Mamadou L Gueye
email: mamadou.gueye@univ-pau.fr

Ernesto Exposito
email: ernesto.exposito@univ-pau.fr

University 4.0: The Industry 4.0 paradigm applied to Education

Keywords: Industry 4.0, Education 4.0, University 4.0, Cyber-Physical Systems, Autonomic Computing, Knowledge Base, Semantic Web

The industry has undergone various industrial revolutions leading to major upheavals in all activities of human life, particularly in the field of education. Technology has become ubiquitous in educational organizations seeking to respond effectively to the demand for improvement, optimization, and personalization of large-scale, technology-supported education. Possibilities for automatically tracking the progress of learners become possible, at least for assessing attendance, progress, and acquisition of knowledge or skills. Knowledge sources are increasingly heterogeneous and complex in learning environments. With continuous innovations in the way we teach and learn, there is a need to rethink and transform the model of integrating technology into teaching in order to achieve intelligent collaboration and coordination between technology and people for learning. In this article, we propose an approach to be taken into account in the natural evolution of educational institutions under the term of University 4.0. The University 4.0 concept is inspired by the Industry 4.0 paradigm and applies its concepts to higher education to provide better responses to the specific needs of each learner. This paper presents a state of the art on the Industry and Education revolutions and in particular the digital and pedagogical transformations in education from Education 3.0 to Education 4.0, as well as the challenges of University 4.0.

Introduction

The industry has undergone various industrial revolutions leading to major upheavals in all activities of human life, particularly in the field of education. Thus, educational organizations can draw inspiration from the new paradigm of the fourth industrial revolution (Industry 4.0), which consists of digitizing organizations and automating business processes in order to better meet the specific needs of each product or service. Indeed, information and communication technologies (ICTs) have become omnipresent in educational organizations seeking to respond effectively to the demand for improvement, optimization, and personalization of large-scale, technology-supported education.

Moreover, we are moving towards ultra-connected universities, characterized by a weak combination of technology and people at the service of learning. In this context of mass education, even without technology, it is already a problem for the teacher to be able to follow each learner. With the plurality of learners with different profiles in universities, it is extremely complex and resource-intensive to provide each learner with the personalized follow-up necessary to improve learning.

Systems for analyzing and adapting learning based on Big Data, Machine Learning, Artificial Intelligence are being developed as new tools for the improvement and personalization of learning. The emergence of the Internet and technological advances have also favored the adoption of several pedagogical approaches (online training, flipped classroom, blended learning, etc.) aimed at improving teaching. These ongoing innovations in the way we teach and learn require us to rethink and transform the model of integrating technologies into teaching in order to achieve intelligent collaboration and coordination of physical and/or virtual actors at the service of education.

In this article, we propose an application of the concepts of Industry 4.0 to higher level educational organizations in order to evolve towards University 4.0 to provide better responses to the adaptation of learning and the differentiation of the pedagogical path of each learner. Our research work is part of the transition towards this new educational revolution in order to ensure an alliance between technology and human beings in the service of improving learning.

This paper presents a state of the art on the Industry and Education revolutions and in particular the digital and pedagogical transformations in education from Education 3.0 to Education 4.0, as well as the challenges of University 4.0, and the proposed solution.

State of the Art

In this section, we present the paradigms of the fourth industrial revolution and the fourth educational revolution, an analysis of the current digital and pedagogical transformations opening the way to a new educational revolution.

The paradigm of the fourth industrial revolution (Industry 4.0)

To better understand the fourth industrial revolution, it is necessary to review the previous industrial revolutions [START_REF] Diwan | Is Education 4.0 an imperative for success of 4th Industrial Revolution?[END_REF]. The first industrial revolution (Industry 1.0) was characterized by the mechanization of the industry with limited production based on the use of oil and steam engines as a source of energy. The second industrial revolution (Industry 2.0) was based on the organization of work and the use of electricity to promote mass production. The third industrial revolution (Industry 3.0) was based on the integration of electronic components and information technology in the industry for the automation of production tasks. Nowadays, as a direct consequence of Industry 3.0, we are witnessing the development of intelligent industrial systems thanks to the permanent integration of advanced technologies (Artificial Intelligence, Cloud Computing, IoT, Big Data, robotics) favoring the advent of the fourth industrial revolution (Industry 4.0). Industry 4.0 is marked by a technological fusion of the boundaries between the physical, biological, and digital worlds in order to design intelligent cyber-physical systems [START_REF] Diwan | Is Education 4.0 an imperative for success of 4th Industrial Revolution?[END_REF][START_REF] Schwab | The Fourth Industrial Revolution: what it means, how to respond[END_REF]. Thus, there is a need to integrate the physical and digital worlds in order to improve the management of products, business processes, and services in Industry 4.0 [START_REF]Industrie 4.0 : la quatrième révolution industrielle[END_REF]. Industry 4.0 also encourages a shift from mass production or service provision to customized products and services based on individual customer requirements [START_REF] Vaidya | Industry 4.0 -A Glimpse[END_REF]. The authors [START_REF] Diwan | Is Education 4.0 an imperative for success of 4th Industrial Revolution?[END_REF] [2] [START_REF]Industrie 4.0 : la quatrième révolution industrielle[END_REF] indicate that the Industry 4.0 paradigm is mainly based on the integration of advanced technologies such as Artificial Intelligence, robotics, big data, cloud computing, the Internet of Things, the Internet of Services, and 3D printing in the industry to automate and digitalize manufacturing processes.

The various industrial revolutions have always led to major upheavals in all activities of human life, especially in the field of education. With Industry 4.0, it has become imperative for educational organizations to move towards a new revolution: Education 4.0.

The paradigm of the fourth educational revolution (Education 4.0)

In order to understand Education 4.0, it is important to show the evolution of education since its origins, which we could consider as Education 1.0. Ernst & Young LLP [START_REF]Leapfrogging to Education 4.0: Student at the core[END_REF] provides a review of previous educational revolutions from antiquity to the present day. The first educational revolution (Education 1.0) was characterized by a mode of teaching that was informal, church-controlled, and accessible to a privileged few in religious institutions. The second educational revolution (Education 2.0) emerged in response to society's need to democratize education and to train as many people as possible, giving rise to mass education with advanced and formal teaching methods focused on educational institutions (schools, colleges, universities). In the third educational revolution (Education 3.0), information, and communication technologies (ICTE) are now being increasingly integrated into education. New models of open and online education (Massive Online Open Courses or MOOC, Corporate Online Open Course or COOC and Small Private Online Courses or SPOC), has completely overturned the way we learn and teach by making education accessible to the general public without constraints of space, time and place and by providing the premises for the next educational revolution. According to [START_REF] Halili | TECHNOLOGICAL ADVANCEMENTS IN EDUCATION 4.0[END_REF], "Education 4.0 will somehow complement the phenomenon of digital inclusion in our daily lives where human beings and machines are lined up to extract the solvent, and of course, discover new theories on innovation". The Education 4.0 paradigm could be defined on the basis of two emerging trends, one based on general innovations and changes in education and pedagogy, and the other on the integration of technologies introduced by Industry 4.0 into education.

On the one hand, Education 4.0 is a vision of the future of education that exploits the potential of digital technologies, personalized data, and the opportunities offered by this connected world to foster lifelong learning [START_REF] Fisk | Education 4.0 … the future of learning will be dramatically different, in school and throughout life[END_REF]. It is an educational revolution that allows learners to be the architects of their learning, characterized by the personalization of learning with flexible, dynamic, and adaptive learning pathways [START_REF]Leapfrogging to Education 4.0: Student at the core[END_REF].

With this first trend, Education 4.0 launches educational organizations into a dynamic of adopting new technological and pedagogical transformations to better respond to the specific needs of each learner.

On the other hand, Education 4.0 is a direct consequence of the emergence of the 4.0 industry. In order to prepare future generations of learners for the fourth industrial revolution, it is necessary to align education with Industry 4.0 [START_REF]The Education 4.0 Revolution. Analysis of Industry[END_REF]. Education 4.0 is about integrating the technological advances of Industry 4.0 such as 3D printing, augmented reality, virtual reality, cloud computing, hologram, biometrics, multi-touch LCD, Internet of Things, artificial intelligence, big data, QR-code for educational purposes [START_REF] Halili | TECHNOLOGICAL ADVANCEMENTS IN EDUCATION 4.0[END_REF]. With this new trend, Education 4.0 encourages the transformation of the process of integrating technological advances into teaching and learning in order to promote alignment between education and industry 4.0.

By combining these two trends, the Education 4.0 paradigm constitutes a set of technological innovations and pedagogical transformations in education that promote a combination of man and technology in the service of improving and adapting learning to better meet the expectations of Industry 4.0.

Analysis of digital and pedagogical transformations in education

Digital transformations

Today, digitalization is changing everything, and we are witnessing major revolutions in education that are disrupting the interaction between the different actors in education. The current context of digital transformations is based on the permanent integration of technology as a learning tool that promotes the development of new innovative learning methods and intelligent environments: Learning Management Systems (LMS) Learning management system solutions provide automated administration services for learning-related activities (management of resources, training paths, learners, trainers, etc.). LMS also offers learners the possibility of learning at their own pace, of consulting learning resources at a distance, and of individualized learning. There are proprietary LMS platforms such as 360Learning, CrossKnowledge, and Dockeos, and open-source platforms such as Canvas, Claroline, Moodle, and Open edX. Moodle is the most widely used LMS solution in the world with its open code which allows great flexibility in the evolution of training digitization needs [START_REF]Digital Learning Book[END_REF].

Mobile learning

The increasing use of computers, tablets, and smartphones in classrooms has become an emerging trend in education. According to a survey by Pearson Education [START_REF]Student Mobile Device Survey[END_REF], nine out of ten (87%) students in US universities use a laptop, electronic notebook, or Chromebook computer every week to do their homework.

Interactive and fun contents

The interactive and playful content immerses the learner in a sensory experience (touch, sight, hearing) with additional information enriching the learner's experience. There are several applications in higher education, e.g. in an astronomy course, teachers can use 3D representations of the earth and the sun so that learners better understand the relationship between the earth and the sun [START_REF] Lee | Augmented Reality in Education and Training[END_REF].

Virtual teaching assistants (Chatbots)

The use of chatbots has become ubiquitous in education [START_REF] Winkler | Unleashing the Potential of Chatbots in Education: A State-Of-The-Art Analysis[END_REF][START_REF] Song | Interacting with a conversational agent system for educational purposes in online courses[END_REF]. These conversational tools (text or audio) based on computer programs offer learners the possibility to study, search for information, or benefit from pedagogical assistance via a virtual agent. For example, at the Georgia Institute of Technology in the United States, a virtual teaching assistant called Jill Watson has been deployed to improve exchanges in MOOCs. Jill Watson independently answered routine questions and frequently asked questions from students while posting weekly announcements [START_REF] Goel | Jill Watson: A Virtual Teaching Assistant for Online Education[END_REF].

Digital interactions (clickers)

To encourage participation, commitment, and motivation of the learner, class response systems (clickers) have been developed. According to [START_REF] Nripendra | A review of literature on the use of clickers in the business and management discipline[END_REF], clickers are small, sophisticated technological devices that allow the learner to quickly answer questions in the classroom. Clickers also provide digital interactions between the teacher and learners to promote learner satisfaction, attention, and enjoyment of learning.

Intelligent Tutoring Systems (ITS)

Intelligent tutoring systems have been developed in order to adapt learning resources to the specific needs of each learner in the context of online learning. According to [START_REF] Marciniak | Building Intelligent Tutoring Systems Immersed in Repositories of Elearning Content[END_REF], with ITSs the learner can receive content that was not available in the repository when the content designer developed a given pedagogical strategy. Depending on the state of the knowledge base at a given time, e-learning elements can be provided to meet the learner's needs. Technological innovations have fostered pedagogical transformations that are changing the way we teach and learn. In this context of large-scale, technology-supported education with different learner profiles, it has become essential for universities to adopt new pedagogical approaches to provide responses tailored to the specific needs of each learner.

Pedagogical Transformations

The current context of universities is marked by the adoption of new pedagogical approaches to facilitate access to educational content and improve the quality of learning. These approaches include Active pedagogy Active pedagogy is a broad concept, most often referring to student-centered and activating teaching methods and teacher-led activities [START_REF] Hartikainen | The Concept of Active Learning and the Measurement of Learning Outcomes: A Review of Research in Engineering Higher Education[END_REF]. It is a pedagogical approach that aims to make the learner an actor in his or her learning process with active participation in the construction of knowledge.

Project-based learning

Project-based learning is a practice of active pedagogy that allows managing learning through the realization of an individual or collective project. This pedagogy allows learners to become familiar with the complexity of the professional world while helping them to build their personal and professional projects. There are several applications [START_REF] Cursus | Pédagogie par projets : une approche pédagogique moderne ?[END_REF] [19] based on this pedagogical approach which places the learner in a complex problem-solving situation.

Flipped-classroom

Flipped-classroom is an approach that consists of reversing the nature of activities in the classroom (lectures) and at home (homework assignments). Reverse class means giving the students autonomous activities of the low cognitive level to be done at home, in order to favor collaborative work and learning tasks of high cognitive level in the classroom, by putting the students in activity and collaboration [START_REF] Dufour | La classe inversée[END_REF]. There are several applications [START_REF] Choi | Applying Inverted Classroom to Software Engineering Education[END_REF] [22] [START_REF] Danker | Using Flipped Classroom Approach to Explore Deep Learning in Large Classrooms[END_REF] of this pedagogical approach aimed at giving the learning environment a mix of the use of technology with practical educational activities.

Game-based pedagogy

Definitions of game-based learning through play emphasize above all that it is a type of game with defined learning outcomes [START_REF] Plass | Foundations of Game-Based Learning[END_REF]. Educational games are seen as beneficial tools for learning and developing skills in a number of areas, particularly in improving education [START_REF] Bellotti | User Assessment in Serious Games and Technology-Enhanced Learning[END_REF].

Blended learning

Blended learning is a hybrid concept that combines face-to-face and online teaching.

According to [START_REF] Castro | Blended learning in higher education: Trends and capabilities[END_REF], blended learning integrates the use of learning theories and teaching practices in a flexible, multimodal, and multi-linear redesign, with multilinear learning referring to individualized and self-paced learning processes.

Technological innovations and pedagogical transformations have fostered enormous needs in teaching and learning. To improve and adapt learning to align with the needs of learners and industry, educational organizations are moving towards the concept of Education 4.0.

Challenges in Education 4.0

Nowadays, proposals for applications or examples of implementation of the Education 4.0 paradigm are increasingly being developed in educational organizations.

Fisk [START_REF] Fisk | Education 4.0 … the future of learning will be dramatically different, in school and throughout life[END_REF] proposes general innovations and changes needed to implement the education 4.0 paradigm. This proposal is based on the adoption of nine trends in the world of learning which are : (i) learning in different times and places, (ii) personalization of learning, (iii) adaptive and dynamic learning processes, (iv) projectbased learning, (v) field experience, (vi) data interpretation, (vii) formative assessment, (viii) student ownership, and (ix) the mentoring system. In this approach, the Nine Trends in Education 4.0 contribute significantly to the transformation of the current role of the teacher by putting the learner at the center of the learning process.

Hussin [START_REF] Hussin | Education 4.0 Made Simple: Ideas for Teaching[END_REF] implements the nine trends in education 4.0 proposed by Fisk [START_REF] Fisk | Education 4.0 … the future of learning will be dramatically different, in school and throughout life[END_REF] in the context of a language course based on the use of several digital tools with a varied content format (text, video, file, website links). The author uses educational technologies (OpenLearning, Mentimeter, Padlet, Kahoot) to implement reverse pedagogy, activity-based learning, diagnostic and formative assessments, active pedagogy, and badges to reward learner participation and creativity. According to the author, despite the instability of the internet connection encountered by the students, the approach was well appreciated by the students who would like other courses to follow this approach.

Intelitek [START_REF]The Education 4.0 Revolution. Analysis of Industry[END_REF] develops an implementation of Education 4.0, based on the transformation of four paradigms of current education which are : (i) the paradigm of the empty brain to be filled, (ii) the requirement of basic knowledge, (iii) the interference of the computer with thinking and learning in individual mode. Learning environments are inspired by Industry 4.0 and the development of transportation systems, health systems, and much more. The Intelitek Education 4.0 learning system is based on fundamental principles of Education 4.0 such as the personalization of learning paths, formative assessment, mentoring, and the divergence and plurality of learner profiles.

Mourtzis et al [START_REF] Mourtzis | Cyber-Physical Systems and Education 4.0 -The Teaching Factory 4.0 Concept[END_REF] present "The Teaching Factory Concept" which is an application of the Education 4.0 paradigm in the teaching of manufacturing skills. This approach developed is based on the integration of cyber-physical systems and industry 4.0 technologies in teaching. This concept is applied to a case of using courses on the manufacture of a remote-controlled car based on a combination of traditional manufacturing techniques with technologies introduced by Industry 4.0. This application introduces students to advanced manufacturing techniques, integration, and analysis of data collected from design to prototype manufacturing in order to better perform performance tests during the process.

In the literature, there are proposals and cases of application of the Education 4.0 paradigm, which in most cases focus on aligning education (Education 4.0) with the next industrial revolution (Industry 4.0). According to Jhingan [START_REF]Leapfrogging to Education 4.0: Student at the core[END_REF]

, universities need to move away from process-oriented, technology-supported mass education systems to a new teaching method that values individualized learning. Flexible learning paths, emphasis on the transmission of life skills, student-centered learning methods, and the use of technology introduces the concept of Education 4.0".

Current research to develop tools to improve, adapt, and personalize learning is part of the solution to the problems encountered in educational organizations.

Analysis of the barriers and obstacles to education 4.0

Today, Education 4.0 promotes the ubiquitous availability of information and increasingly dynamic teaching and learning processes [START_REF] Halili | TECHNOLOGICAL ADVANCEMENTS IN EDUCATION 4.0[END_REF]. The sources of knowledge coming from the teacher, from physical books, enriched by a large amount of multimedia resources on the Internet (Wikipedia, YouTube, learned societies, electronic articles, and books...) are increasingly heterogeneous and complex, thus limiting the capacities of analysis and use of learning data of systems based on learning improvement. Technology has become ubiquitous in educational organizations seeking to respond effectively to the demand for improvement, optimization, and customization of learning open to the general public. With this accelerated integration of technology in education, we are moving towards ultra-connected universities integrating connected people, robots, objects, and services in the service of learning. This cohabitation between technology and humans is characterized by their weak alliance in the service of adapting learning and differentiating the educational path of each learner.

In order to improve the quality of learning in universities, the challenges of learning can be summarized around three major axes: Reactivity: the ability to provide teaching adapted to the specific needs of each learner with progressive assessment and recommendations (feedback to the learner or teacher) during the learning process and not only at the end of the process (summative assessment). Flexibility: flexibility in pedagogical organization, the use of teaching tools, means of communication with the learning environment, as well as at the level of learning pathways in order to better respond to individualized mass education.

Efficiency: optimizing the use of resources (human, financial, technical), i.e. having more successful learners while reducing the cost of their teaching.

Despite the Education 4.0 paradigm, universities are characterized by a plurality of learners with different profiles, interests, and learning rhythms, which makes it extremely difficult to implement certain resource-intensive techniques to provide each learner with personalized follow-up. The need to integrate resources and actors to allow the design of intelligent and self-adaptive cyber-physical systems capable of managing learning processes also slows down the perfect application of the education 4.0 paradigm. Difficulties in adapting to the individual and evolving needs of learners and teachers in the construction of reusable and self-adapting learning objects, guided by training models sharing common semantics on knowledge repositories, skills for better assessment and remediation of learning outcomes are obstacles in the transition to Education 4.0. As noted, [START_REF] Diwan | Is Education 4.0 an imperative for success of 4th Industrial Revolution?[END_REF], "The rapid pace of emergence of the 4.0 industry requires that Education 4.0 also jumps from the current Education 2.0 to Education 3.0 / 4.0 framework. Thus, in this Education 4.0 context, universities need to adopt education automation to produce innovation in educational organizations [START_REF] Diwan | Is Education 4.0 an imperative for success of 4th Industrial Revolution?[END_REF].

Definition of the University 4.0 Model

In addition to considering the requirements of Education 4.0, the University 4.0 provides autonomous management of learning processes based on the integration of the physical and digital worlds in order to improve and adapt learning.

We take inspiration from the different industrial and educational revolutions to draw an analogy of the common features between the different industrial and academic revolutions, illustrated in Figure 1. We have the first university revolution (University 1.0) which is characterized by a mode of learning limited to a privileged few. The second university revolution (University 2.0) is characterized by a massification of education with the democratization of access to knowledge. The third university revolution (University 3.0) represents the era of integration of digital devices as teaching and learning tools. The concept of the fourth university revolution (University 4.0) that we propose aims at applying the Industry 4.0 paradigm in universities to foster the automation, adaptation, and personalization of learning processes. In this article, we propose to move higher education institutions towards a new educational revolution, entitled "University 4.0". In this University 4.0 concept, we draw on the paradigm of Industry 4.0 by applying its concepts to the university to provide better responses to the specific needs of each learner. Our contribution to this issue aims to foster intelligent collaboration and coordination between physical and virtual actors in order to adapt and personalize learning. With our concept, we aim to enable universities to provide adaptive teaching that meets the needs of its learners. Faced with a dynamic learning environment, characterized by a permanent integration of new learning tools, we propose to rethink and transform the model of integration of technology in teaching for a better alliance of technology and human beings at the service of learning.

Actors

In order to better ensure this transition towards University 4.0, we will propose a common space for the multiple actors of University 4.0 (people, data, objects, and connected services, etc.) providing a better representation of events, symptoms, diagnoses, and plans of recommendations or actions for the definition and execution of personalized learning processes. Furthermore, by representing and managing this knowledge, this system allows the automation (or semi-automation) and optimization of learning processes, as well as the capacity to adapt to dynamic and unpredictable changes in their environment. This will enable educational organizations to better adopting the integration of technologies and the autonomous management of learning processes in University 4.0.

Semantic space

In order to automate learning processes, it is necessary to have a format for describing all entities (resources, actors, properties, relationships, events, etc.) that allow for reasoning on this description. With the complexity of the actors in the learning environment, a language that can be understood and interpreted by both humans and machines is indispensable for intelligent collaboration and coordination between the different actors. It is for these reasons that we have adopted a knowledge base with an ontology-oriented approach. This will allow us to have a shared conceptualization leading to a formal and explicit specification language that is understandable by both humans and machines for better collaboration between people, between machines, and between people and machines.

Autonomous learning

The autonomous management of learning processes requires a system capable of implementing functions of description (complete description of actors, events, changes), diagnosis (identifying dysfunctions, problems in learning processes), prediction (capable of making a prediction about what will happen in the future, for example predicting the failure of a student) and prescription (proposing recommendations to the student or teacher in order to improve the quality of learning). This is why we have adopted the IBM MAPE-K reference architecture of Autonomic Computing [START_REF] Kephart | The vision of autonomic computing[END_REF][START_REF]An architectural blueprint for autonomic computing[END_REF] to provide our system with autonomous management modules: Monitoring, Analysis, Planning, Execution.

Autonomous architecture

The architecture of the solution we propose is based on a data source from the learning environment that can be composed of an LMS, learning objects, virtual learning environments, as well as the interaction traces of the actors. After the collection and storage of the learning data using an Learning Record Store (LRS), these data are intended for the customization system constituted by the autonomous learning management based on the IBM MAPE-K reference architecture of Autonomic Computing with the autonomous manager modules around an ontological knowledge base : Monitoring dedicated to the monitoring of the system, its properties, and its environment through the collection of all kinds of information from the LRS in order to determine the symptoms, i.e. to give meaning to the data, so that it becomes relevant information for our educational decision-making process. Analysis processes the information contained in the symptoms received according to the policies and strategies defined in the KB.

Planning develops action plans describing how the required changes will be implemented. Execution implements the planned plans by carrying out the actions in the form of recommendations to the teacher (relevance of an objective).

Evaluation and validation of our proposal

To evaluate and validate our system, we intend to use the Technology Acceptance Model (TAM) which was developed by Davis in 1989. This model will allow us to determine the behaviour of students and teachers in using our solution. The TAM is based on two main and external variables (Perceived Usefulness and Perceived Ease of Use) that affect the level of acceptance and motivation of students and teachers to use our system.

• Perceived Usefulness (PU)

The PU variable is seen as the measure to which students and teachers believe that the autonomous learning management system is useful for improving performance and achieving the desired satisfaction.

• Perceived Ease of Use (PEU)

The variable PEU is defined as the measure to which students and teachers feel that the use of the system is free of physical and mental strain. That is, the fact that the system provides autonomous management of personalized and adaptive learning processes by implementing description, diagnosis, prediction, and prescription functions.

Conclusions and Future works

This article proposes a new concept of University 4.0 to contribute to the transition to Education 4.0. University 4.0 is essentially based on the application of Industry 4.0 concepts in educational organizations. In this concept, we want to adopt automation (or semi-automation) and optimization of learning processes based on the principle of automation and digitalization of manufacturing processes in Industry 4.0. University 4.0 will enable educational organizations to better adopt the integration of technologies and the autonomous management of learning processes in University 4.0 for better management of the adaptation and differentiation of learning paths, as well as the optimization of learning processes. This autonomic management of learning processes is essentially based on the semantic web technologies with an ontological knowledge base and on IBM's reference architecture of Autonomic Computing.

This system will help to facilitate intelligent collaboration and coordination between the multiple actors of the University 4.0 (people, data, objects and connected services, etc.) for the improvement of learning.

In a forthcoming paper, we will publish the results of the solution we are deploying at the level of a distance master's degree with 30 students spread around the world with a total hourly volume of 300 hours of classes.

Fig. 1 .

 1 Fig. 1. Analogy between the different industrial and university revolutions

Fig. 2 .

 2 Fig. 2. Autonomous Learning Architecture

Acknowledgment. The authors would like to thank the Conseil Départemental des Landes (CD40) and the Laboratoire d'Informatique de l'Université de Pau et des Pays de l'Adour (LIUPPA) for their support in carrying out this research project.


Roberto Galbiati
email: roberto.galbiati@sciencespo.fr

Emeric Henry
email: emeric.henry@sciencespo.fr

Nicolas Jacquemet
email: nicolas.jacquemet@univ-paris1.fr

Max Lobeck
email: max.lobeck@psemail.eu

Fetzer

Hensel, Jachimowicz, Haushofer, Ivchenko, Caria Witte

Roth Reutskaja

Fiorin

Götz Kraft-Todd Gómez

Petherick, Phillips Hale Webster

HOW LAWS AFFECT THE PERCEPTION OF NORMS: EMPIRICAL EVIDENCE FROM THE LOCKDOWN

Keywords: JEL Classification: N/ JEL Classification: K1, I12, I18 laws, norms, expressive function, misperception, COVID-19

was established in 1983 as an educational charity, to

Introduction

Individual behavior is affected both by material incentives, in particular those codified in laws, and by societal sanctions or rewards, embodied in norms of behavior. The interactions between laws and norms is of growing interest both in law and in economics. [START_REF] Benabou | Laws and Norms[END_REF] propose a theoretical framework that formalizes two types of interactions. First, laws, by changing material payoffs, affect the norm of behavior understood as an equilibrium object. Indeed, if fewer people take the condemned actions, the social stigma attached to these actions increases. Second, laws, when there is an underlying uncertainty on the prevailing norm, provide information on societal values. Both these mechanisms imply a shift in the perceived norm, in the first case because the norm did actually change and in the second through an informational channel. Taking into account such interactions between laws and norms is key to understand why policies designed to foster cooperation fail or succeed (see [START_REF] Bowles | Policies Designed for Self-Interested Citizens May Undermine "The Moral Sentiments": Evidence from Economic Experiments[END_REF]Bowles and Polania-Reyes, 2012, for recent surveys).

In this paper, we take advantage of the lockdown measures introduced to face the Covid-19 pandemic and of rich survey data, gathered by [START_REF] Fetzer | Perceptions of an Insufficient Government Response at the Onset of the COVID-19 Pandemic are Associated with Lower Mental Well-Being[END_REF] worldwide, to provide causal evidence that laws affect the perception of norms. We show that the law immediately increased the belief that others think that social distancing measures should be followed. In the second part of the paper, we provide evidence that the informational channel in [START_REF] Benabou | Laws and Norms[END_REF] appears to have played the largest role and that a direct shift of the norm seems less likely.

We focus on the case of Boris Johnson's announcement of a nation-wide lockdown in the UK in the evening on March 23 2020. This setting has several key features that we can exploit to test the causal effect of laws on perceptions of the norm, and the possible mechanisms at play. First, the implementation of this law came as a relative surprise. Indeed it represented a sharp change in the UK government's strategy that has previously signaled strong reserves regarding total lockdowns. Second, the law was far reaching, including several different policies, such as lockdown and store closures, that had been typically more gradually implemented in other countries.

The law had an immediate impact on mobility, reducing for instance trips to parks by 30% within days. We provide evidence that this strong effect on behavior is supported by changes in perceptions of the norm. To that end, we examine how the law affected individual's beliefs of whether other people believe social-distancing measures are important. We test the causal effect of the lockdown announcement by comparing daily responses of individuals that were interviewed before March 23 2020 in the UK with those that were interviewed after March 23 2020 in the UK. Trends in the perception of the norm is controlled for by looking at the beliefs on the same days for respondents living in a set of control countries. This event study analysis shows that the lockdown announcement significantly increased the likelihood that individuals believe that their compatriots view positively staying at home, closing stores, and not participating in social gatherings. The effect is very sizable, representing for instance a 15 percentage points increase in the belief that other people think that stay at home measures should be followed. We show that these results are robust to various identification strategies.

In the second part of the paper, we distinguish the two mechanisms proposed in [START_REF] Benabou | Laws and Norms[END_REF] that can explain the shift in the perception of the norm. We study directly the normative beliefs themselves, i.e., the individual response to whether social distancing measures are important. First, we show that, before the law was passed, there was a large gap between the actual average normative belief and the average perception of the norm, a gap we call misperceptions. Second, performing the same event study exercise as on the perceived norm, we show that misperceptions sharply drop after the implementation of the policy. This mostly reflects the fact that the actual normative beliefs did not themselves shift much. Overall, this suggests that the law mostly acted to provide information on the underlying norm, and in particular to correct misperceptions about this norm. There is little evidence that the norm itself immediately shifted, even though this direct effect on the norm operating through equilibrium beliefs, could take longer to operate.

This paper relates to different strands of literature. First, it contributes to a literature in economics studying the interaction between laws and norms. [START_REF] Acemoglu | Social Norms and the Enforcement of Laws[END_REF] study a context where the effectiveness of laws depends on their coherence with social norms that drive social stigma for illegal behavior. 1 In law and economics the interaction between laws and societal values has been the focus of studies analyzing the expressive function of the law. [START_REF] Mcadams | An attitudinal theory of expressive law[END_REF] is the first study to argue that, when people seek social approval, laws both provide information about prevailing social values and affect ones' own perceptions about the latter. Some recent papers have studied the effects of legal interventions on preferences and perceived norms in the laboratory -e.g., [START_REF] Mcadams | Coordinating in the Shadow of the Law: Two Contextualized Tests of the Focal Point Theory of Legal Compliance[END_REF] in a coordination game setting and Galbiati andVertova (2008, 2014); [START_REF] Tyran | Achieving compliance when legal sanctions are non-deterrent[END_REF]; [START_REF] Galbiati | Dynamic effects of enforcement on cooperation[END_REF] in the context of social dilemmas. Using a vignettes experiment, [START_REF] Lane | Law and norms: Empirical evidence[END_REF] study the effect of laws on how people perceive certain behaviors as socially appropriate or not. Their findings show that laws exert an effect on the perception of the social appropriateness of certain behaviors. Their design however does not distinguish the direct impact of laws on normative beliefs from their effect on the perceived norms. In the field, [START_REF] Funk | Is There An Expressive Function of Law? An Empirical Analysis of Voting Laws with Symbolic Fines[END_REF] studies the effect of the removal of voting obligations in Switzerland and shows that, even though obligations to vote were backed only by symbolic fines, their removal drastically reduced turn-out. The study however shows an impact on behavior but does not document whether the effects are driven by preferences, perceived norms, or both. [START_REF] Aksoy | Do laws shape attitudes? Evidence from same-sex relationship recognition policies in Europe[END_REF] study the relationship between legal same-sex relationship recognition policies and attitudes toward sexual minorities in Europe. They find that legal recognition is associated with a significant improvement in attitudes toward sexual minorities. We see this work, focusing on attitudes instead of perceived norms, as a complement to ours. Our study also contributes to an emerging literature studying change in societal norms and its consequences in economics. [START_REF] Bursztyn | Misperceived Social Norms: Women Working Outside the Home in Saudi Arabia[END_REF] study how long-standing social norms can potentially change with the provision of information. They show that, in Saudi Arabia, individuals misperceive the level of societal support of women working outside home and provide experimental evidence that correcting beliefs about others increases married men's willingness to help their wives search for jobs. Our analysis shows that laws similarly provide information which corrects misperceptions about the prevailing norms.

Data

Our data come from a large online survey gathered by Fetzer et al. (2020, henceforth FWH). The survey collects data on individual attitudes and beliefs concerning Covid-19 measures. The survey was launched on March 20 and we use responses up to March 30, resulting in over 99, 000 respondents from up to 58 countries2 The data contains daily information on respondents' beliefs about four distinct social distancing measures: social gatherings, avoiding handshakes, closing stores and implementing a general curfew. For each of these measures, respondents are asked about their perception of the social norm, specifically whether they believe other individuals in their countries think that these measures should be adopted (see the Online Appendix, Section A, for detailed information about the variables and their definition). We complement this information with external daily country-level data on coronavirus cases and deaths in the respondent's country provided by the John's Hopkins University [START_REF] Dong | An interactive web-based dashboard to track COVID-19 in real time[END_REF]. Boris Johnson's March 23 announcement of a full and immediate lockdown in the UK is our main source of identification. 3 The lockdown prohibited citizens to leave their home except for one form of exercise per day, medical visits, shopping basic necessities, and traveling to and from work if work from home is not possible. It also banned gatherings of more than 2 people and ordered non-essential shops to close. Importantly, this decision marked a stark change in the government's approach to contain the epidemic. Indeed, as late as March 22 the prime minister recommended that individuals stay two meters apart when interacting outdoors, noting that he "want [s] people to be able to go to the parks and open spaces and to enjoy themselves -it is crucial for health and mental and physical wellbeing" (office U.K. [START_REF] Government | Prime˜ministeroffice . Prime Minister's statement on coronavirus (COVID-19): 22[END_REF]. The government in fact initially suggested that they would aim at achieving heard immunity. The measures also marked a change in policy relative to other countries that did not implement any further restrictions (e.g., Sweden) or that have already implemented such measures on a large scale (e.g., France, see [START_REF] Hale | Oxford covid-19 government response tracker[END_REF].

It turned out however that the enforcement was not as stringent as in other countries. Over a period of 3 months following the lockdown, less than 16, 000 fines for violation were issued (compared to more than a million in France), whereas the fine of 60 pounds was lower than in many other countries (135 Euros in France). The police force had been instructed to favor discussion and education over sanctions. Nevertheless the law had a strong impact on the behavior of the population. Using Google mobility data and regressing different measures of mobility, controlling for the state of the pandemic in each country, we show in Figure 1 that all types of movements were Note. These figures plot the day-fixed effects of a specification that regresses a measure of mobility on days as well as Covid deaths and confirmed cases. The outcome variable is mobility data provided by Google. It characterizes in percent how many individuals spend time in (a) recreational areas, (b) parks, (c) transit, and (d) stores and pharmacy relative to a baseline. This baseline is the average number of visit on the same weekday between January 3rd and February 6th. A negative value thus means that there are fewer people at a given place than in the baseline period. The unit of observation is percent and the coefficients have to be interpreted as percentage points.

significantly reduced after March 23rd in the UK, in particular those for recreational purposes. 4For example, the lockdown reduced time spent in parks by 29 percentage points compared to the average time spent in parks on the same weekday between January 3rd and February 6th. Note that this is the pure effect of the lockdown, controlling for behavioral changes before the lockdown. Our aim is to examine whether this large impact of the law on mobility is supported by changes in the perception of the social norm.

To that end, we exploit the lag in the implementation of similar policies in other countries.

Figure 2: Timeline of policies implementation in the control group Note. The figure reports the share of countries in the control group where the corresponding policy was enforced on each day provided on the x-axis.

This policy information comes from the Oxford COVID-19 Government Response Tracker that tracks social distancing policies on the country level by day [START_REF] Hale | Oxford covid-19 government response tracker[END_REF]. Figure 2 displays the timeline of the implementation of the following policies: school closing, workplace closing, cancellation of public events, stay at home requirements, closure of public transportation, restrictions on internal movements and restrictions on international travel.5 Figure 2 shows that, even though there was gradual adoption of more stringent policies around the world, there is no discontinuity around March 23rd, the date of the UK lockdown. This will be the basis of our estimation strategy, as described below.

Results

The causal effect of the law on perceived norms

Figure 3 provides descriptive support for our main result. For each of the four policy measures (forbid social gatherings, no handshake, close stores and introduce a curfew), we report the dayfixed effects for the regressions of the perceived norm in the UK and in control group countries. We control for differences in observed heterogeneity by including country, age (measured in bins of 5 years), gender, education, and income-fixed effects, as well as a measure of household composition. For all four social distancing measures the pre-trends are similar prior to the announcement by Boris Johnson. However there is a sharp discontinuity in the trend for the UK after March 23rd. We statistically test for these effects by running difference-in-difference (DiD) regressions on the perceived norm for each of the four policies, measured at the individual level, i, on each day d. We generalize the approach as compared to the usual linear model by introducing day and country fixed-effects (which allow for a non-linear effect of the post-treatment and the treatment-group

y id = α + βP ost d × U K i + Country i γ + Day d φ + x id κ + u id , ∀i, d (1)
The control variables in the x vector notably include (current and lagged) measures of countrydate variations in Covid deaths and confirmed cases. We also include country-age-gender, countryeducation, income quintile, and day fixed-effects as well as a control for the household composition. Last, we account for individual correlation in unobserved heterogeneity both over time within countries and between individuals within countries by clustering the standard errors at countryage-gender level.7

The results of DiD estimates are provided in the first row of Table 1, where we perform the estimation both on the whole set of countries available in the sample (panel A) and on the more homogeneous subset of Western and Northern European countries (panel B; the list is provided in the Online Appendix, Table A). The lockdown announcement has a strong positive effect on the perceived norm, for all of the different social distancing measures (note that their unit is the same). The effect is strongest for the implementation of a general curfew and the closure of stores. It is weaker for social gatherings and positive, small, and for the most part insignificant for the no handshake policy. The effect is similar in magnitude if we only compare the UK respondents to respondents from other North-Western countries (panel B).

Robustness analysis

The main challenge to our identification strategy of the causal effect of the UK announcement on the perception of norms is the risk that our estimates capture the announcement of similar policies in control group countries. To tackle this issue, we run several robustness checks, the results of which are summarized in the Online Appendix, Section D.

Our first set of robustness checks relies on alternative identification strategies. First, as explained in Section 2, our main source of identification is the discontinuity in the government response in the UK on March 23. As an alternative to the difference-in-difference estimates on the whole sample period, we narrow the analysis to the neighborhood of the discontinuity and focus solely on data observed on March 22 and March 24 (see panel A in the Online Appendix, Section D.1). Second, Figure 2 shows that some policy variation does occur in the control group during the sample period -although the trend is very flat around this discontinuity. To wash-out these variations from the estimated effect, we run the difference-in-difference estimation in (1) on the control group made only of countries in which no policy variation happens between March 20 and March 30 (see panel B). Both exercises lead to very similar estimates in terms both of magnitude and statistical significance. Third, we exploit changes in the timing of the introduction of lockdowns in all countries over the time period of interest (which is the case of 49 countries out of the 172 represented in our sample), by regressing perceived norms on country fixed effects, day fixed effects and an indicator variable measuring whether a lockdown is in place (we moreover account for the same control variables as in other regressions; see panel C). The results show that the introduction of a lockdown is correlated with a significant and large increase in perceived norms.

Our second set of robustness checks relies on variations in the composition of the control group used to generate the estimates provided in Table 1. We replicate the estimation based on the same control group, but from which we remove each country one at a time (the results are provided in the Online Appendix, Section D.2). All estimated coefficients are statistically indistinguishable from the baseline coefficient (first line in the figure). This shows that our results are not driven by dynamics in one particular country.

The gap between perceived and actual norm

The results in the previous section clearly show that the law had a strong effect on individual perceptions of the normative beliefs of others. We now examine the mechanism that could lie behind this effect. [START_REF] Benabou | Laws and Norms[END_REF] suggest two main channels: first, the law, by changing material payoffs of the socially desired action, also affects the norm of behavior resulting from equilibrium behavior. In particular, if individuals start adopting the prescribed action because of sanctions imposed by laws, those who still do not take this action will signal their extreme attitudes and carry worse stigma. Here, the law thus directly affects the norm. A second channel is that the law may bring information on the norm, even if the norm remains unchanged. These two explanations notably differ regarding whether the norm actually changes. We build a measure of actual norms thanks to an additional variable in the survey asking respondents about their normative beliefs, i.e. whether they believe each individual policy is important (the variable is described in the Online Appendix, Section A). If the information about the prevalent norm was perfect, the average over the entire population of these normative beliefs should be equal to the average perception of the norm. We thus build a measure of the actual norm based on the average normative belief and taking into account that our sample is not representative of the entire population. We compute the weighted average of this variable at the country level separately before and after March 23, where the weights rescale the data to make our sample representative of the gender-age-income-household size composition of the population at the country level.

Using this measure, we first show that there was an initial gap between the norm and the perception of the norm in the UK, a gap we call misperceptions. Section E in the Online Appendix presents misperceptions before March 23 in the left panel and after in the right panel. The left panel clearly shows that before the lockdown, misperceptions were very high, in other words, the perceptions of the norm were significantly below the norm itself for most dimensions, except for handshake where the discrepancy was much lower. The right panel shows that after March 23, this misperception sharply drop. This evolution observed in the raw data is confirmed in Figure 4 where we replicate Figure 3 but on the misperception measure. As shown in Table 1 (second row in each subpanel), these results all are statistically significant based on DiD estimates from linear models similar to (1) in which the misperception is used as a dependent variable. This effect on misperceptions, that echoes the effect on the perceived norms, is essentially driven by the fact that normative beliefs themselves do not change (see the Online Appendix, Section F; we also ascertain that the effect is not driven by the use of weights thanks to a replication on weighted data of the DiD estimation of the effect on perceived norms, see Section D.1, panel D). This set of results suggest that the most plausible channel is that the law changed the perceptions of the norm without actually changing the norm itself. In fact, for handshakes, the dimension where misperceptions was initially the lowest, the law had virtually no effect on the perceptions of the norm.8

Conclusion

In this paper, we use the announcement of a sudden and drastic lockdown in the UK to provide causal evidence that laws affect the perception of societal norms in the population. We also show that the most plausible mechanism is an informational channel over a direct change in the norms. The UK had several features that favoured this informational channel. First, the population was initially pessimistic about the prevalent norm, as indicated by the large misperception gap before March 23rd, leaving room for new informations to affect beliefs. Second, as described in Section 2, the enforcement of the law was relatively weaker than in other countries, decreasing the potential for a direct impact on a norm change. In this context, our results show the law does provide information, resulting in a large change in what norm the population thinks prevails. Our study thus sheds new light on the mechanisms explaining why and under what circumstances laws are effective and contributes to a better understanding of how perceptions about prevailing norms are formed.

Online Appendix A Sample information A.1 Variables and data source

The entire set of variables available in the data is described in FWH. We only describe below the variables used as the main outcomes in the analysis. Perceived norms. Our measure of perceived norms come from questions about the perception of others' beliefs about Coronavirus measures:

• sob social : How many of 100 people in your country do you think believe that participation at social gatherings should be cancelled because of the coronavirus right now? [slider ranging from 0 to 100 -initiated at 0]

• sob handshake: How many of 100 people in your country do you think believe that one should not shake other people's hands because of the coronavirus right now? [slider ranging from 0 to 100initiated at 0]

• sob stores: How many of 100 people in your country do you think believe that all shops in your country other than particularly important ones, such as supermarkets, pharmacies, post offices, and gas stations, should be closed because of the coronavirus right now? [slider ranging from 0 to 100initiated at 0]

• sob curfew : How many of 100 people in your country do you think believe there should be a general curfew in your country (with the exception of grocery shopping, necessary family trips, and the commute to work) because of the coronavirus right now? [slider ranging from 0 to 100 -initiated at 0] Misperception. In order to build a measure of misperception, we rely on questions about normative beliefs:

• For each policy, we compute the weighted average of this variable at the country level, separately before and after March 23. The weights aim at restoring the national representativity of the sample regarding observed heterogeneity available in the data.

Weights. The dataset also contains information about the distribution of the population in each country over age, gender, education, income and household composition (assuming independence in the population between these characteristics). We use this additional source of information to build weights rescaling the observations available in the sample to make them representative of the country population.

A.2 Verbatim of Boris Johnson's March 23 announcement

According to UK government official communication, the speech reads as follows (https://www.gov. uk/government/speeches/pm-address-to-the-nation-on-coronavirus-23-march-2020, text emphasized by us):

Good Evening, The coronavirus is the biggest threat this country has faced for decades -and this country is not alone. All over the world we are seeing the devastating impact of this invisible killer. And so tonight I want to update you on the latest steps we are taking to fight the disease and what you can do to help.

And I want to begin by reminding you why the UK has been taking the approach that we have. Without a huge national effort to halt the growth of this virus, there will come a moment when no health service in the world could possibly cope; because there won't be enough ventilators, enough intensive care beds, enough doctors and nurses.

And as we have seen elsewhere, in other countries that also have fantastic health care systems, that is the moment of real danger.

To put it simply, if too many people become seriously unwell at one time, the NHS will be unable to handle it -meaning more people are likely to die, not just from Coronavirus but from other illnesses as well.

So it's vital to slow the spread of the disease.

Because that is the way we reduce the number of people needing hospital treatment at any one time, so we can protect the NHS's ability to cope -and save more lives.

And that's why we have been asking people to stay at home during this pandemic.

And though huge numbers are complying -and I thank you all -the time has now come for us all to do more.

From this evening I must give the British people a very simple instruction -you must stay at home.

Because the critical thing we must do is stop the disease spreading between households.

That is why people will only be allowed to leave their home for the following very limited purposes:

• shopping for basic necessities, as infrequently as possible

• one form of exercise a day -for example a run, walk, or cycle -alone or with members of your household;

• any medical need, to provide care or to help a vulnerable person; and travelling to and from work, but only where this is absolutely necessary and cannot be done from home.

That's all -these are the only reasons you should leave your home. You should not be meeting friends. If your friends ask you to meet, you should say No. You should not be meeting family members who do not live in your home. You should not be going shopping except for essentials like food and medicine -and you should do this as little as you can. And use food delivery services where you can.

If you don't follow the rules the police will have the powers to enforce them, including through fines and dispersing gatherings.

To ensure compliance with the Government's instruction to stay at home, we will immediately:

• close all shops selling non-essential goods, including clothing and electronic stores and other premises including libraries, playgrounds and outdoor gyms, and places of worship;

• we will stop all gatherings of more than two people in public -excluding people you live with;

• and we'll stop all social events, including weddings, baptisms and other ceremonies, but excluding funerals.

Parks will remain open for exercise but gatherings will be dispersed.

No Prime Minister wants to enact measures like this. I know the damage that this disruption is doing and will do to people's lives, to their businesses and to their jobs.

And that's why we have produced a huge and unprecedented programme of support both for workers and for business.

And I can assure you that we will keep these restrictions under constant review. We will look again in three weeks, and relax them if the evidence shows we are able to.

But at present there are just no easy options. The way ahead is hard, and it is still true that many lives will sadly be lost.

And yet it is also true that there is a clear way through.

Day by day we are strengthening our amazing NHS with 7500 former clinicians now coming back to the service.

With the time you buy -by simply staying at home -we are increasing our stocks of equipment. We are accelerating our search for treatments. We are pioneering work on a vaccine. And we are buying millions of testing kits that will enable us to turn the tide on this invisible killer. I want to thank everyone who is working flat out to beat the virus.

Everyone from the supermarket staff to the transport workers to the carers to the nurses and doctors on the frontline.

But in this fight we can be in no doubt that each and every one of us is directly enlisted. Each and every one of us is now obliged to join together.

To halt the spread of this disease.

To protect our NHS and to save many many thousands of lives. And I know that as they have in the past so many times. The people of this country will rise to that challenge. And we will come through it stronger than ever. We will beat the coronavirus and we will beat it together. And therefore I urge you at this moment of national emergency to stay at home, protect our NHS and save lives.

Thank you.

B Effect of March 23 lockdown measures on movements in the UK

The Table below

D Results from the robustness analysis D.1 Regression results

The

D.2 Step deletion of countries from the control group

The figure below reports the point estimates along with 95% confidence intervals resulting from the difference-in-difference estimation in (1) performed on control groups resulting from the step deletion of each country one after the other. The countries iso-code are defined in Table A. For each of the four policy measures, the figure below reports the day-fixed effects from individual normative beliefs in the UK and in control group countries, controlling for country-, age-, gender-, education-, and income-fixed effects, as as well as a measure of household composition. The results from difference-indifference estimates of the effect of March 23 announcement on individual normative beliefs, available from the authors upon request, confirms that the announcement has a non-significant effect regarding both handshaking and social gatherings, and a small but statistically significant effect regarding stores closure and a total curfew.

(a) Social gatherings

Day in March

G Heterogeneity in the UK response to the lockdown

The Tables below provide the results from separate regressions in which we allow the DiD estimate in (1) to interact with observed individual covariates (Table E) and subjective variables (Table F). For each set of regressions, we report the coefficient of the corresponding variable, the resulting DiD estimate (Post × UK variable) as well as the interaction. The subjective variables come from the "Perceptions of government/public response and efficacy" part of the survey, and are measured as:

• perceivedeffectivnes: What do you think: How effective are social distancing measures (e.g., through a general curfew) to slow down the spread of the coronavirus? For each variable, we generate dummy variables equal to 1 if the individual's response is above the midpoint of the Likert scale, and 0 if it is below.

Supplementary material (for referring purpose only) H Country variations in the containment stringency index

The stringency index is computed by [START_REF] Hale | Oxford covid-19 government response tracker[END_REF] as the sum of the policy indicators, adding an extra half-point if the policy is general rather than targeted, if applicable. The value is then rescaled by its maximum value to create a score between 0 and 100, with a missing value contributing 0.3. The figure below reports the change in the mean index from before to after March 24. The further to the right a country is, the larger was the change in the stringency index. The vast majority of countries had very little change in that period. 85% of countries have a change in their stringency index that is not even half of the UK's and 75% have a change in their stringency index that is a quarter of UK's change. The change is very small in countries with large sample sizes in the survey, as the US (0.9925003), Germany (5.852), Sweden (0.831428), Brazil (2.578571), Switzerland (0), or Belgium (0). One notable exception is Mexico. Mexico closed schools on March 22, canceled public events, and put restrictions on gatherings. However, work from home requirements was enforced on March 26 and confinement was put into place a week later, on March 30.

I Replication of

J Full results tables from robustness regressions

K Robustness of the DiD estimates to a European control group

The figure below reports the point estimates along with 95% confidence intervals resulting from the difference-in-difference estimation in (1) on the control group made of Northern and Western European countries from which of each country is excluded one after the other. The countries iso-code are defined in Table A. The table below provides the results from linear models similar to (1) but using individual normative beliefs as a dependent variable.

Gatherings Handshake

Figure

  Figure 1: Mobility patterns in the UK (a) Recreation

Figure 3 :

 3 Figure 3: Time pattern of perceived norms in the UK and the control group

  The figure reports the day-fixed effects along with their 95% confidence intervals from separate regressions in the UK and in the control group of the perceived norm measured in the survey about (a) social gatherings, (b) handshaking, (c) stores closure and (d) a total curfew, controlling for country, age, gender, education, and income-fixed effects, as well as household composition. Standard errors are clustered at the country-age-gender level.

Figure 4 :

 4 Figure 4: Time pattern of misperceptions in the UK and the control group (a) Gatherings

  fob social : "What do you think: should people in your country cancel their participation at social gatherings because of the coronavirus right now? " [No = 0; Yes = 1] • fob handshake: "What do you think: should people in your country not shake other people's hands because of the coronavirus right now?" [No = 0; Yes = 1] • fob stores: "What do you think: should all shops in your country other than particularly important ones, such as supermarkets, pharmacies, post offices, and gas stations, be closed because of the coronavirus right now?" [No = 0; Yes = 1] • fob curfew: "What do you think: should there be a general curfew in your country (with the exception of grocery shopping, necessary family trips, and the commute to work) because of the coronavirus right now?" [No = 0; Yes = 1]

  After comparison of misperceptions in the UKThe figure below displays the discrepancy between the norm and the individual perception of the norm in the UK before and after March 23. The horizontal line in the middle of the box characterizes the median. The upper (lower) ends of the box characterizes the 75th (25th) percentile. The upper (lower) ends of the vertical lines are the upper (lower) adjacent values. Points above (below) are outliers.

F

  Time-pattern of normative beliefs in the UK and the control group

  [5-point scale; 1 = Not at all effective; 2 = Not effective; 3 = Neither effective nor ineffective; 4 = Effective; 5 = Very effective] • govtrust: How much do you trust your country's government to take care of its citizens? [5-point scale; 1 = Strongly distrust; 2 = Somewhat distrust; 3 = Neither trust nor distrust; 4 = Somewhat trust; 5 = Strongly trust] • govfact: How factually truthful do you think your country's government has been about the coronavirus outbreak? [5-point scale; 1 = Very untruthful; 2 = Somewhat untruthful; 3 = Neither truthful nor untruthful; 4 = Somewhat truthful; 5 = Very truthful]

L

  DiD estimates of the effect of the UK lockdown on Normative beliefs

Table 1 :

 1 DiD estimates of the effect of the UK lockdown

		Gatherings Handshake	Stores	Curfew
	A. Full sample (N = 99, 613; 1, 617 clusters)
	Perceived norm	7.370***	3.133***	12.907*** 13.950***
		(0.666)	(0.649)	(0.813)	(0.848)
	Misperceptions	-6.182***	-0.279	-6.038*** -3.910***
		(0.723)	(0.724)	(0.888)	(0.937)
	B. Western and Northern Europe (N = 37, 745; 405 clusters)
	Perceived norm	7.823***	4.262***	14.284*** 14.406***
		(0.762)	(0.706)	(1.020)	(1.016)
	Misperceptions	-7.621***	-1.699*	-6.774*** -4.270***
		(0.890)	(0.706)	(1.308)	(1.077)
	Note. This table presents the difference-in-difference estimates (Post × UK variable) from regressions of perceived norms
	(first row in each panel) and misperceptions (second row) on country-age-gender, country-education, income quintile, and
	day fixed-effects as well as controls for household composition and COVID-19 statistics

(lagged and current confirmed cases and deaths). The sample uses all countries and respondents that answered between March 20 and 30. Standard errors are clustered at the country-age-gender level. Significance levels: * 5%, * * 1%, * * * 0.1%. dummy variables) and estimate the following model (bold letters denote column vectors): 6

  Table A reports the distribution of answers across countries, and Table B provides a comparison of the descriptive statistics observed in the UK and in other countries.

Table A :

 A Distribution of responses across countriesNote. Countries in bold letters are part of the Northern and Western European countries sub-sample.

		iso-code	N	%		iso-code	N	%
	Brazil	BR	11, 230 11.27	Vietnam	VN		0.64
	United Kingdom	GB	11, 151 11.19	Slovakia	SK		0.61
	United States	US	11, 060 11.10	Latvia	LV		0.60
	Germany	DE	82, 77	8.31	Belgium	BE		0.55
	Sweden	SE	57, 46	5.77	Dominican Republic	DO		0.55
	Switzerland	CH	4, 152	4.17	Portugal	PT		0.54
	Russia	RU	3, 364	3.38	Chile	CL		0.52
	Mexico	MX	3, 240	3.25	Malaysia	MY		0.51
	Turkey	TR	2, 784	2.79	Denmark	DK		0.51
	Canada	CA	2, 709	2.72	Albania	AL		0.47
	France	FR	2, 632	2.64	South Africa	ZA		0.47
	Belarus	BY	2, 621	2.63	Israel	IL		0.40
	Spain	ES	2, 211	2.22	Singapore	SG		0.40
	Italy	IT	1, 794	1.80	Poland	PL		0.38
	Colombia	CO	1, 633	1.64	Morocco	MA		0.35
	Indonesia	ID	1, 541	1.55	Kenya	KE		0.34
	Ukraine	UA	1, 440	1.45	China	CN		0.33
	Netherlands	NL	1, 346	1.35	New Zealand	NZ		0.33
	Austria	AT	1, 042	1.05	Bulgaria	BG		0.31
	Peru	PE	1, 015	1.02	Greece	GR		0.31
	India	IN	935	0.94	Thailand	TH		0.30
	Qatar	QA	860	0.86	Ecuador	EC		0.30
	Argentina	AR	858	0.86	Norway	NO		0.29
	Australia	AU	852	0.86	South Korea	KR		0.28
	Romania	RO	791	0.79	Japan	JP		0.28
	Finland	FI	756	0.76	Czechia	CZ		0.26
	Philippines	PH	731	0.73	Uruguay	UY		0.24
	Ireland	IE	695	0.70	Hungary	HU		0.23
	Venezuela	VE	655	0.66	Nigeria	NG		0.21
					Total		99, 100.00

Table B :

 B Respondents' covariates

		Control	UK	Overall
	Women	56.6%	50.4%	55.9%
	Years of Education	16.20	17.26	16.33
		(4.815)	(3.713)	(4.711)
	Age	38.22	43.54	38.85
		(12.84)	(12.89)	(12.96)
	Single	45.1%	33.0%	43.7%
	Number of Household Members	2.863	2.664	2.839%
		(1.591)	(1.356)	(1.566)
	First income quintile	8.60%	10.68%	10.43%
	Second income quintile	6.51%	6.66%	6.64%
	Third income quintile	4.90%	7.18%	6.91%
	Fourth income quintile	12.13%	12.56%	12.51%
	Fourth income quintile	67.86%	62.92%	63.50%
	Confirmed COV-19 cases p.c.	0.206	0.0978	0.193%
		(0.290)	(0.0409)	(0.275)
	Lag confirmed COV-19 cases p.c.	0.0259	0.0141	0.0245%
		(0.0339)	(0.00676)	(0.0322)
	Confirmed COV-19 deaths p.c.	0.00591	0.00553	0.00587%
		(0.0169)	(0.00410)	(0.0159)
	Lag Confirmed COV-19 cases p.c. 0.00106	0.000985 0.00105%
		(0.00244) (0.000863) (0.00231)

  reports the results of the Difference-in-Difference estimation (Post × UK variable) of the March 23 lockdown decision in the UK on mobility data collected from Google's community mobility reports. Each outcome variable is the change in spending time at a given place relative to the median value of the same weekday in the January 3-February 6 period. The specification controls for COVID-19 statistics (lagged and current confirmed cases and deaths) as well as a non-linear effect of the group and Post variable through day-and country fixed-effects.

		Retail	Pharmacy	Parks	Transit
		/recreation /Grocery
	A. Full sample (N = 960; 124 Clusters)
	Post × UK	-25.642***	-21.746*** -29.655*** -16.521***
		(1.024)	(1.167)	(2.007)	(0.987)
	Lag confirmed COV-19 cases p.c.	14.350	49.672	3.192	16.562*
		(10.109)	(31.207)	(25.382)	(8.224)
	Lag confirmed COV-19 deaths p.c.	114.559	-39.607	-1378.007	-85.451
		(221.077)	(331.812)	(827.303)	(175.091)
	Confirmed COV-19 cases p.c.	9.915*	8.681*	5.391	9.175*
		(3.825)	(3.393)	(3.855)	(4.151)
	Confirmed COV-19 deaths p.c.	32.310	-24.885	61.112	36.770
		(49.066)	(46.384)	(58.136)	(45.195)
	B. Western and Northern Europe (N = 167; 16 Clusters)
	Post × UK	-30.497***	-26.002*** -29.849*** -20.610***
		(1.379)	(1.470)	(3.774)	(1.064)
	Lag confirmed COV-19 cases p.c.	4.168	24.933	-49.647	2.981
		(6.110)	(34.540)	(28.724)	(5.409)
	Lag confirmed COV-19 deaths p.c.	-703.338	-594.192	-3024.148	-627.219
		(521.176)	(457.703)	(1572.284) (332.433)
	Confirmed COV-19 cases p.c.	2.174	2.860	7.658*	1.882
		(1.618)	(2.114)	(3.262)	(1.693)
	Confirmed COV-19 deaths p.c.	176.052	-60.292	234.398	75.669
		(115.063)	(98.899)	(324.278)	(91.025)

Note. Standard errors are clustered at the country level. Significance levels: * 5%, * * 1%, * * * 0.1%.

C Full results from Table

1

Table C :

 C DiD estimates of the effect of the UK lockdown on Perceived norms

		Gatherings Handshake	Stores	Curfew
		A. Full sample
	Post × UK	7.370***	3.133***	12.907***	13.950***
		(0.666)	(0.649)	(0.813)	(0.848)
	Lagged confirmed COV-19 cases p.c.	-0.087	-7.473	-4.801	-9.287
		(8.158)	(8.261)	(9.369)	(10.884)
	Lagged confirmed COV-19 deaths p.c.	-253.093	-22.475	216.237	299.417
		(142.145)	(148.263)	(179.753)	(192.567)
	Confirmed COV-19 cases p.c.	-7.892***	-7.134***	-6.044***	-8.320***
		(1.177)	(1.239)	(1.524)	(2.147)
	Confirmed COV-19 deaths p.c.	59.287***	25.019	-30.192	-31.511
		(14.467)	(16.208)	(20.655)	(20.911)
	Household size	0.183***	0.087	0.293***	0.475***
		(0.047)	(0.049)	(0.052)	(0.055)
	Constant	68.323***	76.317***	58.687***	48.846***
		(0.234)	(0.256)	(0.303)	(0.390)
	B. Western and Northern Europe
	Post × UK	7.823***	4.262***	14.284***	14.406***
		(0.762)	(0.706)	(1.020)	(1.016)
	Lagged confirmed COV-19 cases p.c.	-1.272	-4.037	-17.840	-34.267*
		(11.062)	(10.246)	(12.330)	(14.180)
	Lagged confirmed COV-19 deaths p.c.	-363.575	-282.274	456.083	1180.253***
		(265.748)	(224.750)	(274.982)	(319.301)
	Confirmed COV-19 cases p.c.	-6.494***	-3.494*	-0.432	-7.232*
		(1.650)	(1.652)	(2.741)	(3.223)
	Confirmed COV-19 deaths p.c.	117.803*	42.210	18.653	-99.948
		(45.941)	(38.431)	(50.102)	(63.483)
	Household size	0.156*	0.214***	0.188**	0.459***
		(0.070)	(0.064)	(0.072)	(0.088)
	Constant	72.505***	83.653***	61.214***	51.874***
		(0.701)	(0.584)	(1.017)	(1.165)

Note. Standard errors are clustered at the country level. Significance levels: * 5%, * * 1%, * * * 0.1%.

Table D :

 D DiD estimates of the effect of the UK lockdown on Misperceptions

		Gatherings Handshake	Stores	Curfew
		A. Full sample
	Post × UK	-6.182***	-0.279	-6.038***	-3.910***
		(0.723)	(0.724)	(0.888)	(0.937)
	Lagged confirmed COV-19 cases p.c.	7.016	13.010	16.391	51.875***
		(8.309)	(8.610)	(9.706)	(12.386)
	Lagged confirmed COV-19 deaths p.c.	343.552*	114.396	115.224	-596.353**
		(159.227)	(148.515)	(200.048)	(185.863)
	Confirmed COV-19 cases p.c.	7.857***	7.408***	-0.073	-1.003
		(1.233)	(1.893)	(1.953)	(2.830)
	Confirmed COV-19 deaths p.c.	-87.475***	28.593	-75.690**	20.147
		(14.339)	(17.255)	(25.099)	(25.043)
	Household size	-0.167***	-0.109*	-0.248***	-0.443***
		(0.048)	(0.051)	(0.053)	(0.058)
	B. Western and Northern Europe
	Post × UK	-7.621***	-1.699*	-6.774***	-4.270***
		(0.890)	(0.706)	(1.308)	(1.077)
	Lagged confirmed COV-19 cases p.c.	2.142	-6.571	-7.531	45.298*
		(10.821)	(10.805)	(13.364)	(18.085)
	Lagged confirmed COV-19 deaths p.c.	326.642	281.212	-709.739*	511.493
		(284.996)	(227.453)	(323.684)	(309.418)
	Confirmed COV-19 cases p.c.	-0.619	2.964	-10.245**	-8.833**
		(1.887)	(1.724)	(3.572)	(3.103)
	Confirmed COV-19 deaths p.c.	-212.339***	76.314	-84.834	-242.882***
		(48.122)	(39.562)	(73.741)	(64.834)
	Household size	-0.155*	-0.214***	-0.180*	-0.447***
		(0.070)	(0.064)	(0.073)	(0.088)

Note. Standard errors are clustered at the country level. Significance levels: * 5%, * * 1%, * * * 0.1%.

  Table below reports the Difference-in-Difference estimates from the robustness analysis described in Section 3.2. The full results are available from the authors upon request.

		Gatherings Handshake	Stores	Curfew	N	Clusters
		A. March 22 vs March 24
	Full sample	5.422***	2.826**	11.969*** 12.447*** 49, 272	1,367
		(0.921)	(1.046)	(1.404)	(1.163)
	Western and Northern Europe	4.789***	2.800**	11.279*** 11.590*** 20, 029	362
		(0.949)	(1.057)	(1.538)	(1.283)
	B. Countries with no change in their lockdown policy
	Full sample	8.147***	3.913***	14.387*** 14.722*** 20, 533	1,211
		(0.718)	(0.699)	(0.887)	(0.897)
	Western and Northern Europe	8.382***	4.475***	14.946*** 14.885*** 7, 588	315
		(0.724)	(0.679)	(0.949)	(0.933)
	C. Effect of a strict lockdown on pooled data
	Full sample	2.721***	0.855*	5.558***	7.193*** 99, 613	1, 617
		(0.370)	(0.418)	(0.517)	(0.540)
	Western and Northern Europe	3.303***	2.058***	7.394***	8.146*** 37, 745	405
		(0.425)	(0.475)	(0.600)	(0.616)
		D. Weighted data
	Full sample	7.086***	3.381*	13.345*** 16.729*** 99, 613	1, 617
		(1.706)	(1.717)	(1.806)	(2.270)
	Western and Northern Europe	7.491***	3.097	15.526*** 18.146*** 37, 745	405
		(1.731)	(1.766)	(1.897)	(2.486)

Note. Standard errors are clustered at the country level. Significance levels: * 5%, * * 1%, * * * 0.1%.

Table E :

 E Heterogeneity of the DiD estimate according to individual covariates Note. Standard errors are clustered on the country-age-gender level (N = 99, 613; 1, 617 clusters). Significance levels:

		Gatherings Handshake	Stores	Curfew
	A: Gender (the direct effect is part of the model FE)
	Post × UK	13.229***	7.962***	17.567*** 18.122***
		(1.811)	(1.735)	(1.513)	(2.273)
	Post × UK × Female	-3.600***	-2.967**	-2.863**	-2.563*
		(1.025)	(0.961)	(1.042)	(1.292)
	B. Income bracket (the direct effect is part of the model FE)
	Post × UK	6.142***	3.193*	10.268*** 13.022***
		(1.362)	(1.480)	(1.522)	(2.224)
	Post × UK × Income bracket	0.295	-0.014	0.633	0.223
		(0.340)	(0.312)	(0.379)	(0.525)
	C. Years of education (the direct effect is part of the model FE)
	Post × UK	9.301***	4.999*	15.891*** 13.023***
		(2.022)	(2.400)	(2.246)	(3.173)
	Post × UK × Education bin	-0.111	-0.107	-0.172	0.053
		(0.100)	(0.126)	(0.114)	(0.164)
		D. Household size
	Household size	0.178***	0.086	0.291***	0.466***
		(0.047)	(0.050)	(0.052)	(0.056)
	Post × UK	6.498***	2.854*	12.579*** 12.379***
		(1.129)	(1.254)	(1.260)	(1.581)
	Post × UK × Household size	0.331	0.106	0.125	0.597
		(0.320)	(0.362)	(0.372)	(0.505)

* 5%, * * 1%, * * * 0.1%.

Table F :

 F Heterogeneity of the DiD estimate according to subjective perception variables

		Gatherings Handshake	Stores	Curfew
	A. Misestimation of Covid cases
	Mistake	-0.002**	-0.003*	-0.003***	-0.001
		(0.001)	(0.001)	(0.001)	(0.001)
	Post × UK	7.259***	3.058***	12.649*** 13.543***
		(0.669)	(0.687)	(0.811)	(0.876)
	Post × UK × Mistake	0.011	0.008	0.025	0.038**
		(0.013)	(0.011)	(0.014)	(0.014)
	B. Subjective effectiveness of containment measures
	Subjective Effectiveness	0.581***	0.515***	0.944***	1.153***
		(0.092)	(0.096)	(0.108)	(0.116)
	Post × UK	8.442*	4.781	17.471*** 14.315***
		(3.419)	(3.682)	(3.324)	(3.337)
	Post × UK × Subjective Effectiveness	-0.272	-0.409	-1.124	-0.114
		(0.805)	(0.852)	(0.785)	(0.789)
	C. Subjective trust in government
	Trust in Government	2.697***	2.453***	2.388***	2.064***
		(0.059)	(0.068)	(0.082)	(0.097)
	Post × UK	6.257***	3.859**	10.352*** 12.422***
		(1.531)	(1.371)	(1.381)	(1.985)
	Post × UK × Trust in Government	0.029	-0.539	0.537	0.243
		(0.445)	(0.400)	(0.453)	(0.613)
	D. Government was truthful
	Post × UK	7.702***	5.245***	11.701*** 11.366***
		(1.655)	(1.537)	(1.750)	(2.793)
	Government was truthful	2.450***	2.266***	2.054***	1.595***
		(0.063)	(0.070)	(0.080)	(0.094)
	Post × UK × Government was truthful	-0.290	-0.800	0.195	0.637
		(0.430)	(0.420)	(0.496)	(0.775)
	Note. Standard errors are clustered on the country-age-gender level (N = 99, 613; 1, 617 clusters). Significance levels: * 5%,
	* * 1%, * * * 0.1%.

  Table 1 controlling for individual normative beliefs Note. Standard errors are clustered on the country-age-gender level. Significance levels: * 5%, * * 1%, * * * 0.1%.

		Gatherings Handshake	Stores	Curfew
	A. Full sample (N = 99, 613; 1, 617 clusters)
	Post × UK	7.399***	3.122***	12.338*** 12.795***
		(0.671)	(0.663)	(0.755)	(0.829)
	Lagged confirmed COV-19 cases p.c.	0.356	-7.424	-3.227	-5.922
		(8.216)	(8.175)	(9.165)	(10.320)
	Lagged confirmed COV-19 deaths p.c.	-266.647	-35.207	178.640	265.042
		(143.899)	(148.032)	(179.054) (177.882)
	Confirmed COV-19 cases p.c.	-7.605***	-6.482***	-5.296*** -9.359***
		(1.172)	(1.239)	(1.454)	(1.859)
	Confirmed COV-19 deaths p.c.	55.910***	19.709	-33.913	-9.016
		(14.358)	(15.991)	(19.694)	(19.562)
	Household size	0.185***	0.091	0.296***	0.433***
		(0.047)	(0.049)	(0.050)	(0.052)
	Normative belief about Gathering	8.018***
		(0.641)
	Normative belief about Handshake		7.275***
			(0.510)
	Normative belief about Stores			9.741***
				(0.303)
	Normative belief about Curfew				12.550***
					(0.295)
	B. Western and Northern Europe (N = 37, 745; 405 clusters)
	Post × UK	7.972***	4.232***	13.536*** 13.497***
		(0.775)	(0.719)	(0.972)	(0.998)
	Lagged confirmed COV-19 cases p.c.	0.516	-4.329	-13.502	-28.392*
		(11.151)	(10.103)	(12.068)	(13.461)
	Lagged confirmed COV-19 deaths p.c.	-364.036	-264.270	317.679	840.815**
		(265.174)	(223.381)	(275.930) (297.682)
	Confirmed COV-19 cases p.c.	-5.556***	-2.932	-0.548	-7.080*
		(1.581)	(1.663)	(2.670)	(2.882)
	Confirmed COV-19 deaths p.c.	109.038*	28.219	19.311	-40.415
		(45.457)	(38.502)	(50.437)	(57.746)
	Household size	0.161*	0.213***	0.208**	0.446***
		(0.068)	(0.063)	(0.073)	(0.081)
	Normative belief about Gathering	9.459***
		(0.826)
	Normative belief about Handshake		6.934***
			(0.636)
	Normative belief about Stores			10.516***
				(0.516)
	Normative belief about Curfew				11.852***
					(0.431)

Table G :

 G DiD estimates in the neighborhood of the discontinuity (data from March 22 and 24)

		Gatherings Handshake	Stores	Curfew
	A. Full sample (N = 49, 272; 1, 367 clusters)
	Post × UK	5.422***	2.826**	11.969*** 12.447***
		(0.921)	(1.046)	(1.404)	(1.163)
	Lagged confirmed COV-19 cases p.c.	76.149	32.384	10.368	55.475
		(53.745)	(53.254)	(61.976)	(84.255)
	Lagged confirmed COV-19 deaths p.c.	-709.442	-49.688	-243.160	476.192
		(491.274)	(496.624)	(572.345)	(687.533)
	Confirmed COV-19 cases p.c.	-19.765*	-7.088	-13.336	-32.480*
		(8.864)	(9.460)	(9.848)	(13.725)
	Confirmed COV-19 deaths p.c.	55.096	-12.194	31.456	-84.846
		(95.326)	(96.188)	(108.342)	(133.483)
	Household size	0.190**	0.044	0.272***	0.490***
		(0.062)	(0.070)	(0.076)	(0.076)
	Constant	68.430***	74.617***	59.613*** 51.494***
		(1.096)	(1.227)	(1.254)	(1.414)
	B. Western and Northern Europe (N = 20, 029; 362 clusters)
	Post × UK	4.789***	2.800**	11.279*** 11.590***
		(0.949)	(1.057)	(1.538)	(1.283)
	Lagged confirmed COV-19 cases p.c.	258.288**	144.476	217.630	406.957**
		(87.466)	(78.589)	(140.199)	(154.193)
	Lagged confirmed COV-19 deaths p.c.	576.443	2387.211*	175.888	1520.588
		(1030.438)	(951.784)	(1835.821) (1848.473)
	Confirmed COV-19 cases p.c.	-10.555	25.440	-19.567	-33.729
		(16.051)	(14.412)	(28.392)	(30.994)
	Confirmed COV-19 deaths p.c.	-276.776	-668.379*	70.852	52.636
		(314.309)	(291.597)	(586.458)	(614.189)
	Household size	0.217*	0.239*	0.335**	0.535***
		(0.090)	(0.098)	(0.114)	(0.137)
	Constant	64.662***	69.846***	58.602*** 42.702***
		(5.758)	(5.204)	(10.499)	(8.971)

Note. Standard errors are clustered on the country-age-gender level. Significance levels: * 5%, * * 1%, * * * 0.1%.

Table H :

 H DiD Estimates using countries with no change in their lockdown policy over the period as a control group Note. Standard errors are clustered on the country-age-gender level. Significance levels: * 5%, * * 1%, * * * 0.1%.

		Gatherings Handshake	Stores	Curfew
	A. Full sample (N = 20, 533; 1, 211 clusters)
	Post × UK	8.147***	3.913***	14.387***	14.722***
		(0.718)	(0.699)	(0.887)	(0.897)
	Lagged confirmed COV-19 cases p.c.	-3.898	-14.335	-16.704	-29.954*
		(11.650)	(10.835)	(12.969)	(14.666)
	Lagged confirmed COV-19 deaths p.c.	-93.210	-77.843	703.419*** 1043.404***
		(177.103)	(167.831)	(211.151)	(218.352)
	Confirmed COV-19 cases p.c.	-6.795***	-7.320***	-6.286***	-14.685***
		(1.537)	(1.844)	(1.875)	(2.929)
	Confirmed COV-19 deaths p.c.	71.849***	6.043	12.734	84.375**
		(18.441)	(21.669)	(28.542)	(29.815)
	Household size	0.126*	0.103	0.240***	0.427***
		(0.056)	(0.064)	(0.066)	(0.068)
	Constant	69.541***	79.025***	60.054***	50.683***
		(0.332)	(0.403)	(0.397)	(0.551)
	B. Western and Northern Europe (N = 7, 588; 315 clusters)
	Post × UK	8.382***	4.475***	14.946***	14.885***
		(0.724)	(0.679)	(0.949)	(0.933)
	Lagged confirmed COV-19 cases p.c.	-10.376	-18.420	-35.567*	-56.212***
		(12.362)	(11.106)	(13.752)	(16.071)
	Lagged confirmed COV-19 deaths p.c.	-99.932	62.532	391.946	872.042*
		(255.148)	(226.923)	(285.891)	(339.995)
	Confirmed COV-19 cases p.c.	-6.479***	-4.189*	-6.652**	-17.863***
		(1.917)	(2.060)	(2.325)	(3.760)
	Confirmed COV-19 deaths p.c.	128.929*	75.916	270.156*** 318.246***
		(58.996)	(49.921)	(72.511)	(91.732)
	Household size	0.182*	0.230**	0.210*	0.486***
		(0.091)	(0.083)	(0.096)	(0.111)
	Constant	70.452***	82.878***	59.715***	50.522***
		(0.698)	(0.604)	(0.847)	(1.077)

Table I :

 I Effect of a Lockdown on perceived norms on pooled data Note. Standard errors are clustered on the country-age-gender level. Significance levels: * 5%, * * 1%, * * * 0.1%.

		Gatherings Handshake	Stores	Curfew
	Panel A: Full sample (N = 99, 613; 1, 617 clusters)
	Strict lockdown (stay at home)	2.721***	0.855*	5.558***	7.193***
		(0.370)	(0.418)	(0.517)	(0.540)
	Lagged confirmed COV-19 cases p.c.	4.689	-6.420	6.123	6.358
		(8.427)	(8.429)	(9.849)	(11.198)
	Lagged confirmed COV-19 deaths p.c.	11.490	118.298	605.512**	609.175**
		(155.188)	(146.696)	(201.843)	(213.642)
	Confirmed COV-19 cases p.c.	-9.525***	-7.927***	-8.643***	-10.738***
		(1.257)	(1.234)	(1.619)	(2.117)
	Confirmed COV-19 deaths p.c.	68.238***	27.850	-11.964	-7.983
		(15.068)	(16.091)	(21.136)	(21.470)
	Household size	0.182***	0.087	0.290***	0.472***
		(0.047)	(0.049)	(0.052)	(0.055)
	B. Western and Northern Europe (N = 37, 745; 405 clusters)
	Strict lockdown (stay at home)	3.303***	2.058***	7.394***	8.146***
		(0.425)	(0.475)	(0.600)	(0.616)
	Lagged confirmed COV-19 cases p.c.	18.628	7.727	23.370	9.763
		(12.270)	(10.660)	(13.910)	(15.412)
	Lagged confirmed COV-19 deaths p.c.	-53.981	-147.435	842.885** 1480.016***
		(266.821)	(220.918)	(289.294)	(322.226)
	Confirmed COV-19 cases p.c.	-10.361***	-5.372**	-6.289*	-12.530***
		(1.802)	(1.650)	(2.913)	(3.183)
	Confirmed COV-19 deaths p.c.	183.598***	78.883*	143.176**	27.860
		(50.628)	(40.041)	(54.450)	(62.731)
	Household size	0.158*	0.214***	0.189**	0.460***
		(0.071)	(0.064)	(0.072)	(0.087)

Table J :

 J DiD estimates using weighted dataNote. Standard errors are clustered on the country-age-gender level. Significance levels: * 5%, * * 1%, * * * 0.1%.

		Gatherings Handshake	Stores	Curfew
	A. Full sample (N = 99, 613; 1, 617 clusters)
	Post × UK	7.086***	3.381*	13.345*** 16.729***
		(1.706)	(1.717)	(1.806)	(2.270)
	Lagged confirmed COV-19 cases p.c.	12.429	-40.196	-6.319	23.645
		(23.435)	(24.120)	(34.768)	(34.362)
	Lagged confirmed COV-19 deaths p.c.	-175.188	61.985	-125.354	-322.006
		(443.363)	(435.784)	(546.836) (596.076)
	Confirmed COV-19 cases p.c.	-3.679	-4.792	0.678	-7.919
		(3.750)	(3.818)	(5.236)	(4.660)
	Confirmed COV-19 deaths p.c.	24.948	76.710	6.382	6.603
		(45.478)	(47.838)	(69.884)	(72.368)
	Household size	0.423**	0.372*	0.500*	0.756***
		(0.149)	(0.170)	(0.207)	(0.192)
	Constant	67.114***	75.460***	58.679*** 50.351***
		(0.816)	(0.860)	(0.987)	(1.022)
	B. Western and Northern Europe (N = 37, 745; 405 clusters)
	Post × UK	7.491***	3.097	15.526*** 18.146***
		(1.731)	(1.766)	(1.897)	(2.486)
	Lagged confirmed COV-19 cases p.c.	1.007	-30.519	-55.669	-35.017
		(20.535)	(22.232)	(36.467)	(35.875)
	Lagged confirmed COV-19 deaths p.c.	-237.564	35.994	-1296.854	-459.676
		(618.567)	(594.357)	(821.596) (883.087)
	Confirmed COV-19 cases p.c.	-6.075	-1.653	0.875	-8.286
		(3.664)	(3.732)	(6.483)	(5.769)
	Confirmed COV-19 deaths p.c.	98.473	164.416	284.337*	33.196
		(97.343)	(104.047)	(141.527) (146.744)
	Household size	0.170	0.344*	0.382	0.596**
		(0.168)	(0.171)	(0.212)	(0.229)
	Constant	73.025***	83.020***	64.591*** 56.270***
		(1.422)	(1.419)	(1.925)	(2.062)

  Note. Standard errors are clustered on the country-age-gender level. Significance levels: * 5%, * * 1%, * * * 0.1%.

				Stores	Curfew
	A. Full sample (N = 99, 613; 1, 617 clusters)
	Post × UK	-0.004	0.002	0.058*** 0.092***
		(0.004)	(0.007)	(0.010)	(0.014)
	Lagged confirmed COV-19 cases p.c.	-0.055	-0.007	-0.162	-0.268
		(0.062)	(0.081)	(0.154)	(0.221)
	Lagged confirmed COV-19 deaths p.c.	1.690	1.750	3.860	2.739
		(1.337)	(1.392)	(2.845)	(3.782)
	Confirmed COV-19 cases p.c.	-0.036***	-0.090***	-0.077**	0.083
		(0.010)	(0.020)	(0.029)	(0.045)
	Confirmed COV-19 deaths p.c.	0.421*	0.730**	0.382	-1.792***
		(0.181)	(0.222)	(0.370)	(0.390)
	Household size	-0.000	-0.000	-0.000	0.003**
		(0.000)	(0.000)	(0.001)	(0.001)
	B. Western and Northern Europe (N = 37, 745; 405 clusters)
	Post × UK	-0.016*	0.004	0.071*** 0.077***
		(0.008)	(0.007)	(0.013)	(0.016)
	Lagged confirmed COV-19 cases p.c.	-0.189*	0.042	-0.413*	-0.496
		(0.089)	(0.091)	(0.190)	(0.292)
	Lagged confirmed COV-19 deaths p.c.	0.049	-2.596	13.161* 28.640***
		(2.331)	(3.011)	(5.135)	(7.123)
	Confirmed COV-19 cases p.c.	-0.099**	-0.081***	0.011	-0.013
		(0.034)	(0.024)	(0.037)	(0.055)
	Confirmed COV-19 deaths p.c.	0.927*	2.018***	-0.063	-5.023***
		(0.380)	(0.565)	(0.952)	(1.326)
	Household size	-0.000	0.000	-0.002	0.001
		(0.001)	(0.001)	(0.002)	(0.002)

Some papers have looked at the effects of laws on social norms in the context of evolutionary preferences adaptation. Notable examples are[START_REF] Huck | Trust, Treason, and Trials: An Example of How the Evolution of Preferences Can Be Driven by Legal Institutions[END_REF] and[START_REF] Bohnet | More Order with Less Law: On Contract Enforcement, Trust, and Crowding[END_REF].

Responses are not representative but representativity can be reconstructed using country-specific weights. We include all countries that had more than 200 respondents and completed the survey before March

 3 The verbatim of the announcement is provided in the Online Appendix, Section A.2.

These changes all are statistically significant, as shown in the Online Appendix, Section B.

We focus on the 'containment and closure' category and restrict only to mandatory policies, disregarding simple recommendations from the governments.

The outcome variable, y id , denotes either one of the four perceived norms, or one of the four measures of misperceptions as defined in Section 3.2.

In the main tables we only report the estimates of the β parameters; the full results tables are provided in the Online Appendix, Section C. Also note that we do not control for normative beliefs in our preferred regressions on perceived norms, since they are likely to be endogenous to unobserved heterogeneity generating differences perceived norms. The robustness check available from authors upon request, shows that the results still holds when normative beliefs are controlled for and, if anything, are stronger both statistically and in terms of magnitude.

This interpretation is further substantiated by the analysis of the heterogeneity of the response of perceived norms to the UK lockdown. When interacting the treatment effect with subjective perception variables in separate models, the only dimension of heterogeneity that seems to matter is how well individuals are informed about COVID itself, measured as the gap between their estimate of the number of COVID cases and the actual number in their country. The higher that gap, the more the perception of the norm relative to the curfew variable shifts up. These results are provided in the Online Appendix, Section G, along with the results from interactions with individual covariates. Non of these interactions with socio-economic variables are significant, except for gender.

This Discussion Paper is issued under the auspices of the Centre's research programmes: Public Economics Any opinions expressed here are those of the author(s) and not those of the Centre for Economic Policy Research. Research disseminated by CEPR may include views on policy, but the Centre itself takes no institutional policy positions. The Centre for Economic Policy Research