infrastructure allocation efficiency.
In contrast, the allocation efficiency of the provincial capital economic circle continues
to decline to 1.073, widening its gap with the Jiaodong and Lunan economic circles. It
only started to rebound in 2019 and improved to 1.150 in 2020, which is higher than the
average level of the province. The quantified range of digital infrastructure allocation
efficiency of the provincial capital economic circle during the study period is 1.073~1.281.
The digital infrastructure allocation efficiency of the Jiaodong economic circle performed
better during the study period, which was higher than the provincial average during
2016–2019 and increased significantly in 2018 with an allocation efficiency of 1.247, far
ahead of the provincial capital and Lunan economic circles.
However, this also led to a yearly decline in the allocation efficiency of the Jiaodong
economic circle in the two succeeding years which was lower than the 2020 provincial
average. The quantified range of digital infrastructure allocation efficiency in the Jiaodong
economic circle during the study period was at 1.090~1.247. The digital infrastructure
allocation efficiency in the Lunan economic circle was already steadily increasing during
the study period, being lower than the provincial average between 2014 and 2016: equal to
the provincial average in 2017 and higher than the provincial average from 2018 onwards.
The quantified range of digital infrastructure allocation efficiency for the Lunan economic
circle during the study period was from 1.077 to 1.163.
5.1.2. Measurement of Cities within Each Economic Circle
This study measured the level of digital infrastructure allocation efficiency of the
cities included in each economic circle to better analyze the digital infrastructure allocation
efficiency of 16 prefecture-level cities in Shandong Province.
Provincial capital economic circle—during the study period, Jinan, as the core city of
the provincial capital economic circle, had a high value of digital infrastructure allocation
efficiency with a stable trend, which is higher than the average level of the provincial capital
economic circle and the quantified range of allocation efficiency was 1.182~1.307. Dongying
is another city with good performance, which was in an overall rising state during the
study period. It was higher than the overall level of the provincial capital economic circle
since 2015 and reached 1.529 in 2020, much higher than other cities in the provincial capital
economic circle. Its quantified range of allocation efficiency is 1.145~1.529.
Liaocheng also had a large change in allocation efficiency during the study period,
with an inverted V changing mode between 2014 and 2017, which later stabilized with an
overall level close to the average level of the economic circle. Binzhou had a high start
and a low end except for 2014, when it ranked the highest in the province with 2.178. In
Systems 2022,10, 205 10 of 22
the following years, however, it was lower than the average of the economic circle, with
a quantified range of 1.016 to 2.178. The overall situation of the cities of Zibo, Tai’an,
and Dezhou are similar, with the allocation efficiency of Zibo, Tai’an, and Dezhou being
the same value as during the study period. The overall situation of efficiency is also
similar with efficiency values lower than the average level of the economic circle during
the study period, a small changes range, and the quantitative range of allocation efficiency
of 1.012~1.076.
Jiaodong economic circle—like Jinan, as the core city of the Jiaodong economic circle,
Qingdao had high values and stable trends in digital infrastructure allocation efficiency:
higher than the average of the Jiaodong economic circle, with a quantitative range of
allocation efficiency of 1.193 to 1.300. Yantai’s allocation efficiency declined yearly in the
early part of the study period until 2018 when it began to increase significantly to 1.719, but
in 2019 it dropped back to 1.156 where it remained stable. Weifang’s allocation efficiency
showed a wave-like change: first decreasing, then increasing, and then decreasing again,
with a quantified range of 1.009 to 1.151. Rizhao’s allocation efficiency showed a stable
trend during the study period, with a quantified range of 1.055 to 1.523. Last, Weihai’s
allocation efficiency was low, and its efficiency was lower than the average of the Jiaodong
economic circle during the study period.
Lunan economic circle—although Linyi’s allocation efficiency varies more, its over-
all level was above the average level of the Lunan economic circle, with a quantified
range of 1.128 to 1.267. Heze’s allocation efficiency was generally on the rise during the
study period, from 1.069 to 1.355, while Zaozhuang’s and Jining’s allocative efficiencies
were below the average level of the Lunan economic circle. There exists a significant gap
between the allocation efficiency of Jining and other cities in the economic circle. The quan-
tified allocation efficiency of Zaozhuang and Jining ranged from 1.030 to 1.141 and 1.000
to 1.064, respectively.
5.2. Time-Series Variance Analysis
The kernel density distribution curves of digital infrastructure allocation efficiency
in Shandong Province as a whole, and the three major economic circles from 2014 to 2020,
was plotted using Stata16.0 to further study the dynamic characteristics of the time-series
distribution of digital infrastructure allocation efficiency values in Shandong Province. The
details are shown in Figure 2.
At the provincial level, the main peak of the kernel density curve from 2014 to 2020
shows a yearly trend of decreasing height and extending width. This indicates that the
efficiency of digital infrastructure allocation in Shandong Province is gradually improving
macroscopically, and there is a certain magnitude of increase in the absolute difference. The
regional distribution curve of the province lacks smoothness and there is also a stage of
multipolar development.
After the promulgation of relevant policy documents on digital infrastructure con-
struction in Shandong Province in 2018, the main peak of the kernel density curve in 2018
substantially decreased and the change interval shifts significantly to the right, indicating
that the government’s emphasis on digital infrastructure construction directly affects the
efficiency of digital infrastructure allocation in each region and the development of related
work. Additionally, 2014, 2018, and 2020 have an obvious right-trailing phenomenon,
meaning that the gap between cities with higher digital infrastructure allocation efficiency
and the provincial average is gradually widening.
At the level of the three major economic circles in Shandong Province, first, the nuclear
density curve of the provincial capital economic circle increases the main peak height yearly
during 2014–2018, and the change interval shows a left-shifting trend, before leading to a
turn from 2019, when the center of the nuclear density curve and its change interval had an
obvious right-shifting trend, and the main peak height starts to decline significantly with
an increasingly extended width. Simultaneously, in 2014 and 2020, there was an obvious
right-trailing phenomenon, indicating that the efficiency of digital infrastructure allocation
Systems 2022,10, 205 11 of 22
in the provincial capital economic circle shows a changing trend that was decreasing and
then increasing.
Systems 2022, 10, x FOR PEER REVIEW 11 of 23
5.2. Time-Series Variance Analysis
The kernel density distribution curves of digital infrastructure allocation efficiency
in Shandong Province as a whole, and the three major economic circles from 2014 to 2020,
was plotted using Stata16.0 to further study the dynamic characteristics of the time-series
distribution of digital infrastructure allocation efficiency values in Shandong Province.
The details are shown in Figure 2.
Figure 2. Kernel density distribution curve of Shandong Province as a whole and the three major
economic circles.
At the provincial level, the main peak of the kernel density curve from 2014 to 2020
shows a yearly trend of decreasing height and extending width. This indicates that the
efficiency of digital infrastructure allocation in Shandong Province is gradually improving
macroscopically, and there is a certain magnitude of increase in the absolute difference.
The regional distribution curve of the province lacks smoothness and there is also a stage
of multipolar development.
After the promulgation of relevant policy documents on digital infrastructure con-
struction in Shandong Province in 2018, the main peak of the kernel density curve in 2018
substantially decreased and the change interval shifts significantly to the right, indicating
that the government’s emphasis on digital infrastructure construction directly affects the
efficiency of digital infrastructure allocation in each region and the development of related
work. Additionally, 2014, 2018, and 2020 have an obvious right-trailing phenomenon,
meaning that the gap between cities with higher digital infrastructure allocation efficiency
and the provincial average is gradually widening.
At the level of the three major economic circles in Shandong Province, first, the nu-
clear density curve of the provincial capital economic circle increases the main peak height
yearly during 2014–2018, and the change interval shows a left-shifting trend, before lead-
ing to a turn from 2019, when the center of the nuclear density curve and its change inter-
val had an obvious right-shifting trend, and the main peak height starts to decline
Figure 2.
Kernel density distribution curve of Shandong Province as a whole and the three major
economic circles.
Second, the nucleus density curve of the Jiaodong economic circle declined in height
year by year during 2014–2018 with a gradual rightward shift in the change interval,
followed by a rebound in 2019 and a stabilization thereafter, coinciding with the overall
level changes in the province. Due to the incentive effect of digital infrastructure policies,
the nuclear density curve of the Jiaodong economic circle decreased significantly in the
main peak height in 2018 and the width appears significantly extended, meaning that
the allocation efficiency gap among cities in the Jiaodong economic circle is large and
polarization occurred in 2018. This is also the reason for the rebound phenomenon of the
curve in 2019.
Furthermore, the curve shows a bimodal phenomenon in 2019 and 2020, indicating
the trend of polarization within the Jiaodong economic circle. Last, the main peak of the
nuclear density curve of the Lunan economic circle shows a yearly decrease in height
and an increasing extension in width, indicating a gradual macroscopic increase in the
allocation efficiency of digital infrastructure in the Lunan economic circle and a certain
magnitude of increase in absolute differences.
5.3. Spatial Variation Analysis
To reflect the spatial agglomeration and dynamic evolution of digital infrastructure
allocation efficiency values in Shandong Province, this study classified the digital infras-
tructure allocation efficiency values of 16 prefecture-level cities in Shandong Province into
five categories: “very high level”, “high level”, “medium level”, “low level”, and “very
Systems 2022,10, 205 12 of 22
low level” using natural breakpoint method. The natural breakpoint method grades and
classifies according to the law of statistical distribution of values, which maximizes the
difference between classes. The breakpoint itself is a good boundary for grading and the
use of the natural breakpoint method helps to analyze the level of digital infrastructure
allocation efficiency and its structural distribution, thereby reflecting the spatial differences
of regional subjects [
51
,
52
]. Here, the measured digital infrastructure allocation efficiency
values of 16 prefecture-level cities in Shandong Province in 2014, 2017, 2018 and 2020 was
followed to analyze the spatial divergence phenomenon of each prefecture-level city in
Shandong Province in terms of digital infrastructure construction. The detailed situation is
shown in Figure 3: blue represents “very high level”, green represents “high level”, pale
yellow represents “medium level”, orange color represents “low level”, and red represents
“very low level” [52].
Systems 2022, 10, x FOR PEER REVIEW 13 of 23
Figure 3. Digital infrastructure allocation efficiency values in Shandong Province.
From 2014, the overall level of digital infrastructure allocation efficiency in Shandong
Province was commendable—only one city, Zibo, belonged to the “very low level”. Jinan,
Binzhou, Qingdao, and Linyi were at “high” or “very high levels”, and most other cities
were at a “low level”. In 2017, the efficiency of digital infrastructure allocation in Shan-
dong Province declined, with “very high level” and “high level” only being Qingdao and
Jinan, respectively. Meanwhile, the two core cities in Shandong Province with “very low
level” had five cities.
Along with the promulgation of policy documents related to digital infrastructure in
Shandong Province, the efficiency of digital infrastructure allocation in Shandong Prov-
ince increased significantly in 2018. Yantai, Jinan, Qingdao, Linyi, and Heze all improved
to become “high level” or “very high level” cities. However, as of 2017, cities at the “very
low level” still included five cities, which means that the digital infrastructure construc-
tion in Shandong Province has a polarizing trend. After the development from 2018 to
2020, the allocation efficiency of digital infrastructure in Shandong Province in 2020 was
relatively evenly distributed among the five categories, and the gap between different cit-
ies in the allocation efficiency was gradually widened with a certain gradient effect. Ad-
ditionally, it can be seen from Figure 3 that the spatial distribution of digital infrastructure
allocation efficiency values in Shandong Province does not form an obvious high-value
cluster in either year, but is distributed in the form of high and low values in between.
The comparative analysis between the selected years reveals five key points: (1) Jinan
and Qingdao are two core cities in Shandong Province. During the study period, the allo-
cation efficiency of digital infrastructure was at or above the “high level”, but the alloca-
tion efficiency of their surrounding cities was low, especially in Jinan, where the allocation
efficiency of the surrounding cities was basically at or below the “low level”. This means
that Jinan and Qingdao, the two core cities, need to further develop their ability to pro-
mote regional common development. (2) The digital infrastructure allocation efficiency of
Zibo, Dezhou, Tai’an, Weifang, Weihai, and Jining during the study period was basically
below the “medium level”, indicating that the above six cities need to strengthen their
own digital infrastructure allocation efficiency. (3) Zaozhuang, Dongying, and Heze have
steadily improved their digital infrastructure allocation efficiency during the study pe-
riod, especially Heze, which has developed from “low level” in 2014 to “very high level”
in 2020. (4) Yantai made full use of the government’s support to achieve a “very high
level” of digital infrastructure configuration efficiency in 2018. (5) In 2014, Binzhou’s dig-
ital infrastructure configuration efficiency value was at a “very high level”, which was
Figure 3. Digital infrastructure allocation efficiency values in Shandong Province.
From 2014, the overall level of digital infrastructure allocation efficiency in Shandong
Province was commendable—only one city, Zibo, belonged to the “very low level”. Jinan,
Binzhou, Qingdao, and Linyi were at “high” or “very high levels”, and most other cities
were at a “low level”. In 2017, the efficiency of digital infrastructure allocation in Shandong
Province declined, with “very high level” and “high level” only being Qingdao and Jinan,
respectively. Meanwhile, the two core cities in Shandong Province with “very low level”
had five cities.
Along with the promulgation of policy documents related to digital infrastructure in
Shandong Province, the efficiency of digital infrastructure allocation in Shandong Province
increased significantly in 2018. Yantai, Jinan, Qingdao, Linyi, and Heze all improved to
become “high level” or “very high level” cities. However, as of 2017, cities at the “very low
level” still included five cities, which means that the digital infrastructure construction in
Shandong Province has a polarizing trend. After the development from 2018 to 2020, the
allocation efficiency of digital infrastructure in Shandong Province in 2020 was relatively
evenly distributed among the five categories, and the gap between different cities in the
allocation efficiency was gradually widened with a certain gradient effect. Additionally, it
can be seen from Figure 3that the spatial distribution of digital infrastructure allocation
efficiency values in Shandong Province does not form an obvious high-value cluster in
either year, but is distributed in the form of high and low values in between.
The comparative analysis between the selected years reveals five key points: (1) Jinan
and Qingdao are two core cities in Shandong Province. During the study period, the
Systems 2022,10, 205 13 of 22
allocation efficiency of digital infrastructure was at or above the “high level”, but the
allocation efficiency of their surrounding cities was low, especially in Jinan, where the
allocation efficiency of the surrounding cities was basically at or below the “low level”. This
means that Jinan and Qingdao, the two core cities, need to further develop their ability to
promote regional common development. (2) The digital infrastructure allocation efficiency
of Zibo, Dezhou, Tai’an, Weifang, Weihai, and Jining during the study period was basically
below the “medium level”, indicating that the above six cities need to strengthen their
own digital infrastructure allocation efficiency. (3) Zaozhuang, Dongying, and Heze have
steadily improved their digital infrastructure allocation efficiency during the study period,
especially Heze, which has developed from “low level” in 2014 to “very high level” in
2020. (4) Yantai made full use of the government’s support to achieve a “very high level”
of digital infrastructure configuration efficiency in 2018. (5) In 2014, Binzhou’s digital
infrastructure configuration efficiency value was at a “very high level”, which was also
the city with the highest configuration efficiency value during the same year. However, in
the following years, Binzhou’s configuration efficiency value showed a downward trend
and remained at a “very low level”. Therefore, there is a need to fully summarize the
shortcomings in the construction process and learn from the advanced experience of the
leading regions.
5.4. Comprehensive Analysis of Digital Infrastructure Allocation Efficiency in Shandong Province
The analysis of digital infrastructure allocation efficiency and spatial and temporal
differences in Shandong Province shows that its overall digital infrastructure allocation
efficiency has been steadily increasing, but varies widely among cities while showing
a multipolar development. There is no high-value agglomeration area in the province.
There is instead a form of distribution between high- and low-value. This section further
summarizes the analysis above and the allocation efficiency values of digital infrastructure
in each city as reflected in each chart. The specific analyses are as follows:
(1) As shown in Table 2and Figure 1, Jinan and Qingdao, the two core cities in Shandong
Province, have achieved good results in digital infrastructure construction, the digital
infrastructure allocation efficiency values are both at “high” or “very high level”,
and the growth rate is relatively stable. However, Figure 3shows that the digital
infrastructure configuration level of the cities around Jinan and Qingdao is relatively
poor. For example, the configuration efficiency values of Zibo, Tai’an, Binzhou, and
Weifang are relatively low. This shows that Jinan and Qingdao need to further play
their role as radiation drivers, promote regional coordinated development, form high-
value clusters, and promote the common progress of digital infrastructure construction
in the province.
(2)
Figures 2and 3show that after Shandong Province issued relevant policies on digital
infrastructure construction in 2018, all cities positively responded and achieved good
construction results. For example, the overall digital infrastructure configuration
efficiency of the Jiaodong Economic Circle and the Southern Shandong Economic
Circle was improved in 2018, especially in Yantai, where the configuration efficiency
value rose from “low level” in 2017 to a “high level” in 2018. Simultaneously, the value
of digital infrastructure allocation efficiency in some regions show a downward trend.
In 2018, the average allocation efficiency of the provincial capital economic circle
showed a reverse growth, and the allocation efficiency of Liaocheng, previously in the
“medium level”, dropped to a “low level”. Therefore, relevant local governments need
to further clarify the importance and necessity of digital infrastructure construction,
fully consider the heterogeneity of regional economic and social development and
resource endowment, and formulate scientific and reasonable digital infrastructure
allocation goals and construction paths.
(3)
From Figures 1and 3, it is evident that during the study period, the digital infras-
tructure allocation efficiency of Zibo, Dezhou, Tai’an, and Binzhou is lower than the
Systems 2022,10, 205 14 of 22
average level of the provincial capital economic circle from 2015 to 2020. Weifang and
Weihai are lower than the average level of the Jiaodong economic circle from 2015 to
2018 and in 2020. Jining and Zaozhuang are lower than the average level of the Lunan
economic circle. Also, the digital infrastructure allocation efficiency values of these
cities are basically at the “lower level” or “very low level”. This shows the obvious
gap and imbalance between many low-level areas in Shandong Province in terms of
digital infrastructure construction. Therefore, Shandong should further increase the
support for low-level areas and improve the level of digital infrastructure therein.
6. Recommendations
The study measures the efficiency of digital infrastructure allocation in Shandong
Province and analyzes its spatial and temporal differences and potential problems. To
address the potential problems, it proposes suggestions for improvement on four specific
aspects: government attention, policy heterogeneity, focus on the development of low-level
areas, and promotion of regional synergistic development. In addition, this study expands
each recommendation to an international context, providing a basis for decision-making in
more countries and regions.
6.1. Promote Synergistic Development and Common Progress
During digital infrastructure construction, we should promote institutional coordi-
nation to improve the overall common development of Shandong Province. However,
the current level of digital infrastructure configuration in Shandong Province remains to
form a high-value cluster, thereby needing the strengthened policy guidance of regional
coordinated development. Therefore, this study puts forward targeted suggestions from
three specific aspects: upgrading industrial digitalization, cultivating human capital, and
strengthening digital rural construction to promote the construction of digital infrastructure
in Shandong Province and achieve coordinated regional development.
(1)
Enhancement of industrial digitization
During digital infrastructure construction, the focus should be on the digital transfor-
mation of traditional industries. Relevant departments and enterprises must use digital
technology as support to transform traditional industries and carry out technological inno-
vation, thereby promoting industrial transformation with technology and helping achieve
high-quality regional development. Along with promoting the digital transformation of
traditional industries, relevant departments and enterprises also need to continuously in-
crease the intensity of investment in research and development, strengthen the research and
development of key core technologies for digital infrastructure, and improve the efficiency
of iterative updating of digital-related technologies.
As a mediating variable between digital infrastructure and high-quality development,
digital capacity is pivotal to high-quality development, hence the need to focus on regional
digital capacity. Simultaneously, relevant departments must strongly support the develop-
ment of digitalization-related enterprises, for example, by giving certain financial subsidies
and tax incentives.
(2)
Cultivating human capital
Digital infrastructure construction needs digital industry talents, and digital talents are
one of today’s important influencing factors of high-quality development. This underlines
the need to establish a perfect talent training system to support and encourage relevant
enterprises and universities to cultivate digital talents with broad industry application
prospects. This in turn strengthens the support for innovative talents to lay high-quality
development for the region’s solid digital foundation.
Additionally, governments at all levels should break institutional barriers to allow the
cross-regional flow of digital talents, promote the cultivation and introduction of talents
by providing a good material foundation and environment, play to the strengths of each
region, provide more incentivizing policies and full autonomy to capable talents in relevant
Systems 2022,10, 205 15 of 22
fields, stimulate their innovative initiatives and enthusiasm, promote the concentration of
human capital, and ultimately accelerate the construction of regional digital infrastructure
and high-quality development.
(3)
Strengthen the construction of digital countryside
Shandong Province is a large agricultural province, hence rural areas and populations
account for a relatively large proportion. Therefore, to achieve a comprehensive high-
quality development and realize a “strong digital province”, we should coordinate and
promote the construction of the countryside and collaborate to promote the integrated
digital development of both urban and rural areas. These include policies to accelerate the
extension of digital infrastructure to the countryside, improve the supply of information
services in rural areas, promote the free flow of urban and rural elements in both direc-
tions, and reasonably allocate public resources to form a digital urban–rural integration
development pattern with urban and rural areas and common construction and sharing.
Digital infrastructure is the foundation of digital countryside construction, and its
popularity and performance equipment determine the breadth and depth of digital econ-
omy development, which has a strong positive spillover. Therefore, when promoting the
construction of rural digital infrastructure, it should be executed in an orderly fashion;
giving priority to areas with large population densities but weak digital infrastructure
allocation. The government should include rural digital infrastructure projects into the
project pool and arrange funding budgets to provide a good environment for the use of
digital technology to be carried out and applied in rural areas.
Governments should also promote the comprehensive application of new-generation
information technology in agricultural and rural economic development by strengthening
the digital integration of urban and rural areas, enhancing the level of rural digitalization
and informatization, and accelerating the digital transformation and restructuring of the
original information infrastructure.
(4)
Policy Extension
The unbalanced development of the world’s regions is a basic economic law, and
the development gap between regions has always existed, and how to narrow this gap
is one of the major challenges facing all countries and regions at present. Governments
need and take more effective measures to control regional disparities and prevent social
unrest that may result from widening disparities. In addition, it is necessary for the
international community to cooperate in promoting coordinated regional development and
controllable regional disparities, jointly coping with the world’s increasingly serious social
contradictions, and at the same time opening up new ways and fields for the world’s future
economic development.
6.2. Further Regard to the Role of the Government and Give Full Play to Its Advantages
The government plays an extremely important role in the process of digital infras-
tructure construction. However, in the context of the National 14th Five-Year Plan, which
explicitly proposes to accelerate the construction of digital infrastructure, local governments
in the provincial capital economic circle do not pay enough attention to the construction
of digital infrastructure. Therefore, this study proposes recommendations to these units
on three contextual aspects: digital infrastructure construction environment, government
financial support, and promotion of enterprise digitalization process.
(1)
Digital infrastructure construction environment
The prerequisite for local cities to improve the level of digital infrastructure con-
struction and accelerate the process of urban digitization is to provide a suitable policy
environment for the construction of digital infrastructure. First, the Shandong provincial
government should insist on optimizing the digital infrastructure construction environment,
continuously improve the top-level design, establish and improve the coordination and
promotion mechanism, and accelerate the cultivation and growth of digital infrastructure
Systems 2022,10, 205 16 of 22
public service platforms. Next, local municipal governments should follow the construction
requirements and development goals of digital infrastructure and develop strategically
oriented short-term and long-term digital infrastructure construction programs according
to their own construction situation, therein forming a systematic construction in multiple
fields and at multiple levels.
(2)
Government financial support
Local governments should also strengthen policy support for digital infrastructure con-
struction in their regions, reasonably allocate and utilize national subsidy funds, financial
funds at this level, government bond funds, etc. They should also fully utilize government
macro-regulation and market competition mechanisms, implement more policy tilts, tax
preferences and financial subsidies, and widely absorb social capital to participate in digital
infrastructure construction. These undertaking must also be fulfilled while guiding local
industrial development investment funds to invest in digital infrastructure construction.
(3)
Promote the digitalization process of enterprises
When formulating policies on digital infrastructure, the government should consider
the characteristics of different enterprises as far as possible. Enterprises with a high degree
of informatization, relatively smooth digital transformation, and relatively intensive digital
technology can realize enterprise upgrading more effectively by building an open, secure,
and good digital ecosystem and using network externalities to adjust their business models
in a timely and appropriate manner.
Enterprises with poor informatization, high difficulty in digital transformation, and
less digital technology, should be supported by the government through development
and application scenarios that integrate new-generation information technology with
enterprise transformation and upgrading. Moreover, the government can select key en-
terprises with better digital foundations and greater influence to carry out pilot work, tap
the leading experience, promote the process of enterprise digitalization, and help enter-
prises integrate innovation and efficient operation, in order to drive the construction of
digital infrastructure.
(4)
Policy Extension
Experience from all over the world shows that although the main body of digital
infrastructure and industrial digitalization construction is enterprises or other auxiliary
organizations, the government has a wide range of roles in the construction process, and in
many cases even plays a central role. When the government formulates support policies
for digital industries and industrial digitalization, it should reduce information asymmetry
and establish a cooperation platform between enterprises and between enterprises and
between enterprises and governments, so as to improve the efficiency of resource input and
resource use. In addition, when formulating policies, governments of various countries
and regions should fully consider the negative effects of policies on the market, so when
formulating relevant policies, local governments need to make it clear that the policies are
based on improving social livelihood, so that the positive effects of policies are significantly
greater than their negative effects.
6.3. Focus on Regional, Inter-Policy Heterogeneity
Accelerating the construction of digital infrastructure is a national policy and social
consensus, and Shandong Province actively responds to the national policy by promul-
gating the Digital Shandong Development Plan to promote the construction of digital
infrastructure in the province. Local governments in Shandong Province should for-
mulate policies appropriate to the construction of local digital infrastructure based on
this document.
(1)
Due to the certain heterogeneity of resource endowment and economic development
level of each city, there are certain differences in the construction content, construction
Systems 2022,10, 205 17 of 22
mode, and construction stage of each city in the process of building digital infras-
tructure. The construction direction and construction path must be determined by
combining the characteristics of the population, background, and informatization
foundation of the region. Therefore, government departments at all levels should
consider the heterogeneous characteristics of economic and social development in
different regions when formulating digital infrastructure construction plans, based on
the actual situation, to carefully sort out the needs, formulate digital infrastructure
construction plans that meet the actual local situation, and essentially optimize the
overall planning of digital infrastructure construction according to local conditions.
(2)
Government departments at all levels should also strengthen the convergence of
national strategies and local policies, enhance synergy and linkage, and establish
different cycles of construction plans to avoid piling up development plans and
duplication of construction.
(3)
Based on regional differences, the contents and ways of digital infrastructure con-
struction differ from place to place. Thus, different standards should be used to
measure the level of digital infrastructure construction, and the quality of local digital
infrastructure construction should also be guaranteed by extending the construction
cycle in less developed areas.
(4)
Policy Extension
Due to the existence of the global digital divide, the content, construction methods
and stages of digital construction in different countries and regions are different, so when
formulating relevant policies, local governments should base themselves on the actual
situation, carefully sort out the construction needs, establish an institutional framework
that is in line with the local and the times, and fully consider the heterogeneity between
regions and policies.
6.4. Increase Support to Enhance the Development of Low-Level Areas
Due to certain differences in the development degree between different cities, Zibo,
Dezhou, Weifang, Zaozhuang, Jining, and other regions are basically at a “low level” or
“very low level” in terms of digital infrastructure construction and allocation efficiency.
To comprehensively promote digital infrastructure construction in Shandong Province,
recommendations for cities with low efficiency are proposed herein.
(1)
In view of the backwardness of digital infrastructure allocation efficiency in the above
cities, local governments should explore the potential problems of backwardness, accel-
erate digital infrastructure construction according to local conditions, comprehensively
reshape production relations, release digital productivity, and ensure the sustainable
growth of digital infrastructure allocation efficiency. This forces them to focus on the
construction quality and investment efficiency of digital infrastructure construction.
Digital infrastructure construction is mainly concentrated in the tertiary industry
and is the first to integrate with the tertiary industry before penetrating primary and
secondary industries. For some regions with poorly developed secondary industries,
they can cross the short board of secondary industries, give full play to their own advan-
tages, and build digital infrastructure by developing the tertiary industries with small
investment, light volume, good efficiency, and large employment capacity to achieve high-
quality development.
(2)
For cities with poorly developed digital infrastructure, it is relatively easy to expand
the scale and application of digital technology, allowing them to fully learn from the
advanced technology and construction system of better-developed cities, maintain
effective communication and close exchange with better-developed cities, promote
the technology transfer of digital technology from high-level areas to low-level areas,
and improve the digital infrastructure construction of poorer cities.
Systems 2022,10, 205 18 of 22
(3)
To prevent the continuous expansion of the Matthew effect (a phenomenon that the
strong are stronger and the weak are weaker.), the provincial governments should
shift policy resources towards cities that need to be further improved for digital
infrastructure configuration efficiency, and make full use of the demonstration and
signaling effects to enhance the financial capital, human capital, and physical capital
of less-developed regions. This improves the solid foundation guarantee for the
digital infrastructure construction of these cities.
(4)
Policy Extension
The global digital divide refers to the trend of further polarization of the information
gap and the gap between rich and poor due to different levels of ICT ownership and
application in the global digitalization process. This trend has intensified the polarization
between the two levels of the world, resulting in a serious shortage and shortage of digital
literacy and digital technology in underdeveloped countries and regions, and seriously
inhibiting the space for the future development and growth of the digital economy in
backward regions. For countries and regions with developed digital levels, they should take
the initiative to assume the core role of governing the global digital divide and supporting
the digital construction of backward regions, and bridge the digital divide and improve the
digital level of backward countries and regions by increasing financial support and technical
assistance, and vigorously promoting digital infrastructure construction and digital talent
training. In addition, the key to whether backward regions can continuously narrow the
digital divide lies in the support of the country and region for digital construction, so
backward regions should take the initiative to summarize the shortcomings of local digital
construction and learn from the advanced experience of leading regions.
7. Conclusions
Digital infrastructure is an important strategic deployment to adapt to the develop-
ment of the new era, which adds new momentum to the construction of a digital-driven
regional innovation system, the overall improvement of the effectiveness of the national
innovation system, and thus accelerate the construction of digital China and a strong
network country. Shandong Province actively responds to the national policy, puts forward
the development goal of “digital infrastructure in the forefront”, and is committed to build-
ing up a digital infrastructure system with ubiquitous connectivity, efficient coordination,
full domain awareness, intelligent integration, security and trustworthiness, creation of a
national information infrastructure pioneer area and convergence infrastructure demonstra-
tion area, and improving the digital infrastructure construction to promote the realization
of high quality.
In the process, it is inevitable that there are problems such as uncoordinated regional
development, and lack of targeted policies. A problem therefore is finding ways to solve
these problems and promote Shandong Province to achieve the strategic goal of a “strong
digital province”.
This study takes 16 prefecture-level cities in Shandong Province and constructs a digital
infrastructure allocation efficiency measurement index system based on the principles of
scientificity, systematization, independence, and operability, takes into account the actual
situation in Shandong Province, adopts the methods of non-expectation super-efficiency
SBM model and kernel density estimation, measures and analyzes the spatial and temporal
differences of digital infrastructure allocation efficiency in 16 prefecture-level cities in
Shandong Province, and forwards policy recommendations for problems of uncoordinated
regional development, insufficient government attention, lack of policy targeting, and more
low-level areas.
This research has three contributions: First, it fully considers the path of digital
infrastructure construction and its impact on society and economy, and identifies the inputs
of two aspects of staff and financial, digital infrastructure, as well as the outputs of four
aspects of social, economic, technological and social injustice, which provides important
insights for promoting digital infrastructure construction. Secondly, the selected method
Systems 2022,10, 205 19 of 22
can reflect the changes in the level of digital infrastructure construction and allocation
efficiency in various regions in recent years, and help identify problems such as shortage of
resource allocation, uncoordinated regional development, and gaps between policies and
their implementation. Finally, intuitive data and graphs and detailed analysis results can
provide guidance and solid basis for decision-makers in various regions to formulate
digital infrastructure-related policies and resource allocation, so as to connect theory
and practice.
The research ideas, research methods, and countermeasure suggestions of this study
also provide references for the construction of digital infrastructure and subsequent related
studies. However, because digital infrastructure is in the construction and development
stage, the amount of data on indicators related to digital infrastructure is relatively small.
Hence, subsequent research can further improve the measurement index system, optimize
the measurement system of digital infrastructure allocation efficiency, and enhance the
allocation efficiency of digital infrastructure.
Author Contributions:
Conceptualization, X.C. and L.W.; methodology, L.W. and S.W.; software,
X.C. and S.W.; validation, X.C., L.W. and S.W.; formal analysis, X.C. and S.W.; investigation, X.C. and
S.W.; data curation, S.W.; writing—original draft preparation, X.C., L.W. and S.W.; writing—review
and editing, J.Š., J.G. and M.J.S.; visualization, S.W. All authors have read and agreed to the published
version of the manuscript.
Funding:
The funding of this study was supported by the Special Project of Shandong Social Science
Planning Fund Program (NO.21CSDJ03).
Institutional Review Board Statement: Not applicable.
Informed Consent Statement: Not applicable.
Data Availability Statement: Not applicable.
Acknowledgments:
The authors would like to thank the anonymous referees for their valuable
comments and suggestions. We are willing to share the data set and estimations codes of this study
with those who wish to replicate the results of this research.
Conflicts of Interest: The authors declare no conflict of interest.
Appendix A
Research method specifics.
The non-expectation super-efficiency SBM model with the help of kernel density esti-
mation was used, to measure the efficiency of digital infrastructure allocation in prefecture-
level cities in Shandong Province and analyze their spatial and temporal differences, which
are expressed as follows:
(1)
Non-expectation super-efficiency SBM model
minρ=
1
m∑m
i=1x
xik
1
r1+r2∑r1
s=1yd
yd
sk
+∑r2
q=1yu
yu
qk (A1)
Which also satisfies:
x≥∑n
j=1,j6=kxijλj
;
yd≤∑n
j=1,j6=kyd
sj λj
;
yd≥∑n
j=1,j6=kyd
qj λj
;
x≥xk
;
yd≤yd
k
;
yu≥
yu
kλj≥0; i =1, 2, · · · ,m; j =1, 2, · · · ,n; s =1, 2, · · · ,r1; q =1, 2, · · · ,r2.
Where, ρis the digital infrastructure allocation efficiency. nis the number of cities. m
is the number of inputs.
r1
and
r2
represent the desired and undesired outputs, respectively.
x
,
yd
,
yu
are the elements in the corresponding input matrix, desired output matrix and
undesired output matrix, respectively.
Systems 2022,10, 205 20 of 22
(2)
Kernel density estimation method
Kernel density estimation generates a smooth surface reflecting continuous changes
in the density of point data in a plane space. In a two-dimensional space, various cases of
calculation methods exist for kernel density estimation. The calculation formula chosen in
this study is as follows:
ˆ
f(x,y)=1
nh2∑n
i=1Kx−xi
h,y−yi
h(A2)
where
ˆ
f(x,y)
is the kernel density estimate of point (x,y).nis the total amount of sample
data in the study area. his the bandwidth. Kis the kernel function.
(xi,yi)
is the coordinate
of the ith sample.
To ensure the reasonability of the kernel density estimation, the kernel function must
satisfy the following three conditions, as shown in Table A1.
Table A1. Kernel function conditions.
Conditions Formula
Symmetry K(x) = K(−x);(x∈R)
Homogeneity R+∞
−∞K(x)dx =1
Non-negativity K(x)>0; (x∈R)
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