mathematics

Article
Advanced Modelling of the Interplay between Public
Governance and Digital Transformation: New Empirical
Evidence from Structural Equation Modelling and Gaussian
and Mixed-Markov Graphical Models
Andreea-Florentina Cr´ciun 1 , Alexandra-M´d´lina T, ´ran 1, * , Grat, iela Georgiana Noja 2 ,
Marilen Gabriel Pirtea 3 and Raluca-Ioana R´c´t´ian 1

1 Doctoral School of Economics and Business Administration, West University of Timisoara,

16 Pestalozzi Street, 300115 Timisoara, Romania
2 Department of Marketing and International Economic Relations, Faculty of Economics and Business
Administration, West University of Timisoara, 16 Pestalozzi Street, 300115 Timisoara, Romania
3 Department of Finance, Faculty of Economics and Business Administration, West University of Timisoara,
16 Pestalozzi Street, 300115 Timisoara, Romania
* Correspondence: alexandra.taran@e-uvt.ro

Abstract: The research conducted in this paper aims to appraise the interlinkages between public
governance and digital transformation at the level of the European Union. We employ two advanced
approaches to modelling longitudinal data compiled at the level of the EU-27 Member States during
the 2010–2021 period, namely, structural equation modelling and Gaussian and Mixed-Markov
graphical models. The main results indicate positive impacts on government effectiveness arise from
the human capital involved in complex activities that engage the use of digital services, e-government
users, and integration of digital technologies, and the effect of demands and supplies of digital public
services using open data. This further supports the government’s capabilities in enforcing regulations
Citation: Crăciun, A.-F.; T, ăran, A.-M.;
and policies to control corruption and sustain the achievement of digital skills, at least at a basic level,
Noja, G.G.; Pirtea, M.G.; Răcătăian,
by the entire society. Moreover, good perceptions and a higher degree of confidence in the rules of
R.-I. Advanced Modelling of the
law have a positive influence on the need for connectivity of digital services, especially the supply
Interplay between Public Governance
and Digital Transformation: New
side of fixed and mobile broadband. Lastly, a relevant impact of regulatory quality is identified in
Empirical Evidence from Structural the digital connectivity of broadband infrastructure, which is enclosed by the public governance
Equation Modelling and Gaussian representative indicators under the influence of a stronger integration of digitalisation.
and Mixed-Markov Graphical
Models. Mathematics 2023, 11, 1168. Keywords: public governance; digital transformation; econometric modelling; European Union countries
https://doi.org/10.3390/
math11051168 MSC: 91-10; 91B82

Academic Editor: Alexander Zeifman

Received: 23 January 2023

Revised: 22 February 2023 1. Introduction
Accepted: 22 February 2023
The World Bank introduced the concept of “governance” as the manner through which
Published: 27 February 2023
governments succeed in managing their political authority in the efficient administration
of resources to support economic and social development while also achieving its actions
within the society [1]. Furthermore, “good governance” is considered an expression of the
Copyright: © 2023 by the authors.
democratic capacities of institutions, and illustrates a contemporary management concept
Licensee MDPI, Basel, Switzerland.
approach that has recently received an increased emphasis regarding public sector effective-
This article is an open access article ness and efficiency; it also includes a significant application in public sector organisations
distributed under the terms and and various effects in different organisational settings [2].
conditions of the Creative Commons Consequently, after the COVID-19 pandemic and other unpredictable circumstances,
Attribution (CC BY) license (https:// the need to implement and adapt to fast digital transformations, along with radical solu-
creativecommons.org/licenses/by/ tions, has led to considering “good governance” as a complex condition for governments
4.0/). and public institutions in offering and improving services in an integrative manner that can

Mathematics 2023, 11, 1168. https://doi.org/10.3390/math11051168 https://www.mdpi.com/journal/mathematics

Mathematics 2023, 11, 1168 2 of 25

satisfy the stakeholders and fulfil objectives that can benefit the whole society, by constantly
defining strategic policies, re-examining past policies, and constantly adopting innovative
techniques and methods [3]. Moreover, the primary forms and characteristics generally
manifested refer to openness, efficiency, responsiveness, transparency, active participation,
respect for the rule of law, equality, and mutual agreement [4].
Altogether, depending on the programs and activity priorities on which they are oper-
ating, several international institutions actively discuss and promote the concept of good
governance within the worldwide community [5–8]. Similarly, the digital transformation
of public governance also leads to worldwide adoption and integration difficulties with a
high level of significance, taking into account the multiple effects and different impacts that
can be produced throughout the entire society. Nevertheless, digital technologies depict
an essential element of digital transformation that comprises all the radical and profound
changes from the level of society [9,10]. The digital transformation of public governance
can be considered a multi-beneficial process that can offer institutions the opportunity to
innovate through digital technologies by creating and sustaining plans, strategies, and
actions that allow embracing the implications and benefits of digital technology [11]. Digital
technology needs data privacy, user protection, and robust cyber security provisions com-
bined with a regulatory framework that fosters innovation and spurs public and private
sector performance and growth.
The European Commission affirms the link between public governance and digital
transformation through Europe’s Digital Decade [12], which defines a paradigm that sus-
tains the digital transformation of public services. Furthermore, the digital transformation
of public governance approaches at the European Union Member States (EU-27 MSs) level
has been debated previously within the existing literature but, as far as we know, their
integrative impact has yet to be discussed.
In this currently complex framework, the present research aims to assess in a new
advanced modelling approach the interlinkages between public governance (captured
by World Governance Indicators—WGIs) and digital transformation (namely, the Digital
Economy and Society Index (DESI) dimensions and subdimensions, and broadband-specific
indicators), considering the EU-27 Member States, for the period between 2010–2021. We
specifically target answering the following research question: is there a notable relationship
between public governance and digital transformation?
To achieve this aim, the methodological endeavour applied consisted of two advanced
econometric procedures that capture an integrative measurement approach (direct, indirect,
and total) of the interplay between public governance and digital transformation through
structural equation modelling (SEM) and Gaussian and Mixed-Markov graphical models
(GGMs, MGMs, respectively).
The subject of digital transformation offers new research directions, and researchers
are focusing on different aspects of the process, such as effects, sectors, and methods of
measuring the implementation of digitalisation [13,14]. The scientific literature reveals that,
regarding the adoption of digitalisation, the authorities were limited to the options that
the pandemic period offered them because the emphasis was on rapid implementation in
response to current needs, and was not based on its efficiency or results expected under
optimal implementation conditions [15]. In addition, other studies have shown that external
factors determine the digital transformation of public governance, instead of the intrinsic
desire of governments to automate internal processes or to increase the range of digital
products offered to citizens [16]. The choice of our research topic was also motivated by
the fact that the governmental digital transformation (DGT) process was accelerated in the
context of the COVID-19 crisis, its intensity being different from country to country, and
the implications generated regarding public governance and citizens were less addressed.
Our study outlines an overview of the relationship between public governance and digital
transformation by analysing a new dataset that extends over a recent period of time, which
also includes the pandemic period, but is not limited to this.
Mathematics 2023, 11, 1168 3 of 25

Considering the ongoing unexpected circumstances (pandemic crisis with COVID-

19, global wars, climate change), our results complement the specialised literature in the
field with the formation of useful guidelines, recommendations, or suggestions that may
be valuable for decision makers, different national strategies, or common international
guidelines regarding the digital transformation of public governance in EU-27 Member
States (specific ways through which digital transformation enables new ways of public
governance functioning). Additionally, to strengthen the knowledge in the scientific field,
this research examines important issues and contributes with results that can sustain further
research on the discussed topic.
Our paper offers new insights that can provide the grounding to identify the essential
conclusions, policy recommendations, mechanisms, and strategies that need to be designed,
adopted, and implemented within all the European Union Member States (EU-27 MS) to
support the integration of digital technologies in public sector governance, with multi-
ple benefits for society as a whole, focusing on digital transformation, for good public
governance, as well as for the well-being of the community.
One of the purposes of this paper is to present a complex empirical analysis that is
performed to identify and highlight the impact and effects of digital transformation and
broadband infrastructure on public governance in the EU-27 Member States. In addition,
this paper investigates the effects of digital transformation and broadband infrastructure
on public governance. It also investigates future answers to the continuous improvement
in the public sector from the perspective of covering existing gaps and increasing responses
to various shocks that occurred over time, which underlined the need to integrate digital
tools and broadband infrastructure elements. Moreover, this study also aims to identify
the multiple effects of digital transformation on public governance and underline how to
provide citizens with high-quality digital services, characterised by speed, easy access, and
equity, in a framework of governance that can be characterised by an essential feature of
openness towards efficient cooperation between the public sector and citizens. The digital
transformation and broadband infrastructure are considered facilitators that can have a
significant positive impact on aggregate levels of economic growth and revolutionise public
governance at the level of EU Member States [17–19].
Accordingly, this paper highlights how digital transformation can contribute to foster-
ing the quality of public governance through a performant broadband infrastructure by
widening its accessibility, application, and equity, and how this can reinforce the knowledge
of the integration of digital tools and broadband elements in public governance, which are
often addressed in the new era of digital transformation of the public sector. In addition,
in practical terms, our results provide indications about digital transformation of public
governance initiatives that can support the plan for digitalisation that the European Union
Member States must implement. Therefore, based on these facts and given the results
obtained, our research contributes several components to the existing literature and brings
new evidence on the perspective of integration of digital tools and high-quality broadband
infrastructure in public governance. First, it can be argued that our research contributes
to the existing literature and brings new insights regarding the interlinkages between
digitalisation-specific indicators and broadband infrastructure representative variables in
public governance coordination. Furthermore, most of the previous research studies are
focused only on the digital transformation of public governance dimensions, with a narrow
focus only in specific European countries, such as Italy [20], Germany [21], Sweden [22],
Portugal [23], Denmark [24], or Greece [25], while fewer papers have focused on and
analysed a panel comprising many countries from the EU-27, which is nuanced aspect of
the novelty of our study. Secondly, our study contributes to the existing literature with a
new empirical framework designed as part of an integrative and updated assessment of
the effects generated by the digital transformation. This framework comprises DESI dimen-
sions and subdimensions and some specific broadband variables in the public governance
dimension represented by worldwide governance indicators and based on an empirical
approach. In contrast, other studies from the existing literature have only focused on a qual-
Mathematics 2023, 11, 1168 4 of 25

itative assessment of the current state of knowledge in the field [26]. Third, the reliability of
our findings is checked by applying two advanced econometric models, namely, structural
equation modelling (SEM), in order to appraise overall interlinkages among considered
variables; and Gaussian and Mixed-Markov graphical models, which allowed us to observe
the intensity and configuration of the interlinkages between all considered variables for all
the EU-27 countries.
Therefore, this research study entails a new in-depth perspective and enhances the
existing body of literature with an integrative assessment of the interlinkages between
public governance and digital transformation. This is achieved by applying two advanced
econometric techniques to create accurate and robust results. This provides a clearer picture
of the tailored specific strategies that the EU-27 states can adopt to rethink the digital
transformation in public governance.
The structure of this research investigation is organised as follows: Section 2 reviews
the relevant literature and presents the derivation of our hypotheses. The data and the
methodology applied are introduced in Section 3. Section 4 reports the main findings and
interprets the empirical outcomes with substantial discussions. Section 5 offers conclusive
notes, followed by additional information in Appendix A, where the empirical results
are detailed.

2. Literature Review
The subject of public governance and digital transformation has been addressed in
several studies [27–30]. The analysis of the existing literature highlighted concepts such as
“smart cities”, “smart citizens”, or “smart governance”, and outlined the state of knowledge
regarding the implications of digital transformation for public governance [31–33]. The
studies selected in the systematic analysis are divided into studies that conceptually define
the elements involved in the digitalisation process of public governance, and empirical
studies that comprise analysis models used to identify the implications and effects of
these elements. Sarker, Wu, and Hossin defined smart governance as a system comprising
components that quickly respond to social changes generated by a complex environment,
effectively using the available resources to make appropriate decisions and achieve social
goals [31]. Smart governance at the local level can embrace the form of smart cities.
Information and Communication Technologies are considered globally to be the basis of
a smart city. Nonetheless, the essential component of ICT is the processing of data from
various sources to ensure the city’s sustainability via its management and development [32].
Public governance represents the sum of processes, decisions, and implementations carried
out by specific actors, where the main actor is the government. Digital transformation refers
to the entire governance process, from interacting with citizens to implementing public
policies or fulfilling socioeconomic objectives [34]. In addition, the digital transformation
of public governance has led to the formation and development of the concept of “good
governance”. Good governance suggests the characteristics that governance must achieve
in the context of digitalisation, and the essential features of good governance refer to respect
for the rule of law, participation, efficiency, and equity [35].
Caragliu, Del Bo, and Nijkamp emphasise that the mere adoption of Information
and Communication Technologies fails to convert a city into a smart city. Many research
studies [32,36] affirm that a smart city must have a set of characteristics that include the
following: (i) the efficient use of technological infrastructure in the political, economic,
social, and development processes; (ii) the stimulation of business development; (iii) the
reduction in disparities between social classes regarding the use of technology and public
services; (iv) the emphasis on the role of creativity and high technology for long-term
development; (v) the development of the role of social relations in urban development;
and (vi) the increase in sustainability. These elements are part of a smart city and protect
natural resources [36]. Each institution plays a crucial role in smart city development, and
their level of involvement leads to different results. The more essential the roles played
by local government in implementing projects, the more emphasis will be placed on these
Mathematics 2023, 11, 1168 5 of 25

institutions’ political goals or interests. The national government must fulfil its role as a
regulator and mediator to ensure the standardisation of development policies [37]. The
dimensions of the previously described terms reflect the potential and purpose that digital
technology must have in the governance process [38].
Thus far, a number of research studies have included specific theoretical frameworks
that address a series of conceptual terms regarding both public governance and digital
transformation, by considering them under different meanings with multilevel measure-
ments [39–41].
In the existing literature that addresses this subject, a series of specific terms can be
identified, as detailed and explained in Table 1.

Table 1. Terms and expressions that form the theoretical framework specific to the process of digital
transformation of public governance.

The Conceptual Framework for Digital Transformation

Expression Reference Definition
“an advanced form of society following agricultural society,
Smart society [42] industrial society, and information society, with digital data
processing system as its main carrier”
“a smart city is a city which invests in ICT enhanced governance and
participatory processes to define appropriate public service and
Smart city [43,44] transportation investments, that can ensure sustainable
socioeconomic development, enhanced quality-of-life and intelligent
management of natural resources”
“smart citizen produces and uses information through systems
Smart citizen [45]
efficiently and sustainably in order to form smart cities”
“a managerial and service delivery point of view of government
Smartness framework [38] initiatives with four dimensions: efficiency, effectiveness,
transparency, and collaboration”
“a system of economic, social and cultural relations based on the use
Digital economy [46,47]
of digital information and communication technologies”
“the totality of cable, fibre and telecommunications networks, data
Digital infrastructure [48] centres and front-end devices that can be manipulated and designed
to achieve the desired strategic results”
The Conceptual Framework for Public Governance
Expression Reference Definition
“the process whereby public institutions conduct public affairs,
manage public resources and guarantee the realisation of human
Good governance [49]
rights in a manner essentially free of abuse and corruption, and with
due regard for the rule of law”
“a commitment to a mode of political and administrative steering
that seek to address societal problems by more or less systematically
Public governance [44]
designed and regulated interaction between public authorities and a
wide array of private actors”
“can be defined as the process and outcome of digital transformation:
Public governance digitalisation [34] the transformation of the “analogue” version of governance into
“digital” governance”
“e-government is the process of changing the public sector through
digitalisation and new information management techniques, a
E-government [50] process whose ultimate goal is to streamline public administration
and increase the degree of citizen participation in the administrative
process”
Source: Authors’ compilation.
Mathematics 2023, 11, 1168 6 of 25

Concluding the previously mentioned aspects [27–32,36–38], we must admit that the
digital transformation of public governance branches out into many research fields and
can have a twofold approach; first, by defining the specific terms and elements involved
in the digital transformation process, and locating the digitalisation of public governance
(institutional, local (rural and urban), regional, or national levels); second, by the area
of implementation, measuring the degree of implementation/performance, measuring
the effects on the socio-economic environment and well-being, addressing the risks in-
volved, measuring the level of investigations, developing specific regulations, and ensuring
information security.
Digital transformation has already been adopted and integrated all over the world, but
the intensity of the process is different from one country to another. The maturity level of
digitalisation is reflected in how requests are processed, from the reception of information
to the provision of an answer, in which minimal human intervention and the integration
of artificial intelligence indicate a high degree of maturation [13]. The process of digital
transformation can be approached from the perspective of two strategies: the creation
of added value through digital innovation (the government can influence the level of
involvement of citizens in the activity of public service delivery); and the creation of added
value through complexity (the government can create added value through information
generated by data provided by public institutions or even by citizens) [51].
There is also a trend in measuring the digitalisation of public governance that ap-
proaches the subject from different perspectives. Similarly, the key points in the research
trends regarding the measurement of digitalisation of public governance are based on
the effects of government digitalisation; the quantitative and qualitative analysis of the
implementation of digital technologies in public governance; and the analysis of the corre-
lation between digital transformation, socio-economic development, and the increase in
the quality of governance [13].
In most studies [27,46,52,53], the digitalisation of public governance has been associ-
ated with efficiency, innovation, or agility. Furthermore, in “World Development Report
2016”, digital technologies and the government services delivery framework is based on
inclusion, innovation, and voice [46]. In addition, Lobont, et al. [54] argued that the inter-
actions between citizens and public authorities could be transformed by the adoption of
e-government services, attesting that the level of e-government adoption is different among
European Union countries, and has significant influences on and implications for large
domains, including social, political, and economic areas.
Moreover, the results of other studies suggest that the growth in innovation is pos-
itively influenced by government efficiency and the rule of law; the correlation analysis
between variables has been carried out on data obtained through the WGI (World Gover-
nance Indicators), Intramural R&D expenditure, The Global Innovation Index, and The
Global Sustainability Competitiveness Index [52]. Accordingly, the increase in the perfor-
mance of the government administration is based on the size of the digital technology
infrastructure and the quality and geographical distribution of the technologies in the
infrastructure [53].
The previously mentioned studies, as well as others, use the WGI in empirical analyses
to measure digital transformation’s effects. However, there are studies [34] that consider
these indicators to be a measuring tool for analogue governance, while digital governance
can be measured through the Digital Economy and Society Index (DESI), Online Service
Index, E-Participation Index, Laws Relating to IT, ICT Use and Government Efficiency,
or Importance of ICT to Government’s Vision. The European eGovernment Benchmark
report evaluates eGovernment services within the European Union and beyond. The digital
government benchmark is analysed from a geographical point of view, emphasising the
measures, programs, and platforms used in each of the 34 countries under analysis from
the perspective of providing public services, transparency, and mobility [55]. Moreover,
the measurement of the level of digitalisation can be approached in a new way in research,
using Digital Economy and Society Index (DESI) subdimensions in regressions as explana-
Mathematics 2023, 11, 1168 7 of 25

tory variables of the dependent variable, the Digital Economy and Society Index (DESI
total index). This enables identification of the particularities specific to each country in
terms of digitalisation dimensions [56]. Noja et al. [57] employed the World Governance
Indicators (WGIs) to identify the implications of public administration and measure public
governance related to economic development. Dima et al. [58] underlined that the EU-27
Member States were confronted with significant discrepancies with respect to the quality
of public governance. Although there are many opinions regarding measuring the digi-
talisation of public governance, we can affirm that the variables and indicators included
in this research study are well grounded in theory the previous research from the existing
scientific literature.
Considering the above arguments, the following research hypothesis (H1) is considered.

Hypothesis 1 (H1). There are positive effects of digital transformation on public governance at the
level of the European Union.

In addition to the benefits to citizens and their well-being, digitalisation is also fol-
lowed by a series of risks that can be reduced or eliminated over time and through the
accumulation of experience. The risks associated with digitalisation include cybercrime,
dependence on the technical infrastructure and information interconnection, reduction in
demand for personnel, lack of synchronisation of systems (educational, administrative,
economic, regulatory), and digital inequality based on differences in infrastructure and
the skills needed to use technology [59]. However, the level of digital shortfall does not
significantly influence the decision to use the digital interfaces to access certain digital
public services [59]. The use of digital technologies negatively affects the well-being of
citizens through the complexity of the technologies, causing a certain level of stress when
they have to use a new technology [60].
However, we can discuss digital transformation only based on the existence of a
technological infrastructure. To expand broadband connections, governments made invest-
ments or relied on economic operators in the field of telecommunications to develop this
network, resulting in public–private partnerships [44]. The final report of the European
Commission that analysed the evolution of broadband coverage of 31 countries in the
European region identified a difference between the objectives of the projects “Universal
Broadband Coverage with speeds at least 100 Mbps, upgradable to gigabit speed, by 2025”
and “Gigabit connectivity for all by 2030”, and the reality in the rural environment, noting
constant differences between the average broadband coverage of countries and rural re-
gions [61]. The European Commission is not the only institution concerned with broadband
quality. Recent studies have analysed the influence of broadband speed on some processes
carried out through applications to provide services such as tax collection. The results
show that the use of connections with low download speed tends to lead to a decrease in
the collection of tax revenues, while the complexity of the applications also blocks some
processes [53]. Considering the importance of broadband quality and coverage at a country
level for public governance and the delivery of digital public services, we can affirm the
relevance of our study in analysing the linkages between digital transformation and public
governance.
Along these lines, it can be hypothesised that:

Hypothesis 2 (H2). There are strong interlinkages (both positive and negative) between digitalisa-
tion dimensions (including technological/broadband infrastructure) and public governance credentials.

3. Materials and Methods

Reviewing the existing scientific literature, we can affirm that the novelty of our
research compared to previous studies resides in the research framework designed and the
approach by which the empirical analysis is carried out, and, more specifically, the methods
used. To capture the interplay between public governance and digital transformation,
Mathematics 2023, 11, 1168 8 of 25

the World Governance Indicators (WGIs) and Digital Economy and Society Index (DESI)
components were selected as variables, and structural equation modelling (SEM), along
with Gaussian and Mixed-Markov graphical models, were applied as analysis methods.
The Stata 17 software was used to process the structural equation modelling (SEM), and
an integrative procedure aimed to appraise overall interlinkages among the considered
variables (direct, indirect, and total). Further, based on the accurate SEM findings, we used
RStudio 4.2.2. software to first design a Gaussian graphical model (GGM), and, second,
a Mixed-Markov graphical model (MGM) that allowed us to observe the intensity and
configuration of the interlinkages between all considered variables for the EU-27 countries.

3.1. Data and Indicators Employed in the Empirical Analysis

Based on the existing literature underpinnings, among the representative variables
comprising our models, we included public governance components [62] and digitalisation-
specific indicators [63], jointly with an integrated set of broadband indicators further
employed in the empirical analysis.
The dataset comprises a sample that includes the 27-EU MSs analysed during the
2010–2021 period, with annual data frequency for all the variables. Consequently, in order
to cope with the missing values in the analysed dataset for some variables, the mathematical
extrapolation method was applied. This method was also implemented by other researchers,
who aimed to predict a future pattern in the statistical data [64]. Furthermore, we applied
linear extrapolation based on the previous data history to approximate the next data point
since they are sampled periodically. The general formula used for extrapolation is presented
in Equation (1) [64]:
x x1
y ( x ) = y1 + ( y2 y1 ) (1)
x2 x1
where: “x1 , y1 and x2 , y2 represents the two endpoints of a linear graph, and x represents
the point which is to be extrapolated” [64].
The following selected indicators that are linked to our main general research objective
were used as proxies for the variables included within the empirical models, clustered in
two dimensions, respectively:
• Public sector governance: WGIs that are presented in standard normal units ranging
from 2.5 to +2.5 [65]: government effectiveness (GE); regulatory quality (RG); the
rule of law (RL); control of corruption (CCOR); voice and accountability (VA); and
political stability and absence of violence/terrorism (PSAV);
• Digitalisation-specific indicators: connectivity (CMB); integration of digital technol-
ogy (IDT); digital public services (DBS); human capital (HC); secure Internet servers
(SECINT); fixed cellular subscriptions (MOBCELL); fixed broadband subscriptions
(FBS); fixed telephone subscriptions (FTS); Internet user skills (INTS); advanced skills
and development (ADVS); e-Government users (EGOV).
Based on the main findings from the literature, we found that T, ´ran et al. [56],
Marino et al. [62], Noja et al. [57], and Dima et al. [63] were the authors that also focused
on this topical subject, by using similar indicators and related methodological credentials.
Table 2 synthesises the description and meaning of the indicators included in the dataset.
Mathematics 2023, 11, 1168 9 of 25

Table 2. Description of dataset indicators.

Acronym Description Unit of Measure Source

Government effectiveness refers to “perceptions of
the quality of public services, the quality of the civil
service and the degree of its independence from
GE ( 2.5, +2.5) The World Bank
political pressures, the quality of policy formulation
and implementation, and the credibility of the
government’s commitment to such policies.” [66]
Regulatory quality “captures perceptions of the
ability of the government to formulate and
RQ implement sound policies and regulations that ( 2.5, +2.5) The World Bank
permit and promote private sector
development.” [66]
The rule of law, which “captures perceptions of the
extent to which agents have confidence in and abide
by the rules of society, and in particular the quality
RL ( 2.5, +2.5) The World Bank
of contract enforcement, property rights, the police,
and the courts, as well as the likelihood of crime and
violence.” [66]
Control of corruption refers to the “perceptions of
the extent to which public power is exercised for
CCOR private gain, including both petty and grand forms ( 2.5, +2.5) The World Bank
of corruption, as well as “capture” of the state by
elites and private interests.” [66]
Voice and accountability “capture perceptions of the
extent to which a country’s citizens are able to
VA participate in selecting their government, as well as ( 2.5, +2.5) The World Bank
freedom of expression, freedom of association, and a
free media.”
Political stability and absence of violence/terrorism
“measures perceptions of the likelihood of political
PSAV ( 2.5, +2.5) The World Bank
instability and/or politically motivated violence,
including terrorism.” [66]
Connectivity—by mobile broadband, reflects the
European Commission,
CMB demand and the supply side of fixed and Weighted score (0 to 100)
Digital Scoreboard
mobile broadband.
Integration of digital technology—by digital
intensity, which covers the measures of business
European Commission,
IDT digitisation and e-commerce, which also have a Weighted score (0 to 100)
Digital Scoreboard
series of representative indicators, including
digital intensity.
Digital public services—by e-government, captures
European Commission,
DBS the demand and supply sides of digital public Weighted score (0 to 100)
Digital Scoreboard
services and open data.
Human capital—by Internet user skills, measured by
European Commission,
HC the number and complexity of activities that involve Weighted score (0 to 100)
Digital Scoreboard
the use of the Internet and digital devices.
Secure Internet servers, “the number of distinct,
SECINT publicly-trusted TLS/SSL certificates found in the per 1 million people The World Bank
Netcraft Secure Server Survey.”
Mobile cellular subscriptions refer to “subscriptions
MOBCELL to a public mobile telephone service that provide The World Bank
access to the PSTN using cellular technology.”
Mathematics 2023, 11, 1168 10 of 25

Table 2. Cont.

Acronym Description Unit of Measure Source

Fixed broadband subscriptions “refers to fixed
subscriptions to high-speed access to the public
FBS The World Bank
Internet (a TCP/IP connection), at downstream
speeds equal to, or greater than, 256 kbit/s.”
Fixed telephone subscriptions “refers to the sum of
an active number of analogue fixed telephone lines,
FTS voice-over-IP (VoIP) subscriptions, fixed wireless The World Bank
local loop (WLL) subscriptions, ISDN voice-channel
equivalents and fixed public payphones.”
Internet user skills, via at least basic digital skills,
“individuals with ‘basic’ or ‘above basic’ digital
European Commission,
INTS skills in each of the following five dimensions: Weighted score (0 to 100)
Digital Scoreboard
information, communication, problem-solving,
software for content creation and safety.”
Advanced skills and development, by ICT
specialists, “individuals with ‘above basic’ digital
European Commission,
ADVS skills in each of the following five dimensions: Weighted score (0 to 100)
Digital Scoreboard
information, communication, problem-solving,
software for content creation and safety.”
e-Government Users, “individuals who used the
European Commission,
EGOV Internet, in the last 12 months, for interaction with (percentage)
Digital Scoreboard
public authorities.”
Source: Authors’ compilation.

The indicators were extracted from the World Bank for public sector governance
dimensions and broadband indicators, Digital Agenda—European Commission, Digital
Scoreboard for digitalisation, and all other variables for the period 2010—2021 (annual data).
A significant effort was devoted to gathering relevant data from official sources and for
longer time spans that are relevant in revealing the amplitude of the public governance and
digitalisation processes. The lesser availability of data for certain indicators is a limitation
often encountered in similar empirical research. Moreover, particular attention was paid to
data analysis and processing methods; respectively, robustness checks and validation were
applied to determine if the chosen variables properly suited the models that we developed,
and were able to capture the effects and interlinkages between digital transformation,
broadband infrastructure, and public governance.
The descriptive statistics of all indicators included within the econometric models are
detailed in Table 3.
Furthermore, in our attempt to provide complementary views of how to present
the differentials among the EU-27 MSs in terms of governance levels and digitalisation
indicators, we selected a graphical representation that is based on a data mapping technique.
Using this approach, we designed visually appealing maps that allowed us to separately
observe the level of each selected indicator with data benchmarking between EU countries.
In addition, the data mapping technique facilitates distinguishing the differences regarding
one specific indicator by offering a general and comprehensive map of the European Union
states. We designed the maps in Stata 17 software, where we engaged different features
in order to reinforce the design of the generally created map, such as (i) different colours
styles—to differentiate the countries of the European Union; (ii) different fonts—for better
visualisation of the level of each indicator; (iii) locations—we established that the variables
need to be represented at the level of EU-27 Member States; and (iv) legend—to identify
the numerical values and the intensity/levels of each indicator.
Mathematics 2023, 11, 1168 11 of 25

Table 3. Descriptive statistics of the variables used in the empirical analysis, compiled at the level of
the EU-27 MSs, for the 2010–2021 period.

Variables N Mean Standard Deviation Minimum Maximum

GE 324 1.096 0.562 0.22 2.24
RQ 324 1.162 0.455 0.15 2.05
RL 324 1.100 0.600 0.13 2.13
CCOR 324 0.974 0.786 0.5 2.41
VA 324 1.079 0.352 0.26 1.69
PSAV 324 0.731 0.355 0.32 1.46
CMB 162 14.031 4.179 3.8 35.69
IDT 162 5.840 2.782 0.02 12.68
DBS 162 57.444 16.523 8.54 91.76
HC 133 25.330 5.988 10.46 38.31
SECINT 297 232,023.5 754,356.8 307 8,109,646
MOBCELL 297 2.002 ⇥ 107 2.67 ⇥ 107 455,579 1.10 ⇥ 108
FBS 297 5,149,675 7,700,996 124,889 3.60 ⇥ 107
FTS 297 6,698,929 1.14 ⇥ 107 211,849 5.29 ⇥ 107
INTS 162 27.668 6.151 13.12 39.75
ADVS 162 13.353 4.252 5.67 25.33
EGOV 134 63.767 18.697 12.09 94.08
N total 324
Source: Authors’ contribution in Stata 17.

For all six dimensions of governance indicators, Nordic countries such as Finland
and Sweden registered the highest levels (Figure 1). Along with these two countries, the
Netherlands, Denmark, and Austria recorded high levels of government effectiveness (1a).
At the opposite extreme, the lowest values belonged to Bulgaria, Romania, and Poland,
with the first two having negative values. Luxembourg, Denmark, and the Netherlands,
together with Finland and Sweden (1b), led the ranking in terms of the recorded values
of regulatory quality, and marked the implementation of policies that support economic
development in general and the development of the public sector in particular. Romania,
Greece, and Bulgaria were again at the bottom of the ranking with the lowest values and,
implicitly, with the weakest levels of policy implementation. The perceived trust in the
country’s rule of law had the highest values in Finland, Denmark, and Austria, while
in Bulgaria, Italy, and Greece, the level of trust and respect for society’s rules and state
institutions was found to be very low (1c). The very high values of control of corruption in
the Nordic countries (Denmark, Finland, Sweden) indicate the existence of a public power
that supports and is exercised for the benefit of citizens. On the other hand, in Bulgaria,
Romania, and Hungary, which registered the lowest values of corruption control, the state
also serves particular private interests (1d). Regarding voice and responsibility, freedom of
expression, and active participation, Finland, Denmark, and Luxembourg led the ranking,
and Bulgaria, Hungary, and Poland tended to place less emphasis on these elements when
it comes to governance (1e). Finally, the last component of the World Governance Indicators,
namely political stability and absence of violence/terrorism, ranked Luxembourg, Sweden,
and Finland first in terms of safety values and predictability of public policies, whereas
Greece, France, and Cyprus were at the bottom of the ranking (1f). There is a tendency
among the Nordic countries to well regulate the role of public governance to support
development, while the governments of central and south-eastern Europe tend to move
away from what the dimensions of governance imply.
 elements when it comes to governance (1e). Finally, the last component of the World Gov-
ernance Indicators, namely political stability and absence of violence/terrorism, ranked
Luxembourg, Sweden, and Finland first in terms of safety values and predictability of
public policies, whereas Greece, France, and Cyprus were at the bottom of the ranking
(1f). There is a tendency among the Nordic countries to well regulate the role of public
Mathematics 2023, 11, 1168 12 of 25
governance to support development, while the governments of central and south-eastern
Europe tend to move away from what the dimensions of governance imply.

Mathematics
Mathematics2023,
2023,10,
10,x xFOR
FORPEER
PEERREVIEW
REVIEW 1212ofof2525

(a) GE (b) RQ (c) RL

(d)
(d)CCOR
CCOR (e)
(e)VA
VA (f)
(f)PSAV
PSAV
Figure
Figure1.1.
Figure 1.Governance
Governanceindicators,
indicators,EU-27,
EU-27,2021.
2021.Source:
Source:Authors’
Authors’research
researchininStata17.
Stata 17.
Stata17.

Regarding
Regarding the
Regardingthe Digital
theDigital Economy
DigitalEconomy
EconomyandandSociety
and SocietyIndex,
Society Index,the
Index, theNordic
the Nordiccountries
Nordic countriesofof
countries ofthe
theEuro-
the Euro-
Euro-
pean
pean Union
peanUnion also
Unionalso recorded
alsorecorded the
recordedthe highest
thehighest levels
highestlevels of
levelsof digitalisation
ofdigitalisation (Figure
digitalisation(Figure 2).
(Figure2).
2).

(a)
(a)CMB
CMB (b)
(b)IDT
IDT

(c)
(c)DBS
DBS (d)
(d)HC
HC
Figure
Figure2.2.
Figure Digitalisation
2.Digitalisation indicators,
Digitalisationindicators, EU-27,
indicators,EU-27, 2021.
EU-27,2021. Source:
2021.Source: Authors’research
Source:Authors’
Authors’ research
researchinin Stata 17.
inStata17.
Stata17.

The
The highest
Thehighest connectivity
highestconnectivity
connectivityby bymobile
by mobile broadbandwas
mobilebroadband
broadband wasfound
was foundinin
found inDenmark,
Denmark,the
Denmark, theNether-
the Nether-
Nether-
lands
lands
landsandand Austria,
andAustria, in addition
Austria,ininaddition to Germany,
additiontotoGermany, Finland,
Germany,Finland, and
Finland,and Spain
andSpain (Figure
Spain(Figure 2a).
(Figure2a). The
2a).The highest
Thehighest
highest
level
levelofof
level integration
integrationofof
ofintegration digital
ofdigital technology
technologyinin
digitaltechnology the
inthe public
thepublic and
publicand private
andprivate sectors
privatesectors was
sectorswas registered
wasregistered
registered
inin Denmark,
inDenmark, Finland,
Denmark,Finland,
Finland,andand Sweden,
andSweden,
Sweden,and and
andinin the
inthe Netherlands,
theNetherlands, Belgium,
Netherlands,Belgium, and
Belgium,and Estonia.
andEstonia.
Estonia.AtAt the
Atthe
the
opposite
opposite extreme, the lowest level of integration of digital technology was registeredinin
opposite extreme,
extreme, the
the lowest
lowest level
level ofof integration
integration of
of digital
digital technology
technology was
was registered
registered in
Bulgaria,
Bulgaria, Romania,
Bulgaria,Romania,
Romania,and and Lithuania
andLithuania (Figure
Lithuania(Figure 2b).
(Figure2b). Mostdigital
2b).Most
Most digitalpublic
digital publicservices
public servicesare
services areoffered
are offeredby
offered by
by
the
the governments
governmentsofof
thegovernments Estonia,
ofEstonia, Denmark,
Estonia,Denmark,
Denmark,and and Finland,
andFinland, and
andofof
Finland,and Malta,
ofMalta, Sweden,
Malta,Sweden,
Sweden,andand Ireland
andIreland
Ireland
(Figure
(Figure2c).
2c).Regarding
Regardinghuman
humancapital,
capital,the
theNetherlands,
Netherlands,Finland,
Finland,and
andIreland
Irelandhave
havethe
the
most people who have developed digital skills. Moreover, a high number of such
most people who have developed digital skills. Moreover, a high number of such peoplepeople
can
canbe
befound
foundininDenmark,
Denmark,Sweden,
Sweden,and
andSpain
Spain(Figure
(Figure2d).
2d).
Mathematics 2023, 11, 1168 13 of 25

(Figure 2c). Regarding human capital, the Netherlands, Finland, and Ireland have the most
people who have developed digital skills. Moreover, a high number of such people can be
found in Denmark, Sweden, and Spain (Figure 2d).

3.2. Research
Mathematics 2023, 10, x FOR PEER REVIEW Methodology 13 of 25

Looking into empirical methods applied for studying public governance and digitalisa-
tion [67–70], we relied on two modern advanced econometric methods specific to modelling
longitudinal data,
Structural namely, structural
equation modellingequation modelling (SEM)
(SEM) represents and network
a measurement analysis
model thatthrough
is em-
Gaussian
ployed toand Mixed-Markov
analyse graphical
the structural modelsamong
relationships (GGMs,measured
MGMs, respectively).
indicators and to provide
robustStructural
estimatesequation
based onmodelling
the sample (SEM) represents
extracted. a measurement
Moreover, multiple and model that is em-
interconnected
ployed to analyse the structural relationships among measured indicators
dependencies between the considered indicators can be assessed in a single analysis and to provide
by
robust estimates based on the sample extracted. Moreover, multiple and
employing a structural equation model (SEM), thus offering a consistent and comprehen- interconnected
dependencies
sive assessment between the considered
of the relations indicators
considered [71]. can be assessed in a single analysis by em-
ploying a structural
Structural equation
equation model (SEM)
modelling (SEM),wasthusemployed
offering ain
consistent and comprehensive
this research to test the first
assessment of the relations considered [71].
working hypothesis (H1) and to capture the accumulated effects of digital transformation
Structural
on public equation
governance. modelling
Hence, (SEM) was
we configured anemployed
SEM that in this research
embeds to test
all relevant the first
digitalisa-
working hypothesis (H1) and to capture the accumulated effects of digital
tion and public governance dimensions in line with our research’s main purpose, as in transformation
on public
Figure 3 governance.
below. The Hence,
model we wasconfigured
estimatedanthrough
SEM that theembeds
maximumall relevant digitalisation
likelihood method
and public
(MLE). governance dimensions in line with our research’s main purpose, as in Figure 3
below. The model was estimated through the maximum likelihood method (MLE).

Figure 3. Configuration
Figure 3. Configuration of
of the
the SEM
SEM model
model designed
designed toto assess
assess the
the interplay
interplay between
between digitalisation
digitalisation
and public governance. Source: Authors’ research in Stata
and public governance. Source: Authors’ research in Stata17.17.

For
For the
thesecond
secondresearch
research hypothesis
hypothesis (H2), we used
(H2), Gaussian
we used and Mixed-Markov
Gaussian and Mixed-Markov graph-
ical models (GGMs, MGMs) as network models of conditional
graphical models (GGMs, MGMs) as network models of conditional associations to ap- associations to appraise
the positive
praise and negative
the positive correlations
and negative and interlinkages
correlations between
and interlinkages digitalisation
between and public
digitalisation and
governance considering all dimensions and subdimensions of
public governance considering all dimensions and subdimensions of both digital trans-both digital transformation
processes (including infrastructure) and public governance.
formation processes (including infrastructure) and public governance.
From a methodological perspective, a Gaussian graphical model (GGM) for a random
From a methodological perspective, a Gaussian graphical model (GGM) for a random
vector X = (X1 , . . . . . . , Xp ) is determined by a graph G on p nodes. “The model comprises
vector X = (X1, ……., Xp) is determined by a 1graph G on p nodes. “The model comprises
all multivariate normal distributions N µ ,✓θ − 1 )) whose
N((µ, inverse correlation matrix satisfies
all multivariate normal distributions
that ✓ jk = 0 when { j, k } is not an edge in G” [72]. “The whose inverse correlation
undirected graph matrix
G =satisfies
(V, E)
that
θ jk = 0
includes a vertex { j, k }
when set V is=not {1,an . . .edge
, p} as
in G”well[72].as an edge
“The set E ⇢graph
undirected V ⇥ V” =[73].
G (V , E )“Let
in-
W = ( w ) = S 1
for Vd=={1,....
1,2 p} the
, be precision matrix for X = E
[ x 1⊂, V
. . ×
. , V
x n1 ] T 2 Rn1xp
cludes
d aij,dvertex dset as well as an edge set ”[73]. “Let
Ω d =Y( ω=ij , d[ y
) 1=, Σ T
d = 1,2 be the precision matrix for Χ = [ xThe x ] ∈ R matrix
−1
and n2 ] 2 Rn2xp . X and Y denote the data matrices.
. .d. , yfor
1
,..., precision n1 T n 1 xp
and
(inverse 1
W = S represents a GGM. A GGM associated with X is a
Y = [ y ,...,covariance
1
y ] ∈ R matrix)
n 2 T n 2 xp
. X and Y denote the data matrices. The precision matrix (inverse
graph; similarly, a GGM associated with Y is also a graph” [73].
covariance matrix) Ω = Σ represents a GGM. A GGM associated with X is a graph; sim-
−1

ilarly, a GGM associated with Y is also a graph” [73].

The interlinkages are graphically reflected in GGMs and MGMs through the
lines/edges that connect the nodes, namely, blue edges for positive connections (partial
correlations) and red edges for negative correlations. The intensity of linkages is shown
Mathematics 2023, 11, 1168 14 of 25

The interlinkages are graphically reflected in GGMs and MGMs through the lines/edges
that connect the nodes, namely, blue edges for positive connections (partial correlations)
and red edges for negative correlations. The intensity of linkages is shown by the absolute
strengths (width and saturation) of the edges between the nodes (variables). The lack of
an edge between two nodes means that the (partial) correlation is zero, and, therefore, no
linkage is identified between those specific nodes (e.g., variables are independent after
conditioning on all other variables in the dataset) [72].
Both structural equation and network models have their origin in path analysis and
imply a variance–covariance matrix, which was employed in this research to identify and
assess the specific ways in which variables are related to each other (direct and indirect
effects of one variable on another) and, more specifically, how digitalisation credentials
affect public governance.

4. Results and Discussion

Structural equation modelling (SEM) results are presented in Figure 4 and detailed
in Appendix A, Table A1. A robustness check was undertaken through a series of specific
tests applied (e.g., root mean squared error of approximation (RMSEA), comparative fit
index (CFI), Tucker–Lewis index (TLI), coefficient of determination (CD), standardised root
mean squared residual (SRMR), average variance extracted (AVE), composite reliability
(CR), and Cronbach’s alpha).
RMSEA reported under the population error dimension of the goodness-of-fit test was
0.045, which suggests a good (close) fit, as also indicated by Browne and Cudeck [74] and
Hu and Bentler [75]. CFI and TLI reported under the baseline comparison have values
close to 1, thus indicating a good fit (CFI = 0.846, TLI = 0.816). Moreover, under the size of
residuals, we reported CD and SRMR. CD = 0.937 and acts like a R2 for the whole model,
where a value very close to 1 indicates a good fit. SRMR = 0.029 and corresponds to a
“small” value (limited by some at 0.08), thus indicating that the model also fits well by
this standard.
The convergent validity of the measurement model was assessed through the AVE
and the composite reliability (CR) (CR tends to be considered to be a less biased estimate of
reliability than Cronbach’s alpha [76]). Fornell and Larcker [77] and Shrestha [78] suggest
that AVE should be greater or equal to 0.5, while Alarcon and Sanchez [76] state that
CR should have an acceptable value of 0.7 or above to confirm convergent validity and
composite reliability, and thus ensure internal consistency. In our model, AVE = 0.621
and CR = 0.854, evidencing the convergent validity and internal consistency in scale
items, namely, a high degree of confidence that the constructs are well measured by
their indicators.
The internal consistency was also assessed, using Cronbach’s alpha coefficients to
test the instrument accuracy and reliability of the data. In general, a value greater than
0.7 indicates a good internal consistency [78]. In Table A2 of Appendix A, all compo-
nents/items have Cronbach’s alpha values greater than 0.9, and the total scale Cronbach’s
alpha value for the factors with total scale reliability is 0.9455 (>0.7). This shows an excel-
lent internal consistency, that is, the variables exhibit a correlation with their component
grouping, with good stability and reliability.
The main results highlight that the digitalisation credentials induce a positive and
significant impact on public governance, as considered in this research through the latent
variable “Governance” constructed from six subdimensions of WGIs. The estimated co-
efficient of 0.031 is positive and statistically significant at the 0.1% threshold. The most
notable positive inferences tend to be related to the control of corruption, rule of law, and
government effectiveness. Hence, agents gain confidence in and abide by the rules of
society and the quality of contract enforcement and institutions. Citizens also improve their
perceptions when sound digitalisation advancements are accomplished. Moreover, gov-
ernment effectiveness (GE) increases under digital developments, while political stability
(PSAV) is slightly (again positively) affected.
Mathematics 2023, 10, x FOR PEER REVIEW 15 of 25
Mathematics 2023, 11, 1168 15 of 25

Figure
Figure 4. Resultsofofthe
4. Results thestructural
structuralequation
equation modelling
modelling (SEM
(SEM model).
model). Source:
Source: Authors’
Authors’ research
research in
in Stata 17.
Stata17.

Our
Our results are in
results are in line
line with
with those
thoseobtained
obtainedby byWandaogo
Wandaogo[79], [79],who
whoalsoalsoidentified
identifieda
apositive
positiverelationship
relationshipbetween
betweendigitalisation
digitalisationand and government
government effectiveness;
effectiveness; thisthis earlier
earlier
study
study used
used aa different
different method,
method, and and applied
applied aa panel
panel model
model with
with fixed
fixed effects,
effects, indicating
indicating
that
that an
an increase
increasein indigitalisation
digitalisationby byoneonepoint
pointcancangenerate
generate ananincrease
increase in in
government
government effec-
ef-
tiveness by 0.1 points. Moreover, Wandaogo [79] indicated that the
fectiveness by 0.1 points. Moreover, Wandaogo [79] indicated that the political stability political stability and
absence
and absenceof violence and/or
of violence terrorism
and/or determines
terrorism determines government
government effectiveness. Dhaoui
effectiveness. [80]
Dhaoui
also
[80] also demonstrated that ICT development has a positive and significant impact on the
demonstrated that ICT development has a positive and significant impact on the
control
control ofof corruption. Therefore, in
corruption. Therefore, in line
line with
with our
our results,
results, the
the same
same positive
positive impact
impact waswas
identified
identified in in the
the case
case of
of e-service
e-service infrastructure
infrastructure and and ICT
ICT infrastructure
infrastructure on on government
government
effectiveness, and the case of e-service infrastructure on quality
effectiveness, and the case of e-service infrastructure on quality regulation, while regulation, while
ICTICT in-
infrastructure and the human capital index do not have a significant impact on quality
frastructure and the human capital index do not have a significant impact on quality reg-
regulation. Using a different approach, employing robust path analysis, do Nascimento
ulation. Using a different approach, employing robust path analysis, do Nascimento et al.
et al. [81] identified some important results related to the number of people who access the
[81] identified some important results related to the number of people who access the
Internet (Internet diffusion) in a country, and its impact on government corruption and
Internet (Internet diffusion) in a country, and its impact on government corruption and
voice and accountability, as our results demonstrate.
voice and accountability, as our results demonstrate.
Therefore, the first research hypothesis, (H1). There are positive inferences of digital
Therefore, the first research hypothesis, (H1). There are positive inferences of digital
transformation upon public governance at the level of the European Union, is fulfilled.
transformation upon public governance at the level of the European Union, is fulfilled.
To further test the second research hypothesis (H2), we configured and estimated two
To further test the second research hypothesis (H2), we configured and estimated
graphical models, a GGM and MGM, based on the extended Bayesian information criteria
two graphical models, a GGM and MGM, based on the extended Bayesian information
and partial correlation methods. The GGM results presented in Figure 5 suggest several
criteria and partial correlation methods. The GGM results presented in Figure 5 suggest
positive linkages, as follows:
several positive linkages, as follows:
• Between the effectiveness of government (GE) and the human capital (HC) involved
• Between
in complex theactivities
effectiveness of government
that engage the use of(GE) andservices;
digital the human capital (HC) involved
• in complex
Between theactivities
change in that
theengage the use
perceptions of of digital
people services;
about the quality of public services
• Between the change in the perceptions of people
(GE) and the decision to use the Internet to actively communicate about the quality of public
with public services
authori-
(GE) and
ties (EGOV); the decision to use the Internet to actively communicate with public author-
• ities (EGOV); abilities to enforce regulations and policies (RG), which can further sus-
Government’s
• Government’s
tain the achievementabilities to enforce
of digital skills,regulations and policies
at least at a basic level, by(RG), which
the entire can further
society (INTS);
• sustainperceptions
Better the achievement of digital
of the people skills,
about theatfreedom
least at of
a basic level, and
expression by the entire
media society
(VA) will
(INTS);
undoubtedly lead to a positive influence on cellular technology by using telephone
• Better perceptions
services (MOBCELL); of the people about the freedom of expression and media (VA)
• will undoubtedly lead
Moreover, good perceptions to a positive influence
and a higher on cellular
degree technology
of confidence in thebyrules
usingof tele-
law
(RL)
phone determine a positive influence on the need for connectivity in digital services,
services (MOBCELL);
• especially
Moreover,the supply
good side of fixed
perceptions and and mobile
a higher broadband
degree (CMB). in the rules of law
of confidence
• Furthermore,
(RL) determine negative correlations
a positive influenceare on
alsothesuggested,
need for such as:
connectivity in digital services,
especially the supply side of fixed and mobile broadband (CMB).
Mathematics 2023, 10, x FOR PEER REVIEW 16 of 25

Mathematics 2023, 11, 1168 16 of 25

Furthermore, negative correlations are also suggested, such as:

•• Between
Betweenthe theperceptions
perceptionsof ofcitizens
citizensabout
aboutpolitical
politicalinstability/terrorism
instability/terrorism(PSAV)
(PSAV)and
and
the use of digital public services of the public administration (EGOV);
the use of digital public services of the public administration (EGOV);
•• AArelevant
relevantimpact
impactofofregulatory
regulatoryquality
quality(RQ)
(RQ)on ondigital
digitalconnectivity
connectivityby bythethebroad-
broad-
bandinfrastructure
band infrastructure(CMB)
(CMB)isisidentified,
identified,which
whichisisreflected
reflectedininthe
thepublic
publicgovernance
governance
representativeindicators
representative indicatorsunder
underthetheinfluence
influenceofofthe
theintegration
integrationofofdigital
digitaltechnology,
technology,
includingthe
including thedigital
digitalintensity
intensity(IDT).
(IDT).

Resultsofofthe
Figure5.5.Results
Figure theGaussian
Gaussian graphical
graphical model
model (GGM).
(GGM). Source:
Source: Authors’
Authors’research
researchininRStudio
RStudio4.2.2.
4.2.2.
Stronger linkages are captured in the MGM shown in Figure 6. Thus, the linkages
between the variables
Stronger linkages capture the following
are captured in the MGM associations
shown regarding
in Figure 6. digital
Thus,transformation
the linkages
and public
between the governance dimensions:
variables capture the following associations regarding digital transformation
Positive
• public
and linkages with
governance government effectiveness (GE) related to e-government users
dimensions:
• (EGOV),linkages
Positive integration
withof digital technologies
government (IDT),
effectiveness therelated
(GE) demands and supplies users
to e-government of the
(EGOV), integration of digital technologies (IDT), the demands and supplies ofofthe
digital public services using open data (DBS), and the existence of basic skills the
Internet users (INTS), on the one hand, and negative synergies with the
digital public services using open data (DBS), and the existence of basic skills of the broadband
connectivity
Internet users(CMB)
(INTS),andon different types and
the one hand, of corruption (CCOR), on
negative synergies thethe
with other hand;
broadband
A favourable
• connectivity influence on the control of corruption (CCOR) regarding
(CMB) and different types of corruption (CCOR), on the other hand; connectivity
• Athrough mobile
favourable broadband
influence on the(CMB), theofInternet
control servers
corruption that are
(CCOR) secure (SECINT),
regarding and
connectivity
the people
through withbroadband
mobile digital skills (among
(CMB), the some dimensions,
Internet servers that such
areas communication
secure (SECINT), and and
information, content creation through different software, safety, and
the people with digital skills (among some dimensions, such as communication and problem solving)
(INTS), and unfavourable influences with Internet users that make less use of the activ-
information, content creation through different software, safety, and problem solv-
ities that involve the use of digital devices, along with other activities on the Internet
ing) (INTS), and unfavourable influences with Internet users that make less use of
(HC), and with public services that have integrated the digital technologies (DBS).
the activities that involve the use of digital devices, along with other activities on the
Internet (HC), and with public services that have integrated the digital technologies
(DBS).
Mathematics 2023, 10, x FOR PEER REVIEW 17 of 25
Mathematics 2023, 11, 1168 17 of 25

Results
Figure6.6.Results
Figure of of
thethe Mixed-Markov
Mixed-Markov graphical
graphical model
model (MGM).
(MGM). Source:
Source: Authors’
Authors’ research
research in
in RStu-
dio 4.2.2.
RStudio 4.2.2.

Theseresults
These results align
align with
with those
those obtained
obtained by by Gulati
Gulatiand andYates
Yates[82],
[82],who
whoapplied
appliedmultiple
multi-
regression analysis models; their results indicate a positive relationship
ple regression analysis models; their results indicate a positive relationship between between broadband
technology technology
broadband and public governance (captured through
and public governance (capturedWorld Governance
through WorldIndicators,
Governance WGIs).
In-
Moreover,
dicators, their results
WGIs). Moreover,evidence
their that
resultsan increase
evidenceofthat oneanunit of the governance
increase of one unit index
of thegener-
gov-
ates a 63.7%
ernance index increase
generates in the number
a 63.7% of broadband
increase subscriptions
in the number per 100 people.
of broadband On the per
subscriptions con-
trary,
100 Yates On
people. et al.
the[83] do not find
contrary, Yatesa relationship
et al. [83] dobetween
not find broadband
a relationship coverage
between andbroadband
regulatory
quality; these
coverage results are contrary
and regulatory to theresults
quality; these secondare hypothesis
contraryformulated
to the second in our researchfor-
hypothesis due
to the reduced regulation of the development market in the telecommunications
mulated in our research due to the reduced regulation of the development market in the industry.
Therefore, the second
telecommunications industry. working hypothesis, (H2). There are strong interlinkages (both
positive and negative)
Therefore, betweenworking
the second digitalisation dimensions
hypothesis, (including
(H2). There aretechnological/broadband
strong interlinkages infras-
(both
tructure)
positive andnegative)
and public governance credentials, isdimensions
between digitalisation fulfilled. (including technological/broadband in-
Based on
frastructure) andthese
publicfindings,
governancetailored policies
credentials, and specific strategies regarding the digital
is fulfilled.
transformation of public governance are necessary.
Based on these findings, tailored policies and specific These are especially
strategies needed the
regarding in terms of
digital
digital public services, Internet user skills, secure Internet servers,
transformation of public governance are necessary. These are especially needed in terms and digital connectivity,
indigital
of order to improve
public the integration
services, Internet user of digital
skills,technologies
secure Internet in public
servers,digital
and services and the
digital connec-
control of different corruption actions, in addition to the stability of the
tivity, in order to improve the integration of digital technologies in public digital services political frameworks
andthe
and stable regulations,
control of differentto increase
corruption the actions,
credibility of citizens
in addition to regarding
the stabilitytheofuse
the of digital
political
technologiesand
frameworks in the relationship
stable regulations,between citizens
to increase theand public authorities.
credibility of citizens regarding the use
The results revealed that the European Union countries accelerated the rate at which
of digital technologies in the relationship between citizens and public authorities.
they were adopting digital technology and Internet usage in the context of the COVID-19
The results revealed that the European Union countries accelerated the rate at which
pandemic and other unpredictable circumstances, thus also impacting public governance
they were adopting digital technology and Internet usage in the context of the COVID-19
with further spill-over effects at both micro- and macroeconomic levels.
pandemic and other unpredictable circumstances, thus also impacting public governance
Our estimations indicate that the use of digital tools in the relationship with and
with further spill-over effects at both micro- and macroeconomic levels.
interactions between the public decision factor (the government, i.e., regulatory quality,
Our estimations indicate that the use of digital tools in the relationship with and in-
government effectiveness, the reduction in corruption, political stability and confidence
teractions between the public decision factor (the government, i.e., regulatory quality,
in rules of law and citizens’ digital skills, use of digital technologies, and digital public
government effectiveness, the reduction in corruption, political stability and confidence
services) defines the transformation of good governance in the digital era through digital
in rules of law and citizens’ digital skills, use of digital technologies, and digital public
technology that contributes to the improvement and simplification of various institutional
services) defines the transformation of good governance in the digital era through digital
aspects, namely, communication, business, quality services, safety, and welfare of the
technology
communitythat as acontributes
large. This wasto the improvement
also substantiated and bysimplification
Chen et al. [42].of Moreover,
various institutional
the control
aspects, namely, communication, business, quality
of corruption can be closely associated with government effectiveness [84],services, safety, and which
welfareindicates
of the
community as a large. This was also substantiated by Chen et al.
that the positive influences of these credentials can stimulate the digital transformation[42]. Moreover, the con-of
public governance.
Mathematics 2023, 11, 1168 18 of 25

According to the SEM, GGM, and MGM results, the digital transformation of public
governance can be increased by efficient and proper collaboration between decision makers
and all levels of society. Thus, the integration of digital technology provides high-quality
services characterised by the ease of exchanging information, faster communication, and
unlimited access to technologies, secure and sustainable digital infrastructures, security, and
connectivity. This is in line with the results obtained by Ludlow and Khan [43]. However,
with digital transformation, many obstacles and limitations have arisen, especially the
requirement to improve the quality of resources, the need for innovative services, and the
technical disparities and policy conflicts that lead to specific ambiguities related to the
application of standard operating procedures [43,85]. Further, governments should adopt
information technology in many areas to increase living standards and boost society’s
evolution [86].

5. Conclusions
Against the background of the increasing global significance of technology investment
and development in the public sector, this research study provides an overview of the
implications of digitalisation on public sector governance, given the notable differences
among European Union Member States, and under consideration of their interlinkages
with technological/broadband infrastructure. In this study, we empirically assessed the
relationship between digital transformation and public governance, with a detailed analysis
of the EU-27 Member States, considering the historical data for 2010–2021. The research
endeavour focused on testing two hypotheses by applying two advanced econometric tech-
niques, namely, structural equation modelling (SEM), in order to analyse the interlinkages
(direct, indirect, total) between the digital transformation credentials and public governance
(captured through World Governance Indicators), and Gaussian graphical models (GGM
and MGM), designed to account for the interdependencies between all considered variables
(including technological/broadband infrastructure representative variables).
Therefore, the main findings that were revealed following the two research hypothe-
ses, by considering the EU-27 Member States, highlighted that: (i) an increase in the
digital transformation level led to significant improvements in public governance captured
through all six World Governance Indicators; all of the Digital Economy and Society Index
(DESI) indicators had a similar positive impact on the World Governance Indicators, by
determining an increase in the government effectiveness, strengthening the rule of law
framework, and providing a more restrictive regulatory quality, while maintaining a low
level of corruption; and (ii) there is a notable contribution of technological progress to the
advancement in the field of digitalisation of public governance in certain EU countries. The
results are consistent with other research from the existing literature [42,79,82].
Consequently, the main contributions of our research provide new empirical evidence
to support an overall vision of the impact of digital transformation on public governance
across the European Union, and the risks and opportunities around EU digital governance,
as countries are constantly concerned with sound digitalisation frameworks and quality
infrastructure in public governance. The digital transformation of public governance can
be highlighted by efficient and proper collaboration between decision makers and all
levels of society; thus, the integration of digital technology provides high-quality services
characterised by the ease of exchanging information, faster communication and unlimited
access to technologies, and secure and sustainable digital infrastructures, security, and
connectivity [87].
Based on the obtained results, a series of recommendations can be made regarding the
interplay between public governance and digital transformation. First, sound institutional
frameworks, which need to be designed and well-oriented public policies, should be
implemented at the level of EU-27 MSs to enhance the capacity to address the digitalisation
process of public governance. Second, it is necessary to promote the integration of digital
technology in order to increase the quality of public governance, to sustain a high level of
innovation and economic development, and to enhance public sector productivity. This
Mathematics 2023, 11, 1168 19 of 25

should be undertaken by encouraging the government of each country to further embrace

the digital evolution of public governance to transform how the public sector tackles social
and economic challenges. In addition, governments can consider increasing the degree of
transparency in the public sector and integrating digital technology in public governance as
a measure to reduce corruption, thus encouraging and facilitating the active participation
of citizens in the decision-making process.
In addition, the main implications of our findings highlight that the digital transfor-
mation of public governance can be boosted by improvements in the design of targeted
policies and specific strategies related to digital technology integration. This will increase
the credibility of citizens regarding the use and integration of digital tools that can deci-
sively boost the quality of public governance, the creation of well-supported measures,
and public government support for the improvement in digital transformation of public
governance, especially for developing countries, thus ensuring the specific framework that
can be implemented for all of the EU-27 MSs.
The research has limitations resulting from the relatively poor availability of data
for specific indicators required to capture the amplitude and complexity of digitalisation
processes. Future research will consider a separate analysis of subpanels of EU Member
States to enhance tailored impacts, dissimilarities, and distinctive features of the interplay
between digitalisation and public governance.

Author Contributions: Conceptualization A.-M.T, ., R.-I.R. and A.-F.C.; methodology, G.G.N., M.G.P.
and R.-I.R.; software, G.G.N., A.-F.C. and A.-M.T, .; validation, M.G.P. and G.G.N.; formal analysis,
A.-F.C. and R.-I.R.; investigation, R.-I.R., A.-M.T, . and A.-F.C.; resources, M.G.P. and R.-I.R.; data
curation, A.-M.T, ., M.G.P. and G.G.N.; writing—original draft preparation, A.-F.C., A.-M.T, . and
G.G.N.; writing—review and editing, G.G.N., A.-M.T, . and M.G.P. All authors have read and agreed
to the published version of the manuscript.
Funding: This research received no external funding.
Data Availability Statement: The dataset supporting the results reported in this article can be made
available by the authors upon request.
Conflicts of Interest: The authors declare no conflict of interest.

Appendix A

Table A1. Detailed SEM results, maximum likelihood method (with missing values).

Variables Coefficients
/SE
GOVERNANCE
0.0311 ***
DIGITAL
(0.00369)
CMB
1
DIGITAL
(.)
8.116 ***
_cons
(0.407)
IDT
0.550 ***
DIGITAL
(0.0362)
3.521 ***
_cons
(0.175)
Mathematics 2023, 11, 1168 20 of 25

Table A1. Cont.

Variables Coefficients
DBS
3.139 ***
DIGITAL
(0.214)
44.21 ***
_cons
(1.026)
HC
0.888 ***
DIGITAL
(0.0745)
23.81 ***
_cons
(0.345)
EGOV
2.229 ***
DIGITAL
(0.264)
60.75 ***
_cons
(1.237)
SECINT
0.266 ***
DIGITAL
(0.0264)
10.12 ***
_cons
(0.129)
INTS
0.951 ***
DIGITAL
(0.0883)
26.92 ***
_cons
(0.407)
ADVS
0.721 ***
DIGITAL
(0.0562)
11.35 ***
_cons
(0.267)
PSAV
1
GOVERNANCE
(.)
0.731 ***
_cons
(0.0211)
RQ
1.825 ***
GOVERNANCE
(0.144)
1.167 ***
_cons
(0.0262)
RL
2.627 ***
GOVERNANCE
(0.197)
1.103 ***
_cons
(0.0349)
Mathematics 2023, 11, 1168 21 of 25

Table A1. Cont.

Variables Coefficients
CCOR
3.397 ***
GOVERNANCE
(0.257)
0.975 ***
_cons
(0.0457)
VA
1.489 ***
GOVERNANCE
(0.114)
1.079 ***
_cons
(0.0204)
GE
2.409 ***
GOVERNANCE
(0.183)
1.092 ***
_cons
(0.0325)
/
24.47 ***
var(e.CMB)
(2.202)
1.602 ***
var(e.IDT)
(0.219)
68.14 ***
var(e.DBS)
(7.695)
15.72 ***
var(e.HC)
(1.478)
331.1 ***
var(e.EGOV)
(28.21)
3.215 ***
var(e.SECINT)
(0.280)
26.74 ***
var(e.INT)
(2.406)
8.295 ***
var(e.ADVS)
(0.777)
0.0820 ***
var(e.MOBCELL)
(0.00678)
0.0343 ***
var(e.RQ)
(0.00301)
0.0121 ***
var(e.RL)
(0.00163)
0.0345 ***
var(e.CCOR)
(0.00371)
0.0109 ***
var(e.VA)
(0.00104)
0.0195 ***
var(e.GE)
(0.00200)
0.0267 ***
var(e.GOVERNANCE)
(0.00471)
24.85 ***
var(DIGITAL)
(3.628)
Note: “Standard errors in parentheses, *** p < 0.001”. Source: Authors’ research in Stata 17.
Mathematics 2023, 11, 1168 22 of 25

Table A2. Cronbach’s alpha for the SEM model, EU-27, 2010–2021.

Test Scale = Mean (Standardized Items)

Average EU-27
Item Obs Sign Inter-Item Correlation Alpha
CMB 324 + 0.5747 0.9461
IDT 324 + 0.5528 0.9414
DBS 324 + 0.5524 0.9413
HC 324 + 0.5444 0.9395
EGOV 324 + 0.5730 0.9458
SECINT 297 + 0.5915 0.9496
INTS 324 + 0.5495 0.9407
ADVS 324 + 0.5461 0.9399
PSAV 324 + 0.5767 0.9466
RQ 324 + 0.5412 0.9388
RL 324 + 0.5351 0.9374
CCOR 324 + 0.5351 0.9373
VA 324 + 0.5378 0.9380
GE 324 + 0.5359 0.9375
Total scale 0.9455
Source: Authors’ research in Stata 17.

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