Waris Radji

Corentin Léger

Lucas Bardisbanian

Early Empirical Results on Reinforcement Symbolic Learning

Keywords: Reinforcement Symbolic Learning, Ontology, Edit Distances, Learning Sciences

Reinforcement learning is a subfield of machine learning that is concerned with how agents learn to make decisions in an environment in order to maximize some notion of reward. It has shown a great promise in a variety of domains, but it often struggles with generalization and interpretability due to its reliance on black-box models. One approach to address this issue is to incorporate knowledge representation into reinforcement learning. In this work, we explore the benefits of using symbolic representation in reinforcement learning and present preliminary results on its performance compared to standard reinforcement learning techniques. Our experiments show that the use of symbolic representation can significantly improve the generalization capabilities of reinforcement learning agents. We also discuss the potential challenges and limitations of this approach and suggest avenues for future research.

Premiers résultats empiriques sur l'apprentissage par renforcement symbolique

Résumé : L'apprentissage par renforcement est un sous-domaine de l'apprentissage automatique qui s'intéresse à la manière dont les agents apprennent à prendre des décisions dans un environnement afin de maximiser une récompense. Il s'est avéré très prometteur dans divers domaines, mais il se heurte souvent à des problèmes de généralisation et d'interprétabilité en raison de sa dépendance à l'égard de modèles de type "boîte noire". Une approche pour résoudre ce problème consiste à incorporer la représentation des connaissances dans l'apprentissage par renforcement. Dans ce travail, nous explorons les avantages de l'utilisation de la représentation symbolique dans l'apprentissage par renforcement et présentons des résultats préliminaires sur sa performance par rapport aux techniques d'apprentissage par renforcement standard. Nos expériences montrent que l'utilisation de la représentation symbolique peut améliorer de manière significative les capacités de généralisation des agents d'apprentissage par renforcement. Nous discutons également des défis potentiels et des limites de cette approche et suggérons des pistes de recherche pour l'avenir.

Mots-clés : Apprentissage symbolique par renforcement, Distances d'édition, Ontologie, Sciences de l'éducation.

Introduction

The human brain has evolved to process and interpret the world symbolically [START_REF] Alexander | The human mind: The symbolic level[END_REF], by utilizing abstract concepts such as language and reasoning, and by drawing connections between seemingly dissimilar observations, such as perceiving oranges and lemons as similar due to their shared sensory characteristics. However, classical artificial intelligence agents operate differently by processing information through numerical values and statistical patterns, which may not always be intuitively understandable to humans. One popular approach to reinforcement learning is Q-learning [START_REF] Christopher | Learning from delayed rewards[END_REF], which uses a value function known as the Q-function to estimate the expected cumulative reward for each action in a given state.

The Q-function is updated iteratively using the Bellman equation, which expresses the expected value of the Q-function in terms of the expected reward for taking a given action in a given state, plus the discounted expected value of the Q-function in the resulting state. The Bellman equation is expressed as follows:

Q[s, a t ]+ = α(r t+1 + γmax a Q(s t+1 , a) -Q[s, a t ]) (1)
Here, s t and a t represent the current state and action, r t+1 represents the immediate reward received after taking action a t in state s t , γ is the discount factor (used to give less weight to future rewards), and α is the learning rate (used to control the rate at which the Q-function is updated).

Q-learning has proven to be a powerful technique for a variety of problems, including game playing, robotics, and control systems. However, one limitation of Q-learning is that it can struggle to generalize to new and unseen states. This is because Q-learning relies on an explicit representation of the state space, which can be difficult to achieve for complex and high-dimensional environments.

In order to address this limitation and better understand how humans learn, the Inria Mnemosyme team has introduced a paper where they present an alternative of Q-Learning with symbolic data, called reinforcement symbolic learning [START_REF] Mercier | Reinforcement Symbolic Learning[END_REF]. This technique is based on the fact that it is possible to define an edit distance between two symbolic objects under certain representation constraints, and therefore use the knowledge acquired from previous experiences to adapt faster and better with new states.

In the context of symbolic objects, the edit distance is a metric that measures the minimum number of operations (insertions, deletions, or substitutions) required to transform one symbolic object into another. It is a way of quantifying the similarity between two symbolic objects.

Considering a space of symbolic states S in a reinforcement learning environment, a distance d is defined as ∀s i ∈ S, s j ∈ S, d(s i , s j ). The operation of updating the Q-value (at each step in the environment), proposed by the reinforcement symbolic learning approach is :

Q[s, a t ]+ = αe -d(s,st)/ρ (r t+1 + γmax a Q(s t+1 , a) -Q[s, a t ]) (2)
where ρ is the exponential weighting of radius, α the learning factor and γ the discount factor. In classical Q-Learning, a Q-Value is updated at each iteration. In this approach all Q-Values are updated according to the radius ρ which updates with a stronger intensity the states s which are closest to s t according to the edit distance. This theoretically allows to have agents that have better generalization capabilities, which can also be similar to embedding generation in deep reinforcement learning.

In this paper we present some preliminary results of the application of reinforcement symbolic learning on a self-defined environment and edit distance. Some details of the implementation of reinforcement symbolic learning will also be given. For the reproduction of the results the code can be found on this GitHub repository.

2 The Symbolic Environment: A creature that must survive in the unknown

For the experiments, we decided to create an environment called SymbolicEnv which is built on top of an ontology, which allows us to have a standard way of representing our symbolic data (OWL in our case), and to take advantage of the power of symbolic reasoners. Figure 1 graphically illustrates the ontology of the SymbolicEnv.

In the SymbolicEnv, an agent will have to use its four senses (sight, taste, touch, smell), to choose the most appropriate actions and survive for the longest time, driven by emotions and sensations. To illustrate this, it is possible to identify several parts in the ontology:

Entity The instances that inherit from this class are the entities that the agent may encounter in the environment, e.g. example apple and stone.

ExternalSense The external senses that the agent can perceive, based on these 4 senses, e.g. the texture or colour of an entity.

Inria

InternalSense What the agent feels internally, e.g. his mood, his health level or his hunger.

Action Actions that can be taken in the environment, such as eating or attacking.

At each step, the agent receives an observation which is composed of an integer that represents the internal state of the agent, and another integer that represents the entity that the agent encounters.

To create the internal state of an agent, statistics that can evolve naturally over time, or through events, are maintained. Positive stats (energy, health, joy) have a value between 0 and 20 and negative stats (anger, sadness, fear) have a value between 0 and 10. A function allows to discretize the value of a stat into 4 bins and returns an integer between 0 and 3, representing the bin that the value belongs to.

From each positive statistic and the average of the negative ones, it is possible to construct a vector of dimension 4 which represents each discretized value. Since each vector is unique, we can calculate a unique identifier by associating each vector with a value between 0 and 4 4 -1.

The SymbolicEnv is composed of 6400 observation combinations (256 internal states and 25 entities).

The agent must then choose an action that corresponds to an integer between 0 and the number of action -1, and the agent's statistics are updated accordingly (with an internal logic that is created by reading properties in the ontology).

Edit distance

The edit distance used in this study quantifies the similarity between two observations, each consisting of an internal state i and an associated entity e. The distance between two observations is defined as the average of the distances between their internal states and their associated entities.

d(s 1 , s 2 ) = d((i 1 , e 1 ), (i 2 , e 2 )) = (d(i 1 , i 2 ) + d(e 1 , e 2 ))/2
The distance between two internal states d(i 1 , i 2 ), is calculated by the Euclidean distance normalized distance between 0 and 1 of their two representation vectors.

For the entities, each property p is associated with an ExternalSense, and an empirical "distance" is defined between ExternalSense of the same type. For example, the distance between yellow and orange might be defined as 1, while the distance between yellow and red might be defined as 2.

To calculate the distance between two entities d(e 1 , e 2 ), the method combines the "tree distance" and "properties distance". The tree distance is defined as the sum of the length of the ancestors of each individual in the ontology. The properties distance is calculated as the sum of the distances between the properties of the two entities, normalized by the maximum distance value of ExternalSense of the same type. Finally, the distances are normalized by the maximum distance value.

Implementation details

The ontology are initially written in the YAML format, and translated thanks to Python scripts into the OWL format. This allows to automate the creation of some objects in the ontology, because even with very few entities the amount of information to be specified in the ontology becomes very large. We also use SPARQL queries to retrieve information efficiently from the database.

The SymbolicEnv is built on top of OpenAI Gym [START_REF] Brockman | Openai gym[END_REF] (a standard API for reinforcement learning) which makes agents testing simple.

The Reinforcement Symbolic Agent

The SymbolicAgent is built on top of a classical Q-Learning agent, with a modification in the method that updates the Q-table at each step in the environment. In the case of the SymbolicEnv, the Q-table is of dimension 256×25×9 (number of internal states × number of entities × number of actions).

The agent takes as argument the distance function to compute the distance between two observations, and for faster computation, distances between each observation are pre-computed and stored in a matrix of size 256 2 .

Equation 1 (Symbolic Q-Learning) is implemented in the agent using vectorized operations. Operations likely to be repeated multiple times are stored in the cache.

It will take at least 57600 steps in the SymbolicEnv for a classical Q-Learning agent to be updated at least once every value in its Q-Table, assuming that the agent visits a different state and performs differently at each step. The SymbolicAgent should have much better generalization capabilities and should need far fewer steps in the environment to perform.

Preliminary Results

We trained our agents in the SymbolicEnv for 10000 steps, using a linear epsilon greedy policy, and evaluated the agents performances every 10 training steps. The evaluation involved performing 100 rollouts in 100 SymbolicEnv with fixed seeds, and the score of an agent was calculated as the sum of the cumulative rewards obtained during each rollout.

All agents have the same hyperparameters, except for the radius ρ which we vary in the case of the SymbolicAgents. The experiment consists in observing the differences in performance between a classical Q-Learning agent, and the SymbolicAgents with several values of ρ. Figure 2 shows the evolution of the scores of the different agents throughout the training. Unsurprisingly, the Q-Learning agent struggles to learn, which is simply due to the fact that Inria the Q-Table is too large, and updating the elements one by one would take much longer to get a good agent. The results of the SymbolicAgents are interesting and we can propose several hypotheses:

• With a very small ρ for example (0.01) Symbolic Q-Learning will not update the Q-Table significantly, so the performance will be close to that of classical Q-Learning.

• With a slightly larger radius (0.04) it is possible to obtain performances that are significantly better than the classical Q-Learning, so we see that the ρ hyperarameter is very sensitive, and a small change can drastically change the results.

• When ρ is a bit too large (0.06) the SymbolicAgent seems to try to generalise too much, and probably has to update values that it shouldn't, which makes its learning go quite badly, and even performs worse than Q-Learning.

It should be noted here that the results are quite stable, which is not the case with larger radius values as shown in Figure 3. Figure 3 shows the same experiment but with agents that have a radius ρ greater than 0.1. The results are very stochastic and difficult to interpret, but it is easy to see that the irregularity is considerable. In these cases many elements of the Q-Table are updated, whether they are relevant or not. This means that the choice of a bad action by the agent can be very penalizing.

These agents are able to reach very high scores early in the learning process, but these are rarely maintained over time.

We can imagine having a variant of reinforcement symbolic learning that lowers the radius over time in order to have an agent that will be more and more stable over time

Conclusion

In conclusion, we have presented a framework to create a symbolic environment based on an ontology (with OWL), and connect it to an gym environment to make it easier to train agents in it. With this tool, we have created a symbolic environment where an creature needs to adapt to a complex environment in order to survive. We have compared the performance of Q-learning and symbolic Q-learning with varying radius values in this environment, and the results show that the performance of the symbolic Q-learning approach can be significantly improved with an appropriate choice of the radius parameter.

It is important to note that although the results we obtained with Symbolic Q-Learning are promising, we still do not fully understand how the radius parameter affects the learning process. As we have seen, small changes in the radius value can have a significant impact on the agent's performance and the stability of the learning process, which suggests that the relationship between radius and performance may not be linear. One possible direction for further investigation is to explore ways of dynamically adjusting the radius parameter over time or allowing the agent to learn the optimal radius value. These approaches could potentially improve the adaptability and robustness of the Symbolic Q-Learning algorithm, making it more effective in a wider range of environments.

Despite this, our work has demonstrated the potential of using symbolic environments in reinforcement learning, and we have provided a framework that makes it easy to create symbolic environments using an ontology. We have also shared the Symbolic environment used and the code for our experiments on our open source GitHub repository, which can be used by other researchers and developers to create their own symbolic environments and test new algorithms.

In conclusion, our work highlights the potential benefits of incorporating symbolic reasoning into reinforcement learning and provides a tool for creating symbolic environments that can be used by the research community. The results we obtained with Symbolic Q-Learning suggest that this approach could be a promising direction for future research in the field of RL.

Figure 1 :

 1 Figure 1: Ontology of the SymbolicEnv.

  Symbolic Q-Learning with ρ = 0.01 Symbolic Q-Learning with ρ = 0.04 Symbolic Q-Learning with ρ = 0.06

Figure 2 :

 2 Figure 2: Comparison of Q-Learning and Symbolic Q-Learning Performance with Varying ρ (< 0.1)

Figure 3 :

 3 Figure 3: Comparison of Q-Learning and Symbolic Q-Learning Performance with Varying ρ (> 0.1)

RR n°9509

avenue de la Vieille Tour 33405 Talence Cedex Publisher Inria Domaine de Voluceau -Rocquencourt BP 105 -78153 Le Chesnay Cedex inria.fr ISSN 0249-6399

Acknowledgment

We would like to thank the Inria research team Mnemosyne and AEx AIDE for their support during this project. Special thanks go to our supervisors Chloé Mercier, Thierry Viéville, and Axel Palaude for their guidance and expertise, which were instrumental in the development of our work. We also acknowledge their contribution in proposing a version of symbolic Reinforcement Learning that we adapted for our experiments, and without which this project wouldn't have existed.

Work done during a Master project at ENSEIRB-MATMECA.


Theresa Neef

Panayiotis Nicolaides

Lucas Chancel

Thomas Piketty

Gabriel Zucman

Theresa Written

Panayiotis Neef

Lucas Nicolaides

Thomas Chancel

Gabriel Piketty

Zucman

Effective sanctions against oligarchs and the role of a European Asset Registry | 1 Effective sanctions against oligarchs and the role of a European Asset Registry

This note provides data on wealth inequality in Russia and advocates for a European Asset Registry. Russia exhibits the highest wealth inequality in Europe. Further, Russia's wealthiest nationals conceal a large share of their wealth through tax havens. The current architecture of the global financial system impedes comprehensive knowledge on beneficial ownership across asset types and jurisdictions. Under the roof of a European Asset Registry, the already existing but currently dispersed information could be gathered. This would change the state of play, resulting in better-targeted sanctions and effective tools to curb money laundering, corruption and tax evasion. The European Union could have a pioneering role in taking the next step towards more financial transparency.

This note provides data on wealth inequality in Russia and advocates for a European Asset Registry. Russia exhibits the highest wealth inequality in Europe. Further, Russia's wealthiest nationals conceal a large share of their wealth through tax havens. The current architecture of the global financial system impedes comprehensive knowledge on beneficial ownership across asset types and jurisdictions. Under the roof of a European Asset Registry, the already existing but currently dispersed information could be gathered. This would change the state of play, resulting in better-targeted sanctions and effective tools to curb money laundering, corruption and tax evasion. The European Union could have a pioneering role in taking the next step towards more financial transparency.

Wealth Inequality in Russia and Offshore Wealth

Russia exhibits the highest wealth inequality in Europe. The top 10% wealthiest Russian residents own about 74% of total household wealth. In comparison, the 10% wealthiest in France own about 59%. In the U.S. this share amounts to about 71%, in Poland to about 62%, and in China to about 68%. The wealthiest 1% in Russia own about half of Russian household wealth (48%). In comparison, this share is about 27% in France, 35% in the U.S., 31% in China and 30% in Poland (see Figure 1). The foundations of this strong wealth concentration among a small group were laid by the rapid and highly unequal privatization process in Russia in the early 1990s after the collapse of the Soviet Union. i severance of their financial ties from the rest of the international financial system, is expected to worsen labour market conditions, and lead to a gradual deterioration in standards of living in the Russian population. In addition, a 37% devaluation of the rouble (against the Euro) since the start of the war, has destabilized the economy substantially. v With at least half of Russia's foreign reserves frozen, the central bank was forced to increase its key interest rate from 9.5% to 20% overnight, with significant impact on borrowers. vi Moreover, the instability in the rouble works its way to consumers' and firms' purchasing power through import-led inflation, while the imposition of capital controls in Russian banks erodes trust, strangles the real economy and restricts the population's access to their savings. The combination of these factors will most likely affect savers, wage-earners and pensioners in Russia disproportionately. vii Undoubtedly these measures increase the pressure on the Russian government to change course on Ukraine, but they come at the expense of lower standards of living and economic hardship for the general Russian population.

Media Contacts

In contrast, part of the wealth of rich Russian nationals is hidden in tax havens.

Sanctions directed towards the wealthiest Russians are targeting the so-called

Offshore wealth and financial transparency

Hiding wealth is more pervasive in Russia due to the high concentration of wealth, but by no means does it constitute a Russian-specific phenomenon.

Alstadsaeter, Johannesen and Zucman (2018) estimate that the equivalent of 10% of global GDP is held as offshore wealth. This share has been relatively stable throughout the 2000s and 2010s. About $8.3 trillion were held in tax havens in 2016. xii Recent leaks from offshore financial institutions underline that the users and beneficiaries of shell companies come from all over the world. xiii The international dimension of this practice requires a broader, more systematic approach: EU countries can improve the effectiveness of sanctions by addressing long-standing problems in the financial governance structure. Namely, addressing the existence and role of tax havens, the use of financial and asset secrecy, and the use of shell companies to hide company ownership and wealth. In recent years, EU laws and a number of OECD policies have improved the framework of financial transparency in Europe:

Evidence of worldwide interlinkages of

• The 5 th Anti-Money Laundering Directive introduced public beneficial ownership registries in Member States for companies, trusts and other legal arrangements.

However, in practice gaps in the ownership records remain. For instance, evidence from the Open Lux investigation indicates that the identity of the final beneficial owner oftentimes continues to remain hidden from the public. xx In addition, a number of exceptions exist, such as on the ownership structure of listed companies in the stock market. To this date, not all EU Member States have made their registries available.

• New regulations are currently being discussed on setting up a new EU Anti-Money Laundering Authority, complemented by a 6 th Anti-Money Laundering Directive.

This will seek to harmonise rules and procedures while enhancing cooperation between the Member States' Financial Intelligence Units. Importantly, the scope of the new regulations extends beyond Member States since they will require "foreign entities" (i.e. shell companies in tax havens outside the EU) to register their beneficial owners when purchasing real estate in the EU. xxi

• At the EU, there is renewed effort to tackle the misuse of shell companies by ensuring real economic activity and automatic exchange of information. The "Unshell" proposal seeks to establish more rigorous criteria to identify shell companies, and exclude them from tax reliefs and benefits of Member States' tax treaty networks.

Figure 1 :

 1 Figure 1: Own visualization based on data on the World Inequality Database (https://wid.world).

"

  oligarchs". The EU list comprises about 680 Russian nationals & 53 entities. viii Part of these oligarchs' wealth is held in foreign financial & non-financial assets (therefore, not in roubles), which are hard to trace due to financial secrecy and lack of a comprehensive record of beneficial owners. In terms of targeting, the group of rich Russian nationals or residents benefiting from keeping wealth offshore is considerably larger than the 680 sanctioned individuals: Alstadsaeter, Johannesen and Zucman (2018) estimate that in 2007 the richest 0.01% of Russian nationals (about 10,000 individuals) owned more than 12% of the total Russian household wealth and held 60% of their wealth in offshore tax havens (see Figure2). According to the latest data from the World Inequality Database, there were about 20,000 individuals in Russia (0,02% of the adult population) with net wealth above 10 million euros in 2021 ix and about 50,000 individuals (0,05% of the adult population with net wealth above 5 million euros. x About one-half to two-thirds of these individuals' assets are held offshore.xi Effective sanctions against oligarchs and the role of a European Asset Registry | 4

Figure 2 :

 2 Figure 2: Visualization by the EU Tax Observatory reproducing results by Alstadsaeter et al. (2018).

which aim at isolating the Russian economy, have a large impact on the general population. The

	latest projections on the macroeconomic
	impact of the sanctions point to a modest economic contraction (about 1.5% in 2022
	and 2.5% in 2023) under current measures. iv Prospects might worsen further as more
	sanctions are announced in the coming weeks. This impact, in combination with the
	ongoing exodus of Western firms, international isolation of Russian banks and

). Novokmet, Piketty, and Zucman (2018) estimate that about half of total Russian household wealth is held abroad. To give a sense of scale, "there is as much financial wealth held by rich Russians abroad-in the United Kingdom, Switzerland, Cyprus, and similar offshore centers-than held by the entire Russian population in Russia itself". ii This offshore wealth of Russian nationals amounted in 2015 to roughly 85% of national income; that is, 85% of what Russian residents earn in an entire year. iii

Recent sanctions,

Effective sanctions against oligarchs and the role of a European Asset Registry | 3

Systematic collection of asset ownership information would close gaps further and facilitate the ongoing development of national registers.

  , was common practice. Firstly,[START_REF] García-Bernardo | Uncovering Offshore Financial Centers: Conduits and Sinks in the Global Corporate Ownership Network[END_REF] find that Russian companies used chains of shell companies via the British Virgin Islands and Cyprus to invest. xiv Secondly, evidence draws a link between Russian nationals investing in real estate in many European countries -often via shell companies. xv And thirdly, Russian nationals (among many other nationalities) utilised golden visa schemes offered by several European countries, e.g. Malta, Cyprus and the UK, thereby acquiring residence or citizenship in exchange for investments.xvi With the current sanctions in place and with European countries hardening their stance, Russian wealth might start shifting to non-European tax havens. Currently, anecdotal evidence points to Russian investors reallocating their wealth towards destinations outside of the sanctioning countries. .S. companies, and Clearstream and Euroclear for securities issued in the European Union), the access of which is not always free or publicly available.xviii In the past years, many countries have been developing government-held beneficial ownership registries. Despite substantial progress, these still exhibit blind spots and exceptions from registration obligations.xix

	For instance,
	information on real estate is typically held in land registers, but in many countries
	reporting obligations do not require the individual beneficiary of a property. The use of
	shell companies is regularly employed to report only the legal entity and to disguise
	the individual controlling it. Moreover, national commercial registers record the
	ownership of companies registered in the country. However, their access is sometimes
	restricted and the registered ownership structures remain obscure (for instance, due

Russian wealth to tax havens are abundant. In recent years the use of different schemes, many of which in European Effective sanctions against oligarchs and the role of a European Asset Registry | 5 countriesxvii A comprehensive database tracking where and by whom wealth is held could increase the efficiency of targeted sanctions. Information on asset ownership of different asset types is held in private companies, banks, national beneficial ownership registries (yet incomplete), central securities depositories, and financial authorities. Governments find themselves in a disadvantaged position since databases are not comprehensively linked and restricted in access. As a result, they lack key information that can prove crucial in designing and implementing sanctions. Access to this information must be gained first in order to make sanctions more effective. The dispersion of information across different locations and institutions currently facilitates tax avoidance and evasion as well as money laundering. to a lack of reporting obligation for minor shareholders). Lastly, information on securities (bonds and stocks) is recorded by national and private central security depositories (e.g. the Depository Trust Company in the U.S. for securities issued by Effective sanctions against oligarchs and the role of a European Asset Registry | 6 U

guide for a European Asset Registry A Task Force for Asset Ownership could be set up to collect information on hidden wealth in a unified structure in the EU.

  At the OECD level, the automatic information exchange under the Common Reporting Standard provides information to tax authorities regarding certain financial assets, namely bank accounts, securities, and interest income in Effective sanctions against oligarchs and the role of a European Asset Registry | 7 investment entities. However, the current Common Reporting Standard leaves several loopholes that allow beneficial owners to keep their wealth undetected. The task force will collect, crosscheck and analyse all available information on wealth and assets held in EU Member States by wealthy individuals (above a given threshold). To utilise information in the Member States, the task force can be mandated by EU leaders and supervised by the Eurogroup. Its form can follow that of the Task Force for Coordinated Action -a special working group of the Eurogroup that has coordinated the setup of even more ambitious EU structures such as the Banking Union and the European Stability Mechanism.

	This

xxii • xxiii A

task force could pave the way for establishing a permanent European Asset Registry, tasked with systematically gathering and linking wealth information across all asset types.

  The ultimate objective of the registry would be to record

	comprehensively the ownership and movement of assets. Thus, the registry would
	provide highest-quality data on the total amount of wealth held by individuals. It would
	combine information from all available national and international sources, while
	establishing new sources in the case where information is currently neither present
	nor sufficiently recorded. Importantly, it should leave no gaps in the type of assets held
	and it should rely on automatic exchange of information procedures between the
	different sources. The medium-term goal in the EU would be a new institution (based
	on EU law or created by a new inter-governmental treaty) tasked with collecting and
	analysing information centrally.

Information gathered in the new structure could be cross-checked by specialised personnel and be made available to all Member States to fight financial crime.

  If beneficial ownership information includes information on nationality and country of residence, hidden wealth would be revealed and sanctions targeting wealthy individuals could become more efficient.

Effective sanctions against oligarchs and the role of a European Asset Registry | 8

The

work of the task force could be complementary to an ongoing feasibility study.

  The study was ordered by the European Commission last autumn, with expected deliverables in April 2023.xxiv The task force could create a fast-track pilot project that will implement the registry and run in parallel to the findings of the feasibility study.

	A

European Asset Registry could prove key in addressing long-standing issues of financial secrecy such as avoidance and evasion, money and corruption.

  By and large, most recent developments against tax evasion and tax avoidance have rested on increased transparency and cooperation between countries. The current juncture provides a unique opportunity for European countries to play a pioneering role in establishing this powerful instrument.programs e.g. in Spain. Sunak (2020) finds based on data mainly requested from national immigration offices that "Of the total applications approved in the EU, China accounts for the greatest demand, with nearly 50%, followed by Russians with 27%".Scherrer and Thirion (2018) give an overview of Citizenship-by-Investment and Residency-by-Investment programmes in the EU but underline that much of the evidence remains anecdotal. For Latvia, see this journalistic piece presenting data from the Latvian Immigration and Citizenship Office: https://www.occrp.org/en/goldforvisas/latvias-once-golden-visas-lose-their-shine-but-why.xvii Reported e.g. in the Financial Times, and Reuters. xviii For more information on existing data sources, see Zucman (2015): The hidden wealth of nations. University of Chicago Press, Chapter Four; Tax Justice Network (2022): 10 measures to expose sanctioned Russian oligarchs' hidden assets. xix See for a comprehensive assessment Harari et al. (2020). xx https://www.occrp.org/en/openlux xxi See European Commission (2022): https://ec.europa.eu/info/publications/210720-anti-money-launderingcountering-financing-terrorism_en. xxii https://ec.europa.eu/taxation_customs/taxation-1/unshell_en xxiii Several behavioral reactions were reported such as the relocation of financial assets to uncooperative tax havens(Johannesen & Zucman, 2014; Johannesen, 2014) or to jurisdictions not participating in the agreement such as the U.S.(Casi et al. 2020). Further, its coverage excludes for example real estate assets. This loophole has probably led to shifts from financial to more real estate wealth to avoid detection (see Bomare, Le Guern Herry (2021): Automatic Exchange of Information and Real Estate Investment. Mimeo.) xxiv See https://etendering.ted.europa.eu/cft/cft-display.html?cftId=8792.


Claudiu F Bisu
email: cfbisu@gmail.com

Alain Gérard
email: alain.gerard@u-bordeaux1.fr

Jean-Yves K'nevez •

Raynald Laheurte
email: raynald.laheurte@u-bordeaux1.fr

• Olivier

O Cahuc

J-Y K'nevez •

Self-excited vibrations in turning : Forces torsor analysis

The present work deals with determining the necessary parameters considering a three dimensional model to simulate in a realistic way the turning process on machine tool.

This paper is dedicated to the study of the self-excited vibrations incidence on various major mechanics characteristics of the system workpiece / tool / material. The efforts (forces and moments) measurement using a six components dynamometer confirms the tool tip moments existence.

The fundamental frequency of 190 Hz proves to be common to the tool tip point displacements, the action application point or at the torque exerted to the tool tip point. The confrontation of the results concerning displacements and efforts shows that the applications points of these elements evolve according to similar ellipses located in quasi identical planes. The large and the small axes of these ellipses are increasing with the feed rate motion values accordingly to the mechanical power injected into the system. Conversely, the respective axes ratios of these ellipses are decreasing functions of the feed rate while the ratio of these ratios remains constant when the feed rate value is increasing.

In addition, some chip characteristics are given, like the thickness variations, the width or the hardening phenomenon.

Angle of main tool displacements direction included in the plane (x,y) (degree); α κ(yz)

Angle of main tool displacements direction included in the plane (y,z) (degree); ∆t Time corresponding of phase difference between two signals (s); Φ Primary share angle (degree); ϕ c

Chip width slopes angle between each undulation (degree); ϕ f ui Phase difference between the tool tip displacements components i=x, y, z (degree); γ Cutting angle (degree); λ s Inclination angle of tool edge (degree); κ r Direct angle (degree); θ e(xy)

Stiffness principal direction angle related to the plane (x,y) (degree); θ e(yz)

Stiffness principal direction angle related to the plane (y,z) (degree); ξ c Chip hardening coefficient;

1 Introduction

In the three-dimensional cutting case, the mechanical actions torsor (forces and moments), is often truncated: the moments part of this torsor is neglected fault of adapted metrology [START_REF] Mehdi | Dynamic behavior of thin wall cylindrical workpiece during the turning process, Part 2: Experimental approach and validation[END_REF]. However, efforts and pure moments (or torque) can be measured [START_REF] Couétard | Capteurs de forces à deux voies et application à la mesure d'un torseur de forces[END_REF]. Recently, an application consisting in six components measurements of the actions torsor in cutting process was carried out for the case of high speed milling [START_REF] Couétard | Mesure des 6 actions de coupe en fraisage grande vitesse[END_REF], drilling [START_REF] Laporte | A parametric model of drill edge angles using grinding parameters[END_REF], [START_REF] Yaldiz | Design, development and testing of a four-component milling dynamometer for the measurement of cutting force and torque[END_REF], etc. Cahuc et al., in [START_REF] Cahuc | Experimental and analytical balance sheet in turning applications[END_REF] presents another use of this six components dynamometer in an experimental study: the taking into account of the cut moments allows a better machine tool power consumption evaluation. The present paper is dedicated to the six components dynamometer use to reach with fine accuracy a vibrations dynamic influence evalu-ation in turning on the system Workpiece/Tool/Machine tool (WTM). The concepts of slide block system, moments and torsor (forces and moments) are directly related to the work, undertaken to the previous century beginning, on the mathematical tool "torsor" [START_REF] Ball | A treatise on the theory of screws[END_REF]. Unfortunately, until now the results on the cutting forces are almost still validated using platforms of forces (dynamometers) measuring the three components of those [START_REF] Lian | Self-organizing fuzzy control of constant cutting force in turning[END_REF], [START_REF] Marui | Chatter vibration of the lathe tools. Part 2 : on the mechanism of exciting energy supply[END_REF]. The actions torsor is thus often truncated because the torsor moment part is probably neglected fault of access to an adapted metrology [START_REF] Yaldiz | Design, development and testing of a turning dynamometer for cutting force measurement[END_REF], [START_REF] Yaldiz | A dynamometer design for measurement the cutting forces on turning[END_REF].

However, recent experimental studies showed the existence of cutting moments to the tool tip [START_REF] Cahuc | Metrology influence on the cutting modelisation[END_REF], [START_REF] Laheurte | Metrological devices in cutting process[END_REF], [START_REF] Laheurte | Evaluation de l'énergie mise en jeu et du comportement des outils de coupe dans l'usinage[END_REF], [START_REF] Toulouse | An experimental method for the cutting process in three dimensions[END_REF]. Their taking into account allows thus the best machine tools output approaches [START_REF] Cahuc | Experimental and analytical balance sheet in turning applications[END_REF], [START_REF] Darnis | Energy balance with mechanical actions measurement during turning process[END_REF]. Nowadays, the use of a dynamometer measuring the mechanical actions torsor six components [START_REF] Bisu | Nouvelle analyse des phénomènes vibratoires en tournage[END_REF], [START_REF] Couétard | Caractérisation et étalonnage des dynamomètres à six composantes pour torseur associé à un système de forces[END_REF], [START_REF] Laporte | A parametric model of drill edge angles using grinding parameters[END_REF] allows a better cut approach and should enable to reach new system WTM vibrations properties in the dynamic case.

Moreover, the tool torsor has the advantage of being transportable in any space point and in particular at the tool tip in O point. The study which follows about the cut torsor carries out in several stages including two major; the first relates to the forces analysis and second is dedicated to a first moments analysis to the tool tip during the cut.

After this general information on the torsor concept, an analysis of the efforts (section 2) exerted in the cutting action is carried out. Thanks to this analysis and experimental tests, we establish that the points of variable application exerted on the tool type are included in a plane, more precisely following an ellipse. Then, accordingly in section 3, the first moments analysis obtained at the tool tip in O point is performed. The torsor central axis is required (section 4) and the central axes beams deduced from the multiple tests strongly confirm the moments presence to the tool tip.

Some chip characteristics are presented in the section 5, and compaired to experimental data base. Before concluding, a correlation (section 6) displacements / cutting forces shows that these two dual elements evolve in a similar way following ellipses having the similar properties.

Forces analysis

Tests results

The experiments are performed within a framework similar to that of Cahuc et al [START_REF] Cahuc | Metrology influence on the cutting modelisation[END_REF]. For each test, except the feed rate values, all the turning parameters are constant. The mechanical actions are measured according to the feed rate (f) using the six components dynamometer [START_REF] Couétard | Capteurs de forces à deux voies et application à la mesure d'un torseur de forces[END_REF] following the method initiated in Toulouse [START_REF] Toulouse | Contribution à la modélisation et à la métrologie de la coupe dans le cas d'un usinage tridimensionnel[END_REF], developed and finalized by Couétard [START_REF] Couétard | Caractérisation et étalonnage des dynamomètres à six composantes pour torseur associé à un système de forces[END_REF] and used in several occasions [START_REF] Cahuc | Experimental and analytical balance sheet in turning applications[END_REF], [START_REF] Couétard | Mesure des 6 actions de coupe en fraisage grande vitesse[END_REF], [START_REF] Darnis | Energy balance with mechanical actions measurement during turning process[END_REF], [START_REF] Laheurte | Metrological devices in cutting process[END_REF], [START_REF] Laheurte | Evaluation de l'énergie mise en jeu et du comportement des outils de coupe dans l'usinage[END_REF]. On the experimental device (Fig. 1) the instantaneous spindle speed is permanently controlled (with an accuracy of 1%) by a rotary encoder directly coupled with the workpiece. During the tests the insert tool used is type TNMA 16 04 12 carbide not covered, without chip breeze. The machined material is an alloy of chrome molybdenum type 42CrMo24. The test-workpieces are cylindrical with a diameter of 120 mm and a length of 30 mm. They were designed starting from the Finite Elements Method being coupled to a procedure of optimization described in [START_REF] Bisu | Optimization and dynamic characterization system part in turning[END_REF]. Moreover, the tool geometry is characterized by the cutting angle γ, the clearance angle α, the inclination angle of edge γ s , the direct angle κ r , the cutting edge radius r ǫ , and the sharpness radius R [START_REF] Laheurte | Application de la théorie du second gradient à la coupe des matériaux[END_REF]. In order to limit to the wear appearance maximum along the cutting face, the tool insert is examined after each test and is changed if necessary (Vb ≤ 0.2 mm ISO 3685). The tool parameters are detailed in the Table 1. Two examples of resultant efforts measurements applied to the tool tip are presented: one of these for the stable case, ap = 2 mm (Fig. 2), and other for the case with instability, ap = 5 mm (Fig. 3). In the stable case it appears that the force components amplitudes remain almost independant from time parameter. Thus, the amplitude variation is limited to 1 or 2 N around their nominal values, starting with 200 N for (F x ) and until 600 N for (F y ). These variations are quite negligible. Indeed the nominal stress reached, the component noticed as the lowest value is the (F x ) one, while the highest in the absolute value is (the F z ) one. While taking as reference the absolute value of (F x ) the following relation between these three components comes:

γ α λs κr rǫ R -6 • 6 • -6 • 91 • 1,2 mm 0,02 mm
|F x | = |Fz| 2 = |Fy| 3 .
In the unstable case we observe that the efforts components on the cutting axis (F y ) has the most important average amplitude (1 500 N). It is also the most disturbed (± 700 N) with oscillations between -2 200 N and -800 N. In the same way the effort according to the feed rate axis (F z ) has important average amplitude (1 000 N) and the oscillations have less width in absolute value (± 200 N) but also in relative value (± 20%). As for the effort on the radial direction (F x ) it is weakest on average (200 N) but also most disturbed in relative value (± 200 N). These important oscillations are the tangible consequence of the contact tool/workpiece frequent ruptures and thus demonstrate the vibration and dynamical behaviour of the system WTM.

Finally, we note that the amplitudes of all these efforts components applied to the tool tip are slightly decreasing functions of time in particular for the component according to the cutting axis.

Frequency analysis

The signals frequency analysis performed by using FFT function enables to note in Fig. 4 the presence of frequencies peaks around 190 Hz. Around this frequency peak, we note for the three forces components, a quite high concentration of energy in a wide bandwidth around 70 Hz (36% of the fundamental frequency). All things considered, this width of frequency is of the same order of magnitude as observed (13% of fundamental) by Dimla [START_REF] Sr | The impact of cutting conditions on cutting forces and vibration signals in turning with plane face geometry inserts[END_REF] for a depth of cut three times lower (ap = 1.5 mm) but for an identical feed rate (f=0.1 mm/rev) and a cutting speed similar.This remark confirms that the efforts components is proportionnal to the depth of cut ap as indicated by Benardos et al., [START_REF] Benardos | Prediction of workpiece elastic deflections under cutting forces in turning[END_REF]. Let us recall that the same frequency of 190 Hz was observed in the tool tip displacements case (in conformity with [START_REF] Bisu | Nouvelle analyse des phénomènes vibratoires en tournage[END_REF]). Consequently, the cutting forces components variations and the self-excited vibrations are influenced mutually, in agreement with [START_REF] Ispas | Vibrations des systèmes technologiques[END_REF], [START_REF] Kudinov | Dinamica Masinilor Unelten[END_REF], [START_REF] Marot | Coefficient dynamique de coupe. Théories actuelles et proposition d'une méthode de mesure directe en coupe[END_REF], [START_REF] Tansel | The chaotic characteristics of three dimensional cutting[END_REF]. Also, in agreement with research on the dynamic cutting process [START_REF] Moraru | Vibratiile si Stabilitatea Masinilor Unelte[END_REF], we note that the self-excited vibrations frequency is different from the workpiece rotational frequency which is located around 220 Hz.

Forces decomposition

The forces resultant components detailed analysis highlights a plane in which evolves a variable cutting force F v around a nominal value F n (see further). This variable force is an oscillating action (Fig. 5) which generates u tool tip displacements and maintains the vibrations of elastic system block-tool BT [START_REF] Bisu | The regenerative vibration influence on the mechanical actions turning[END_REF].

Thus, the cutting force variable (Fig. 5) and the selfexcited vibrations of elastic system WTM are interactive, in agreement with research work [START_REF] Koenigsberger | Machine Tools Structures[END_REF], [START_REF] Moraru | Vibratiile si Stabilitatea Masinilor Unelte[END_REF]. The cutting forces variable part can be observed and compared. Not to weigh down this part, the cutting forces analysis is voluntarily below restricted at only two different situations:

-stable process using cutting depth ap = 2 mm (Fig. 7a), -unstable process (with vibrations) using cutting depth ap = 5 mm (Fig. 7b) The vibrations effects on the variable forces evolution are detailed on the Fig. 7b. Moreover, the variable forces and displacements analysis associated with the tool tip at the time of the unstable process shows that the forces variation ratio is equivalent to the tool tip displacements variation ratio (in conformity with [START_REF] Bisu | Etude des vibrations auto-entretenues en coupe tridimensionnelle: nouvelle modélisation appliquée au tournage[END_REF]). This aspect will be quantified further. Also we concentrate our attention mainly on the unstable case (ap = 5 mm).

Plane determination attached of the forces application points

The tests analysis shows that, in the vibratory mode, the load application points describe an ellipse (Fig. 8), that is not the case in the stable mode (without vibrations, Fig. 7a)).

The method used in [START_REF] Bisu | Displacements analysis of self-excited vibrations in turning[END_REF] to determine the tool tip displacements plane is taken again here (in conformity with Appendix, section 8.1) to establish the plane P f , place of the load application points, characterized by its normal n f (Table 2). As for the tool tip displacements study related, a new reference system (n fa , n fb ) is associated at the load application points ellipse place. In this new reference system (in conformity with section 8.2) the ellipse large (respectively small) axis dimensions a f (respectively b f ) are obtained (Fig. 9). The values of a f , b f as that of their ratio a f / b f are consigned in the Table 3. It should be noted that a f and b f are increasing feed rate (f ) functions. It is thus the same for the ellipse surface which grows with (f ), in perfect agreement with the mechanical power injected into the system which is also an increasing feed rate function. On the other hand, the ratio a f / b f is a decreasing feed rate function. Thus the ellipse elongation evolves in a coherent way in dependence with the feed rate. Table 3 Large and small ellipse axes attached of forces application points depending on feed rate parameter; case study using ap = 5 mm, f = 0.1 mm/rev and N = 690 rpm.

Let us look at now the moments evolution to the tool tip.

3 First moment analysis

Experimental results

For each test, the mechanical actions complete torsor is measured according to the method already detailed in the section 2.1 [START_REF] Couétard | Caractérisation et étalonnage des dynamomètres à six composantes pour torseur associé à un système de forces[END_REF]. Measurements are taken in the six components dynamometer transducer O' center and then transported to the tool point O via the moment transport traditional relations [START_REF] Brousse | Cours de mécanique (1 er cycle et classe prépa[END_REF]. As for the forces, the moments variable part is extracted from measurements. An example of the results measurement is given on the Fig. 10 which zooms on the moments variable part is presented in the Fig. 11. Taking into account the recordings chaotic aspect obtained, an accurate moments components frequency analysis is necessary. It is the object of the following section.

Moments frequency analysis

An example of moments signals frequency analysis during the vibratory cutting is presented in the Fig. 12. As for the forces analysis, the moments components FFT shows that the most important frequency peak is localized around 190 Hz.

Moreover of all the components, the most important fundamental amplitude is that corresponding to the moments components following to the cutting axis (y) as its Fig. 11 The moments components variable part zoom that action on the tool tip following the three cutting directions; case study ap = 5 mm, f = 0,1 mm/rev and N = 690 rpm.

transport at the tool tip confirms it. It should be noted that the force component following to this same axis is also most important but has obviously no influence on the moments related to this axis due to co-linearity of these two elements. Conversely, the least important vibration amplitude is that of the moment component located on z axis. However, the number of revolutions being important according to this axis the M z component contribution to the torques power consumption remains significant. The appearance of other peaks, which are harmonics, slightly modifies the three-dimensional moments representation (Fig. 13) which is not exclusively any more in a plane although the ellipse essence is in a plane. This representation approaches a light form of letter eight contrary to the elliptic planar form efforts characteristic. 4 Central axis

Central axis determination

It is well-known that with any torsor, it is possible to associate a central axis (except the torsor of pure moment), which is the single object calculated starting from the torsor six components [START_REF] Brousse | Cours de mécanique (1 er cycle et classe prépa[END_REF].

A torsor [A] O in a point O is composed of a forces resultant R and the resulting moment M O :

[A] O = R, M O . (1)
The central axis is the line defined classically by:

OA = R ∧ M O |R 2 | + λR, ( 2
)
where O is the point where the mechanical actions torsor was moved (here the tool tip) and A the current point describing the central axis. OA is thus the vector associated with the bi-point [O, A] (Fig. 14).

This line (Fig. 14-(a)) corresponds to points geometric place where the mechanical actions moment torsor is minimal. The central axis calculation consists in determining the points assembly (a line) where the torsor can be expressed according to a slide block (straight line direction) and the pure moment (or torque) [START_REF] Brousse | Cours de mécanique (1 er cycle et classe prépa[END_REF].

The central axis is also the points place where the resultant cutting force is co-linear with the minimum mechanical moment (pure torque). The test results enable to check for each point of measurement the co-linearity between the resultant cutting force R and moment M A calculated related to the central axis (Fig. 14-(b)).

The meticulous examination of the mechanical actions torsor six components shows that the forces and the moment average values are not null. For each measure point, the central axis is calculated, in the stable (Fig. 15-(a)) and unstable mode (Fig. 15-(b)). In any rigour the case ap = 2 mm should be described as quasistable movement, because the vibrations exist but their amplitudes are very low -of the order of the µm -, thus quasi null compared to the other studied cases. Considering the cutting depth value ap = 3 mm, the recorded amplitude was 10 times more important. In the presence of vibrations (ap = 5 mm) for a 68 rpm the workpiece speed (44 points of measure by rpm), the dispersive character of the central axes beam, compared to the stable mode, can be observed, where this same beam is tightened more and less tilted compared to the normal axis on the plane (x,y). This central axes dispersion can be explained by the self-excited vibrations which cause the variable moment generation.

Analysis of central axis moments related

While transporting the moment from tool tip to the central axis, the minimum moment (pure torque) M A is obtained. From the moment values to the central axis, the constant and variable part of this one is deduced. As for the efforts, the variable part is due to the self-excited vibrations as revealed below (Fig. 16).

Using this decomposition, the moments contribution on the zones of contact tool / workpiece / chip is expressed. The observations resulting from the analysis show that the tool vibrations generate rotations, cause variations of contact and thus generate variable moments, confirming the efforts analysis detailed in the section 2.1. This representation enables to express the moments along the three axes of the machine tool: swivel moment in the y direction and the two moment of rotation along x and z directions. Moments components analysis determined at the central axis allows noting a moments localization mainly on two distinct zones. Taking into account this aspect, the variable moments components are divided into two noted parts d 1 and d 2 on to the three directions related to the machine. The components of these variable moments on x, y, z, axes are noted respectively (M axv ), (M ayv ) and (M azv ).

In the vibratory case (ap = 5 mm), the first points family is located (Fig. 16) according to a line d 2 and d 1 (the large ellipse axis). In the case without vibrations (ap = 2 mm), the two d 1 and d 2 families merged to only one family located according to only one line. Thus, the elliptic form appearance around the right-hand side d 1 seems quite related to the self-excited vibrations (cas ap = 5 mm) [START_REF] Bisu | The regenerative vibration influence on the mechanical actions turning[END_REF]. In particular, the frequency associated with the d 1 part is higher than those associated the d 2 part. Furthermore, these frequencies are related to the frequencies domain found during moments FFT analy-sis Fig. 12. Finally, on the central axis, the d 1 families and d 2 seem to correspond to distinct elements from the generated surface.

5 Workpiece and chip geometry

Roughness measurements

In the processes of matter per cutting tool removal, it is well-known that the manufactured pieces surface quality is closely connected to the thrust force imposed on the matter [START_REF] Chen | A stability analysis of regenerative chatter in turning process without using tailstock[END_REF]. In particular, the more the thrust force exerted on the object surface is important, the more the imprint left by the tool on surface is consequent. The surface roughness east thus closely related to the thrust force intensity. The surface roughness is connected confidentially to the thrust force intensity. The self-excited vibrations have an influence on the workpieces quality surface. Now, in the self-excited vibrations case examined here, we have just noticed that the forces and moments are maximum with the resonance frequency which is situated around 190 Hz.

Taking into account the link between roughness and efforts applied to the surface, we should find a maximum of surface roughness around this frequency. In this purpose, we propose to control the profile of a generator length roughness of the cylindrical manufactured piece. Indeed, in every rotation of the machined piece, the tool leaves a imprint force function applied to the generator point observed which corresponds to a given and known moment. Along a given generator, each point of this one is the force image applied to the surface at a known given moment because the rotation speed of the workpiece is known.

The surface roughness examination along a generator should thus necessarily reveal the amplitudes of roughness associated with the efforts periodically applied by the tool in these points. Also the roughness profile FFT presents along a generator of the cylindrical part manufactured should pass, like the efforts, by a maximum around the frequency of 190 Hz. It is indeed what can be observed on the figure 16 where the roughness data FFT analysis shows a frequency peak located around 190 Hz (precisely 191,8 Hz), which is coherent with the previous data.

In addition, the surface roughness analysis gives a total roughness value R t = 1,6 µm.

Chip characteristics

Chip measurements under the Scanning Electron Microscop were carried out and enabled to determine the thickness variation and the chip width. All chips are type 1.3 (ISO 3685) with undulations.

The chip thickness variations between the maximum (h max ) and the minimal (h min ) thickness are about 2, and feed rate values independent. An example is presented (figure 18) for a sample of chip during a test with the feed rate f=0.05 mm/rev. Values obtained h max = 0,23 mm and h min = 0,12 mm. The measure of chip length corresponding to an undulation enables to find the self-excited vibrations frequencies starting from the cutting speed (in conformity with equation 3):

f cop = V l 0 .ξ c , (3)
with f cop the chip segmentation frequency, V chip speed, l 0 one chip undulation length and ξ c the chip hardening coefficient.

To determine the total chip length, it is necessary to measure the wavelength, taking into account the rate of hardening phenomenon (in conformity with equation 4) [19] of the chip during cutting process and the primary shear angle φ,

ξ c = cos(φ -γ) sin(φ) . (4)
In our case, it is measured on the chip undulation length l 0 = 11 mm, with a chip hardening rate ξ c = 1.8 and the cutting speed V = 238 m/min. A frequency of 206 Hz is then obtained, very near to the frequencies of tool tip displacements or of the load application points during cutting process.

The chip width is then measured with similar techniques. Substantial width variations are observed, about 0.5 mm. Indeed, the measured maximum width w max is 5.4 mm while the evaluated minimal width w min is 4.9 mm, which means a width variation about 10% -Fig. 19.

The chip width slopes angle ϕ c measurement (Fig. 10) between each undulation, close to 29 • , is equal, with the same errors, to the phase difference measured on the signals of tool tip displacements (28 • ) (cf. [START_REF] Bisu | Etude des vibrations auto-entretenues en coupe tridimensionnelle: nouvelle modélisation appliquée au tournage[END_REF]).

6 Correlation between displacements of the tool tip / applied forces A synthesis between the work-paper two parts is essential. It is carried out below in order to put in evidence the various correlations which exist between stiffness / displacements, displacements of tool / stiffness center or stiffness center / central axis.

Correlation between the plane of the displacements tool tip / the applied forces

The tool tip point displacements are localized (cf. [START_REF] Bisu | Nouvelle analyse des phénomènes vibratoires en tournage[END_REF]) in a tilted plane. Inside the stiffness matrix determined in the paper ( [START_REF] Bisu | Optimization and dynamic characterization system part in turning[END_REF]), a correlation exists between tool tip displacements and the cutting forces applied. In particular, the ratios between the large and the small ellipses axes of tool displacements (a u /b u ) and the efforts applied (a f /b f ) decrease feed rate functions while the ratio of these ratios remains constant (equal to 1,64) when the feed rate increase. These elements enable to determine accurately the real configuration of cutting process. 4 The normals (nf ,nu) of the tool points displacements planes and the forces applied along the three cutting directions, depending on feed rate.

These correlations are analyzed using the direct normal to the tool tip point displacements plane and the direct normal to the load application points place (Table 4). The existence of these two planes is particularly interesting and adapted to the establishment of a cutting process real configuration. This new aspect is in the course of implementation in order to express and exploit a simplified dynamic three-dimensional model in the reference system associated with these planes [START_REF] Bisu | Dynamic model of the threedimensional cut, 18 th Int[END_REF].

Self-sustained vibrations: experimental validation

From these studies, it comes out that the self-excited vibrations domain is around 190 Hz with accuracy of a few per cent. It is around this common fundamental frequency that the whole of the major characteristics (displacements, efforts, and moments) of system WTM have the most important amplitude variations. The analysis carried out to the measures of tool point displacements and the points for load application enables to evaluate existing constant phase difference between the forces components and corresponding displacements (Fig. 20 These phase differences confirm the efforts delay compared to the tool tip displacement. The self-excited vibrations appearance can be also explained by the delay force / displacement, which increases the system energy level. The existence of this delay could be explained by the machining system inertia and more particularly by the cutting process inertia [START_REF] Koenigsberger | Machine Tools Structures[END_REF]. Moreover, it is noted that the phase difference with the same range between efforts / displacements (Table 5) remains constant according to the feed rate.

Because of parts elasticity intervening in the operation of turning, it is logical that the response in displacements of unit BT-BW is carried out with a certain shift compared to the efforts variation applied to the tool, variation induced by the lacks of machined surface cir-cularity in the preceding turn which imply variations of the contact tool/workpiece (Fig. 17). Phase difference between the efforts and displacements thus remains a possible explanation to the self-excited vibrations appearance. Moreover, when the tool moves along the ellipse places e 1 , e 2 , e 3 (Fig. 23), the cutting force carries out a positive work because its direction coincides with the cutting direction. On the other hand, on the side e 3 , e 4 , e 1 , the work produced by the cutting force is negative since its direction is directly opposed to that of displacement. The comparison between these two ellipse parts, as shows that the effort on the trajectory e 1 , e 2 , e 3 is higher as on the trajectory e 3 , e 4 , e 1 because the cutting depth is more important. At the time of this process, work corresponding to an ellipse trajectory remains positive and the increase of result energy thus contributes to maintain the vibrations and to dissipate the energy in the form of heat by the assembly tool/workpiece.

Conclusion

The experimental procedures proposed in this work-paper, as well at the static and dynamic level, enabled to determine the elements necessary to a rigorous analysis of the tool geometry influence, its displacement and evolution of the contacts tool/workpiece and tool/chip on the machined surface.

In particular, by analyzing the efforts resultant torsor applied during turning process, the experimental results enabled to establish an efforts vector decomposition highlighting the evolution of a variable cutting force around a constant value. This variable effort evolves into a plane inclined compared to the machine tool reference system.

This cutting force, whose application point describes an ellipse, is perfectly well correlated with the tip tool displacement which takes place under similar conditions. In particular, the ellipses axes ratios remains in a constant ratio when the feed rate varies with a proportionality factor equal with 1,64.

Moreover, the highlighted coupling between the system elastic characteristics BT and the vibrations generated by cutting enabled to demonstrate that the selfexcited vibrations appearance is strongly influenced, as it was expect to, by the system stiffness, their ratio and their direction. We also established a correlation between the vibratory movement direction of the machine tool elastic structure, the thickness variations and the chip section.

These results enable to now consider a more complete study by completely exploiting the concept of torsor. Indeed, thanks to the six components dynamometer, we confirmed, for an turning operation, the moments existence to the tool tip not evaluated until now by the traditional measuring equipment.

The originality of this work is multiple and in particular consists in a first mechanical actions torsor analysis applied to the tool tip, with an aim of making evolve a model semi analytical cutting 3D. This study allows, considering a turning operation, to establish strong correlations between the self-excited vibrations and the mechanical actions torsor central axis. It is thus possible, thanks to the parameters use defining the central axis, to study the vibrating system tool/workpiece evolution. It also leads to the description of a "plane of tool tip displacements" in correspondence with "the load application points plane".

Thus, using the plane that characterizes the BT behaviour enable to bring back the three dimensional cutting problem, with space displacements, with a simpler model situated in an inclined plane compared with the reference system of machine tool. Nevertheless, that remains a specific model of three dimensional cutting.

Appendix

Determination of the place points plane of load application on the tool

The plane P u definition being load application points geometrical place on the tool starting from the experimental results is carried out using the computation Mathcad c software. We seek to determine the plane which passes by the load application points cloud on the tool (Fig. 8 section 2.4): ax + by + cz + d = 0.

Fig. 1

 1 Fig. 1 Experimental device and associated measurement elements.

Fig. 2

 2 Fig. 2 Signals related to the resultant components of cutting forces following the three cutting directions; test case using parameters ap = 2 mm, f = 0,1 mm/rev and N = 690 rpm.

Fig. 3

 3 Fig. 3 Signals related to the resultant components of cutting forces following the three (x, y, z ) cutting directions; test case using parameters ap = 5 mm, f = 0,1 mm/rev and N = 690 rpm.

Fig. 4

 4 Fig.4Cutting forces magnitude FFT signal on the three (x, y, z) directions; test case using cutting parameters ap = 5 mm, f = 0,1 mm/rev and N = 690 rpm.

Fig. 5

 5 Fig. 5 Cutting force Fv evolution around the nominal value Fn; test case using cutting parameters ap = 5 mm, f = 0,1 mm/rev and N = 690 rpm.

Fig. 6

 6 Fig.6The resultant cutting force components variable zoom on the three cutting directions; test case using parameters ap = 5 mm, f = 0,1 mm/rev and N = 690 rpm.

Fig. 7

 7 Fig. 7 Stable process (a) and unstable process (b).

Fig. 8

 8 Fig.8The ellipse plane P f attached of range of the forces application points considering ap = 5 mm, f = 0,1 mm/rev and N = 690 rpm.

Fig. 9

 9 Fig.9Ellipse approximation attached of forces application points; case study using parameters ap = 5 mm, f = 0,1 mm/rev and N = 690 rpm.

Fig. 10

 10 Fig.10The moments components time signals that action on the tool tip following the three directions; case study using ap = 5 mm, f = 0.1 mm/rev and N = 690 rpm.

Fig. 12

 12 Fig. 12 Signal FFT related to the moment on the three (x, y, z) directions; case study using ap = 5 mm, f = 0.1 mm/rev and N = 690 rpm.

Fig. 13

 13 Fig. 13 Moments place space representation.

Fig. 14

 14 Fig. 14 Central axis representation (a) and of the colinearity between vector sum R and minimum moment MA on central axis (b).

Fig. 15

 15 Fig. 15 Central axes representation obtained for 68 rpm the workpiece speed and feed rate f = 0,0625 mm/rev; a) -stable process ap = 2 mm; b) -unstable process ap = 5 mm.

Fig. 16

 16 Fig. 16 Moment representation related of central axes; case study using ap = 5 mm, f=0,1 mm/rev and N = 690 rpm.

Fig. 17

 17 Fig. 17Machined surface and FFT data related to the roughness; case study ap = 5 mm, f = 0,1 mm/rev, N = 690 rpm.

  Fig. 17Machined surface and FFT data related to the roughness; case study ap = 5 mm, f = 0,1 mm/rev, N = 690 rpm.

Fig. 18

 18 Fig. 18 Chip thickness variation evaluation.

Fig. 19

 19 Fig. 19 Chip width evaluation.

Fig. 20

 20 Fig. 20 Phase difference evaluation between forces / displacements along x axis.

Fig. 21

 21 Fig. 21 Phase difference evaluation between forces / displacements along y axis.

Fig. 22 Table 5

 225 Fig.22Phase difference evaluation between forces / displacements along z axis.ϕ f ux ϕ f uy ϕ f uz 13 • 23 • 75 •Table5Values of phase difference forces / displacements (ap = 5 mm, f = 0,1 mm/rev, N = 690 rpm.)

Fig. 23

 23 Fig. 23 Movement tool / workpiece elliptical trajectory.

  Keywords Self-excited vibrations • Experimental model • Turning • Torsor measurement • Torsor central axis

	Nomenclature continuation
	P u	Plane attached to the tool point displace-
		ments;
	R	Cutting forces vector sum who actuate on the
		tool (N);
	r ǫ	Cutting edge radius (mm);
	R	Sharpness radius (mm);
	R t	Roughness (µm);
	T	Time related to one revolution of workpiece
		(s);
	u	Tool tip point displacement (m);
	V	Cutting speed (m/min);
	w max	Maximum chip width (mm);
	w min	Minimum chip width (mm);
	WTM Workpiece-Tool-Machine tool;
	x	Radial direction;
	y	Cutting axis;
	z	Feed rate direction;
	α	Clearance angle (degree);
	α κ(xy)
		Nomenclature
		A	Central axis point;
		[A] o	Actions torsor exerted on the tool tip
			in O point;
		ap	Cutting depth (mm);
		a f (b f )	Large (small) ellipse axis attached to
			the geometrical place of forces applica-
			tion points;
		BT	Block Tool;
		BW	Block Workpiece;
		d i	Directory line of moments projection to
			the central axis (i = 1, 2);
		e i	Ellipse point belong attached of forces
			application points (i=1-5);
		f	Feed rate (mm/rev);
		f cop	Chip segmentation frequency (Hz);
		F v (F n )	Variable (nominal) cutting force (N);
		F x	Effort on cross direction (N);
		F y	Effort on cutting axis (N);
		F z	Effort on feed rate axis (N);
		h max	Maximum chip thickness (mm);
		h min	Minimum chip thickness (mm);
		l 0	Chip undulation length (mm);
		M A	Cutting forces minimum moment in A
			who actuate on the tool (N.m);
		M O	Cutting forces moment in the O point
			who actuate on the tool (N.m);
		N	Spindle speed (rpm);
		n f	P f normal direction;
		n f a (n f b ) Normal direction projection to the P f
			on the a f (b f );
		O	Tool point reference;
		O'	Dynamometer center transducer;
		P f	Plane attached to the forces application
			points;

Table 1

 1 Tool geometrical characteristics.

Table 2

 2 Directory normal of the plane P

f attached of forces application points on the tool; case study using ap = 5 mm, f = 0,1 mm/rev and N = 690 rpm.

Acknowledgements The authors would like to thank the CNRS (Centre National de la Recherche Scientifique UMR 5469) for the financial support to accomplish the project.

Claudiu F. Bisu et al.

The errors are noted with e rr and we have : e rr (x, y, z, x p , y p , z p , x n , y n , z n ) = [M (x, y, z) -P (x p , y p , z p ).n f (x n , y n , z n )] ,

where:

Here the superscript t indicates the operation of transposition.

Expressing the E rr function using e rr and introducing the displacements components (u xi , u yi , u zi ) of the tool load application points into the three space directions, it comes:

e rr (u xi , u yi , u zi , x p , y p , z p , x n , y n , z n ), and :

Now, the vector V is calculated by minimization:

where

It results from it that the direct normal n f components to the plane of the load application points on the tool are given by:

For the case study presented in the section 2.4 (Table 2), with ap = 5 mm and f= 0.1 mm it comes:

The required plane equation is then:

where s and t are constants, and V p is equal to :

and u 1 is given by:

with the plane u 0 orientation vector is:

Ellipse approximation

Using the ellipse plane determination [START_REF] Bisu | Displacements analysis of self-excited vibrations in turning[END_REF], it is possible to determine the characteristics given in Table 3.


Sarah Godar

Manon Francois

Panayiotis Nicolaides

Mona Barake

Country-by-Country Reporting is a key data source for understanding the activities of multinational firms. This note explores public Country-by-Country Reports (CbCRs) published by multinational companies to highlight several important trends. First, while only a small number of large multinationals currently publish their CbCRs, the number of companies is increasing rapidly for both large and smaller multinational firms. However, these reports are scattered across different sets of documents, making collecting and analysing them challenging. Second, CbCR publishing is driven by European companies, especially companies active in the extractive sector. Finally, published reports are generally not complete in terms of variables included but present a satisfactory geographical disaggregation in most cases.

Introduction

A decade of data leaks1 have revealed the extent of profit shifting conducted by multinational companies. Confidence in these multinationals has eroded, making the general public, non-governmental organizations, investors and institutions increasingly request transparency about multinationals' tax contributions around the world. Only last year, shareholders requested the publication of tax information at the annual meetings of major multinationals such as Amazon, Cisco and Microsoft (FACTCOALI-TION, 2022). In the coming years, public disclosure will become a reality in Europe,2 and potentially in Australia3 while in the United States, the bill requiring public tax information publication passed in the House in 2021 but stalled in the Senate (United States Congress, 2021).

In this context, Country-by-Country Reports (CbCRs) play a crucial role as a new source of information on multinational firms' activities. These reports are compiled by multinationals and provide for the first time a comprehensive and detailed overview of the country-level distribution of key tax-related financial items such as profit, taxes and economic activities. As such, they will be a central input in evaluating future corporate tax reforms and monitoring the tax avoidance behaviour of multinationals.

The two main initiatives that have accelerated the adoption of Country-by-Country Reporting are led by the public multilateral Organization for Economic Co-operation and Development (OECD) and the Global Reporting Initiative (GRI). The OECD minimum standard requires large firms to privately disclose CbCRs with the appropriate tax authority starting from the fiscal year 2016 for early adopters, while GRI 207 Tax 2019 sets expectations for voluntary public disclosure of CbCRs alongside a tax strategy and governance description.

In this note, we investigate the uptake of voluntary CbCR disclosure by multinationals. We are asking three main questions: How many companies are currently publishing their CbCRs? Which are the characteristics of these companies? How complete are their disclosures?

To investigate the uptake of public disclosures of CbCRs, we rely on the new Public CbCRs database4 built at the EU Tax Observatory which standardizes and compiles the reports of over 100 multinationals into a single dataset. These CbCRs, which are usually scattered throughout annual reports, sustainability reports and other types of reports, are collected in one single place. To the best of our knowledge, this database covers the large majority of multinationals publishing CbCRs on a voluntary basis.

Our main findings are the following: first, overall CbCR publishing rates are low (97 reports for 2020), but increasing rapidly. Second, CbCR publishing is concentrated in European countries and in the extractive sector. Last, there remains significant room for progress on the completion of the information provided and the accessibility of these reports: 55% of the reports do not include all the recommended variables and reports are published in a wide variety of documents. This note is structured as follows: section 2 explains what a CbCR is, section 3 shows trends in CbCR publication, section 4 characterises publishing multinationals, section 5 analyses reports' completeness.

2 What is a Country-by-Country Report?

Country-by-country reporting is the reporting of financial, economic and tax-related information for each jurisdiction in which a multinational operates. Its core item consists of a table where the different columns correspond to the required variables and each row corresponds to each jurisdiction in which the multinational is present. For each jurisdiction, the financial figures of all the resident entities are aggregated in one number, representing the total activities of the multinational in that specific country.

For example, in the CbCR of Shell, Figure 1, the first row aggregates the activities of all Shell's entities present in Albania.

Companies mainly follow two closely related frameworks when providing CbCRs: OECD BEPS Action 13 and GRI 207-4 (GRI, 2020). OECD's Action 13 final report provides a template for multinationals to disclose information for each tax jurisdiction in which they operate. This includes aggregated data on: related party, unrelated party and total revenues, profits before income taxes, income tax paid and accrued, stated capital, accumulated earnings, number of employees and tangible assets other than cash and cash equivalents. It is mandatory for the largest multinationals (with previous year consolidated revenues larger than €750 million) and does not entail public disclosure.

In terms of the required information, GRI 207-4 is closely related to the OECD standard: it requires the same set of variables with the exception of accumulated earnings and stated capital. In terms of scope, the GRI standard is wider as compared to the OECD as there is no size restriction to CbCR disclosure.

A crucial difference is that the GRI mandates voluntary public disclosure. 2.1 Where are the reports published?

Currently the reporting of this information is far from standardised, with no defined place where multinationals are required or recommended to publish the data. This translates in companies disclosing CbCRs in a wide variety of documents and formats, making it challenging to find and extract the data. For example, some multinationals use standalone tax payments reports, while others use tax transparency reports or sustainability reports and annual reports. Figure 2 shows a few examples of the collected reports.

FIGURE2

Examples of reports

Source: Publicly available reports, 2019-2021 3 How many reports have been published so far?

Although public reporting at a country-by-country level remains largely voluntary, a number of firms already disclose this information publicly. As can be seen in Figure 3, the number of reporting firms has been steadily increasing over the past years: 97 reports have been collected relative to the fiscal year 2020, compared with 20 for the fiscal year 2018. Reports are generally published with a one-or two-year lag, hence for the fiscal year 2021 reports are expected to be published between 2022 and 4 Which multinationals are publishing their Country-by-Country Reports?

Breakdown by company size

Few large multinationals publish CbCRs: as reported in Table 1 only 2.7% of the top 15005 firms publish CbCRs and this number is only slightly higher if focusing on the top 1000 (3.2%), the top 500 firms (4%)

or the top 100 firms (7%).

It could be expected that publishing is concentrated among large multinationals (with revenues above €750 million) that potentially face a reduced administrative burden and already comply with the requirement to file CbCRs with tax authorities. We find that this is partly the case: out of the 65 multinationals reporting revenues data, only about 14% (9/65) are below the €750 million threshold.

Percentage of top multinationals publishing CbCRs

Top Firm Source % of Firms Publishing

Forbes Global Index

Top 100 7%

Top 500 4%

Top 1000 3.2%

Top 1500 2.7%

Note: The Forbes Global Index contains the top 1500 firms -excluding banks -based on a composite index weighting sales, profits, assets and market value. We use the Public CbCRs database, EU Tax Observatory (2022), as a proxy for firms publishing.

There is some evidence that smaller multinationals are also publishing: only about 29% (32/111) of firms in our database are in the top 1000 Forbes firms and about 37% (41/111) are in the top 1500

Forbes firms. This means that almost two-thirds of multinationals in our database are not in the top 1500 largest global multinationals, pointing to significant reporting by smaller multinationals.

Breakdown by headquarter country

With minimal regulation and few reporting standards, the extent of public disclosures by firms varies significantly across countries and regions. This could be related to recent changes in disclosure requirements. In Italy, before the adoption of the Non-Financial Reporting Directive 2014/95/EU, non-financial information reporting had been largely voluntary (with the exception of banking). The transposition of the directive into national law with Legislative Decree No. 254/2016 made mandatory the disclosure of non-financial and diversity information in particular related to environmental issues, social and employee-related matters, respect for human rights and anti-corruption and bribery matters.

In Spain, the Law 11/2018, 6 amended the applicable rules on the disclosure of non-financial and diversity information introducing a requirement that large Spanish firms 7 disclose tax information as part 6 7 Firms with an average of over 500 employees during the year or meeting two of the three following criteria over the last two years are required to disclose: total assets amount to more than €20 of their non-financial reporting. Importantly, the disclosure of profits earned, tax paid on profits and public subsidies received is required on a country-by-country basis.

In the United Kingdom, the 2016 UK Finance Act has played a role in increasing tax transparency for large multinationals. This act requires firms to disclose their tax strategy if they have a turnover in the UK of over £200 million or a UK balance sheet of over £2 billion. International firms with sub-groups in the UK or with a global turnover of over €750 million are also required to report their tax strategy.

Breakdown by sector

There is significant variation in CbCR disclosure across sectors. The high level of disclosures for these sectors has likely been driven by sector-wide initiatives. For examaverage number of workers exceeds 250. Starting in 2022, the law will be strengthened and any firm meeting the previous criteria or with an average of over 250 employees during the year will be required to disclose. 8 "This does not take into account the mandatory reporting of European banks under the Capital Requirements Directives IV. See [START_REF] Barake | Tax planning by european banks[END_REF] for additional information on reporting by banks. " Other sectors might be exposed to specific tax risks driven by the nature of their business models. The financial sector is under greater scrutiny since the financial crisis and the technology sectors have faced greater tax scrutiny as their reliance on intellectual property assets and exposure to digitization could be exploited for aggressive tax planning.

FIGURE4 Multinationals disclosing CbCRs by sector

Note: This figure shows the number of multinationals in the Public CbCRs database and the number of these firms that are in the top 1500 of the Forbes Global Index for each sector.

As the disclosure of CbCR information is still voluntary, there is considerable variation in the amount of information reported by companies both in terms of variables disclosed and geographical disaggregation.

Concerning variables, in almost all reports firms publish at least profit and one tax variable (either tax paid or accrued) with the exception of a few companies displaying only tax information. It is rare for companies to publish complete reports according to the OECD standard, only 11% of them do so. On the other hand, almost half (45 %) publish all recommended variables according to the GRI 207-4 standard.

It is crucial for companies to publish all variables and not limit them to a subset, including both profit, taxes and variables describing real economic activities such as number of employees or tangible assets.

This allows to fully appreciate where a company performs its economic activities and whether these are aligned with where profits are booked and taxes paid. Including only profit or tax variables limits this kind of analysis.

FIGURE5

Percentage of multinationals disclosing all variables required. Concerning geographical disaggregation, both the OECD and GRI require the information on all jurisdictions to be disclosed, but not all multinationals apply this requirement when publishing their CbCR reports.

This practice is widespread in CbCR: about 44% (49/111) of multinationals in our database make use of aggregated geographical reporting categories. They account for a relatively small amount of activities:

across the whole sample, these aggregated geographical categories account for 4.9% of total related revenues, 3.6% of total unrelated revenues, 5.7% of total tax paid, 4% of total employees, 2.1% of total positive profits.

Overall the geographical disaggregation provided by companies is quite complete, but a minority of Tax Transparency by Multinationals | 10 companies report only the top countries in which they are present and others present groups of countries or entire regions in aggregated categories. In addition, in a small number of companies the aggregated geographical categories account for a large share of activities (close to 30% of revenues). Only one company reports extremely aggregated activities disclosing separate figures for the headquarter jurisdiction and aggregating foreign jurisdictions in regional categories such as Europe and Latin America.

The use of these aggregated categories should be limited, as it decreases transparency facilitating the dissimulation of tax avoidance activities. This is because aggregate activities could include information on tax havens summed with those of other countries, dissimulating tax avoidance activities.

Conclusion and way forward

This note has underlined several important trends. First, while only a small number of large multinationals currently publish their CbCRs, the number of companies is increasing rapidly for both large and smaller multinational firms. However, these reports are scattered across different sets of documents, making collecting and analysing them challenging. Second, CbCR publishing is driven by European companies, especially companies active in the extractive sector. Finally, published reports are generally not complete in terms of variables included but present a satisfactory geographical disaggregation in most cases.

The EU public CbCR directive 2021/2101 will be a considerable step forward in increasing the public availability of these data: large multinationals present in the EU will be required to publish CbCRs in a machine-readable format from fiscal years starting in July 2024.

However, there will still be some obstacles to exploiting this data and fully enhancing tax transparency.

First, the directive will require limited geographical disaggregation, which might hamper the analysis of profit-shifting activities. Second, it requires a more restricted set of variables as compared to GRI and OECD. Third, there is no single place in which all published reports will be automatically collected. In the future, several improvements could include: requiring a specific publication title that facilitates finding the reports regardless of the language, requiring worldwide country-level data and extending the set of variables included.

Tax Transparency by Multinationals | 11

FIGURE1

  FIGURE1Country-by-Country Report example

  FIGURE3Country-by-Country Reports collected for fiscal years between 2016 and 2021

  Figure 4 shows the number of firms in the Public CbCRs database by sector and the number of these firms that are in the top 1500 Forbes firms. The most represented sectors in the Public CbCR database are Mining and Extraction (17 firms), Chemicals, Petroleum, Rubber and Plastic (15 firms) and Banking, Insurance and Financial Services (14 firms). 8 Two of these sectors also concentrate the highest number of top 1500 firms: Mining and Extraction (7 top 1500 firms) and Banking, Insurance and Financial Services (8 top 1500 firms). Utilities and Chemicals, Petroleum, Rubber and Plastic are the next sectors with the most top 1500 firms. 9

9

  [START_REF] Bourne | Global trends in corporate tax disclosure[END_REF] find similar sectoral results.Tax Transparency by Multinationals | 8 ple, there have been multiple initiatives in the extractive sector, such as Publish What You Pay and the Extractive Industries Transparency Initiative, that have long focused on transparency around payments to governments. This might explain why the Mining and Extraction and the Petroleum and Utilities sectors account for a large portion of the reported CbCRs and the top 1500 firms.

Note:

  The figure shows the percentage of CbCRs included in the sample that discloses all OECD variables and all GRI variables according to the Public CbCRs database, EU Tax Observatory (2022). The two standards require the same set of variables with the exception of "Accumulated earnings" and "Stated Capital" which are not required by the GRI.

countries account for about 80% of multinationals publishing CbCRs while

Table

2

presents the five countries and regions with the highest number of firms publishing CbCRs according to the Public CbCR database. The top five countries -Italy, Spain, the United Kingdom, the Netherlands and Norway -account for about 64% of multinationals publishing CbCRs. At the regional level, European other regions have a lower number of publishing multinationals, accounting for between 0.9% and 8.1% of the overall sample.

Consistent with

[START_REF] Bourne | Global trends in corporate tax disclosure[END_REF]

, these results point to a concentration in CbCR disclosure in a small group of European countries, showing that firms in European countries have the most comprehensive disclosures for tax policy reporting.

TABLE2 Countries and Regions with most multinationals publishing CbCRs

	HQ Country or Region % of public CbCRs
	Top Countries
	Italy	20.7%
	Spain	16.2%
	United Kingdom	13.5%
	Netherlands	8.1%
	Norway	5.4%
	Total	63.9%
	Top Regions
	Europe	80.1%
	Americas	8.1%
	Asia	6.3%
	Oceania	4.5%
	Africa	0.9%

million, annual net revenues exceed €40 million or Tax Transparency by Multinationals | 7 Note: The table shows the percentage of multinationals headquartered in the top five countries and regions in the Public CbCRs database.

Such as the Luxembourg Leaks (2014), the Panama Papers (2016) and the Pandora Papers (2021).

For fiscal years starting after July 2024, EU (2021) for the full legal text.

The Australian Treasury made a proposal for mandatory CbCR in October 2022(Australian Treasury Department, 2022).

The EU Tax Observatory developed a public exploration tool where this dataset can be freely downloaded.Tax Transparency by Multinationals | 3

To identify the largest multinationals we rely on the Forbes Index, that ranks top firms using a weighted index including the firms' sales, profits, assets and market value. Results are consistent when using market capitalisation as the size proxy. We exclude banks as their CbCRs are published under directive CRD IV, introduced before the BEPS framework.

This note has received funding from the European Union (GA No. TAXUD/2022/DE/310). The views expressed in this note are those of the authors and do not necessarily reflect the views of the European Commission.