Taxonomic analysis of the level of private equity / 2 venture capital market development in Europe 3

Determining the level of PE/VC market development and the way it operates is extremely 8 difficult. Despite countless reports and analyses concerning the PE/VC market, there is a lack of 9 study on that sector based on a synthetic index. The usage of taxonomic methods in the PE/VC 10 market analysis may be extremely useful in its proper characterizing. An in-depth study allows the 11 identification of weaknesses and strengths as well as opportunities and threats related to a specific 12 stage of PE/VC market development in a given country, that gives the opportunity to determine 13 public activities that could affect the acceleration of this market development in future. The main 14 objective of the study was to conduct a taxonomic analysis of the level of PE/VC market 15 development in Europe, in 2010-2015. It is worth mentioning that the term "level of development" 16 does not refer only to the value of investment or its dynamics, but to a set of objectified features that 17 create one synthetic indicator. The conducted analysis using the Hellwig method allowed to 18 determine the ranking of European countries in terms of the level of PE/VC market development, 19 which reveal some significant differences in the functioning of the this market within Europe. 20 Further detailed analysis of the designated groups of countries made it possible to determine the 21 characteristics of such clusters. The construction of the level of private equity/venture capital market 22 development ranking over the years enabled defining the current status and indicating the direction 23 of possible changes. 24


Introduction
Nowadays, PE/VC market is seen as the factor stabilizing the financial and capital market, especially during the economic crisis.European Union institutions as well appreciate the role of these investments, especially VC, which is proved by the multiple use of PE/VC entities as the intermediary of capital in the EU financing programs implemented.The analysis of the current state and level of development of this market and its reaction to market turbulences in recent years, in relation to the situation of other European countries, is therefore important for understanding the mechanisms of its existence, in order to identify areas of actions accelerating its development.
Despite considerable interest in the subject of venture capital, there is lack in the literature of the analysis of the level of PE/VC market development based on a synthetic index.Countless reports and analyses concerning the PE/VC market were created, containing a lot of information presented from different perspectives, however, they do not give the possibility to make comparisons on a global basis.
The construction of the level of private equity/venture capital market development ranking over the years, such as for example -already existing over 10 years -Innovation Index (European Innovation Scoreboard), would enable defining the current status, indicating the direction of possible changes and verifying the validity of the implemented strategies.
The main objective of the study was to conduct a taxonomic analysis of the level of PE/VC market development in Europe, in 2010-2015, when the comparable data were available.The analysis allowed to determine the ranking of European countries from the perspective of PE/VC market.It is worth mentioning that the term "level of development" does not refer only to the value of investment or its dynamics, but to a set of objectified features that create one indicator of the level of PE/VC market development.Thanks to the study and the analysis of other countries experience, weaknesses and strengths, as well as, opportunities and threats arising from a particular stage of PE/VC market development of the can be identified.It gives the opportunity to plan certain activities that could affect the acceleration of the development of this sector, and indirectly the economy of a particular country.
In the study there were used data collected and processed by research agencies and public institutions such as Invest Europe (previously EVCA), Eurostat, State Statistics Service of Ukraine (due to the limited data in Eurostat for Ukraine, information were obtained directly from the Department of International Cooperation and Integration European Statistical Office of Ukraine and data published by this Office).

Methodology
The PE/VC market is a complex object, thus the level of its development is determined by many characteristics.Such as in the case of technical progress assessment, social and economic development valuation, living conditions or technical infrastructure evaluation, the assessment of the level of PE/VC market development in particular countries generates a significant problem.The level of market similarity in two countries measured by one indicator may be high, however, due to another feature, can be low.Therefore, it is worth using the methods of taxonomic comparative analysis.
A taxonomic analysis is a scientific discipline that allows the study of complex objects, which variation is simultaneously influenced by many factors.Professor Zdzislaw Hellwig defined it as "methods and techniques for comparing multi-feature objects" (Hellwig 1981).Taxonomic analysis covers research activities such as assessing the similarity of individual units, their sequence and classification (Nowak 1997).These methods are used in economic studies to determine the order of objects difficult to be classified on the basis of only one feature, such as the classification of countries due to the level of economic development of enterprises or due to their financial condition (Bąk 2016).They can be determined only by measuring the values of aggregate variables comprising of individual observations (Bąk 2013).
In the literature there are presented many classifications of a multi-parameter methods.They differ by procedure, area of application, level of calculation effort, formalization degree or duration.
Such a large diversity of taxonomic methods results from the complexity of the multi-feature classification as well as from the fact there are many ways to create groups of units with similar characteristics.In this regard, the choice of appropriate classification method is not simple.Professor Z. Hellweg (Hellwig 1968) was the first who founded a synthetic development measure method.
Hellwig's method synthesizes information from series of diagnostic measures and assigns to the analyzed phenomenon one aggregate feature (Krakowiak-Bal 2005) presented by one numerical value, which facilitates all comparisons between European countries.It is a method that was used to analyze the level of PE/VC market development in European countries.

Hellwig method scheme
The Hellwig method is a linear ordering method, which is based on projecting on a straight line individual points located in a multidimensional space.The analyzed objects are put in order based on the development index formula, which is a synthetic measure, combining information from a series of variables into one aggregate indicator (Grabiński 1992).
To analyse the level of PE/VC market development in European countries using the taxonomic cluster analysis, it is necessary to identify the factors describing the development of this market.It allows to establish the hierarchy of objects by ordering them from the highest to the lowest and thus distinguish groups of objects similar to each other by achieving factors that are considered to be important for determining the level of PE/VC market development (when these objects are described for more than one feature).
The construction of the Hellwig's taxonomic measure (Hellwig 1968) begins with determining the set of diagnostic variables marked with the appropriate symbol X (X1, X2,…, Xk) and the fulfilled information matrix of particular objects.The matrix is saved as (1): Where: -value of the j diagnostic variable for the i object; Afterwards, there should be determined the nature of the diagnostic variable.If higher values of a given variable allow to qualify the object as better within the general criterion, this is called a stimulant.On the other hand, when the higher values of the property cause a worse assessment of the object, then it is the destimulant (Depta 2005).In taxonomic analysis, it is also important to unify the level of variability of features in order to ensure their comparability.To bring the characteristics to be comparable, it is necessary to standardized them based on the formula (2) below: where: -empirical value of j diagnostic variable for i object, ̄ -arithmetic average of diagnostic variable xj,  -standard deviation from diagnostic variable xj.
As a result of standardization, there is obtained a standard synthetic variable, called development model P0j (Hellwig 1968) presented in the formula (3): where: = (  ) for variables that are stimulants,  = (  ) for variables that are destimulants.
This formula can be defined by the best observed value or on the basis of expert knowledge by adopting arbitrary values of the standard.
For the destimulant, you can transpose variables into stimulants using below formula (4): In the further stage of the research, for each analysed object, the distance from development model P0j should be determined.The Euclidean distance formula (Shraddha, Suchita, 2011) (or its square) is most commonly used (5): where: zij-normalized value of j variable for i object, z0j-normalized development index model value for j variable.Then a relative taxonomic development index measure for individual objects is calculated in order to normalize the coefficient di0: where: -the arithmetic average of the designated distances from the development model,  -standard deviation from the determined distances from the development model.
The higher the value of the distance, the more object is closer to the pattern and the better is its' situation.A result close to zero indicates a very unfavourable situation of the analysed object.On the basis of the value of taxonomic development measure, it is possible to set in order the objects due to the level of PE/VC market development.
On the basis of the calculated synthetic measure, a linear arrangement of objects is made.The determination of Hellwig's synthetic development index can be additionally supplemented by division of units into clusters (Grabiński, Wydymus, Zeliaś 1989), using the arithmetic average and standard deviation from the relative value of the development measure.The objects can be divided into four typological groups: from very good to insufficient.It should be noted that the proposed assessments are relative, i.e.only within countries taken into account in the analysis and due to available diagnostic variables (Warzecha 2013).

Identifications of factors for analysis
The concept of "level of development" is characterized by the structure and therefore it should be verified to what extent certain results for the factors considered to be relevant in given case, have been achieved (Grajewska 2013).Proper market specification is extremely important as it allows a better understanding of the mechanisms affecting its development.The particular features were selected on the basis of substantive and statistical prerequisites.The selection of indicators for the study was made taking into account different spheres of the PE/VC market, so that the final result allowed to determine which of the European countries belong to the group with very high, high, moderate and low level of development of the analysed market.
Due to the fact that the aim of the study was to determine the level of PE/VC market development, by key factors there were considered to be those that determine its shape, form and condition.Thus, the study contains information that characterizes the market, i.e. its size, dynamics of development, industry structure, investment structure due to stage of enterprises development, etc.Because external factors, which determine the country's economic, technological and social level, also have an (indirect) impact on the PE/VC market, they could not be completely neglected.
However, it is important not to introduce too many external factors that could "flatten" the results of the research and bring them to the general economic dimension.External factors affecting the PE/VC market in European countries have been identified by using own econometric method and earlier analyses and researches conducted by, among others, Artur Zimny (Zimny 2013).
The study covered a period of six years, until 2015, due to the fact that the most recent statistical  data and the limited availability of some variables have reduced the number of factors that could have been used in the proposed study.
To visualize deviations from the synthetic index, there were constructed radar charts (Figure 1).These graphs can be described as linear, in which the axis "x" is represented by the central point, and the values of individual objects are marked on separate axes "y".In the following radar charts on the y-axes there were marked the values of the synthetic measure of PE/VC market development in European countries in particular years, according to the results of Hellwig's analysis.According to the above radar charts, over the 6 analysed years, some countries, such as France, United Kingdom, Germany, Netherlands, were distinguished by the highest value of the measure, while Greece, Bulgaria, Ukraine and Romania by the lowest.Although some pattern can be observed in the case of the countries indicated, there were relatively significant changes in the level of PE/VC market development among other European countries.Therefore, more detailed analysis is necessary.
On the basis of the calculated synthetic index, European countries have therefore been ranked in a linear manner, according to the obtained measures, from countries with the best condition of the PE/VC market, to those in which the market is still underdeveloped.In addition, countries were grouped into four clusters separated by an arithmetic average and standard deviation for a relative development measure.This way, four categories of countries were selected, as presented in Table 4.The results of the conducted ranking and assignment to the distinguished groups are presented in table 5.
The typological grouping of countries based on the average and standard deviation provided groups of different size.It should be noted that the proposed assessments are relative, i.e. within analysed countries and due to available diagnostic variables.In Table 5 appropriate groups, for a clear distinction, are marked in colour according to the division rules presented in Table 4. Analysis of the PE/VC market using the taxonomic method, which is a Hellwig synthetic development

Discussion
The Hellwig method enabled creation of the ranking of countries and classify them into groups.
Analysis of particular groups of similar countries, gives the opportunity to formulate general characteristics of the PE/VC market in Europe.These characteristics including the size of investments, their share in GDP, source of origin, industry structure etc., were presented in a tabular form in Table 6 below.Such an analysis, using taxonomic methods were not presented in researches yet.2.000 -20.000 100 -6.000 15 -1.500 1 -100 The range of PE/VC share in GDP 0,2% -0,7% 0,2% -0,7% 0,0% -0,5% 0,0% -0,1% The results of the analysis shows that unquestionable leaders of the European PE/VC market are: Great Britain, Germany and France.It is not surprising, as these countries constitute the core of PE/VC investment covering over 70% of all PE/VC investments in Europe (76% in 2015 -total 33622917 thousand euro).What's more, according to the International Innovation Index (a global index measuring the level of innovation of a country, produced jointly by The Boston Consulting Group -BCG), these countries are in the world top 20 countries with the highest level of innovation (Dutta, Lanvin 2013).The level of economy innovativeness has a very strong impact on the pace of PE/VC market development and vice versa.The first group includes, in some years, also countries such as the Netherlands, Austria, Portugal and Switzerland.These countries were characterized by the highest level of PE/VC investments in Europe and their high share in GDP in 2010-2015.55% of the PE/VC funds invested in that period were foreign capitals.The industry structure was diversified -all market sectors received private equity financing, but the sectors that gained the most capital were: life sciences, consumer goods & retail and business & industrial services.Up to 25% of invested PE/VC funds supported high-tech projects.Investments in the final phases of companies development dominated in that group of countries (more than half of the PE/VC resources went to companies at buyout stage), while the financing of businesses in the early stages of development was negligible.These countries presented a strong share of human resources employed in science and technology and the high number of patent applications reaching the EUP.
The second group, associating countries with a high level of PE/VC market development, is relatively diverse and consists of, among others, from: Belgium, Luxemburg, the Netherlands, Austria, Denmark, Sweden and Switzerland.In some years there were also included the Baltic countries, Portugal, Spain, and Norway.Although depending on the year of the study countries change places in the hierarchy within the group, the overall structure remains relatively stable.These countries are also included in the first 20 countries with the highest International Innovation Index.
Although the structure of PE/VC market is similar to the previous group G1, most of the analysed

Conclusions
Determining the level of PE/VC market development and the way it operates is extremely difficult.
Moreover, economic turbulence has also had an impact on the volatility and transformation of this sector in recent years.

214b
The total European patent applications refer to requests for protection of an invention directed either directly 215 to the European Patent Office or filed under the Patent Cooperation Treaty and designating the EPO (Euro-PCT),216regardless of whether they are granted or not.The data shows the total number of applications per country.

Figure 1 .
Figure 1.The distance of the synthetic index for particular European countries from the Hellwig development formula in 2010-2015 measure, gives the opportunity to determine the current level of PE/VC market development by using a single numerical value and the classification of countries from those with the highest level to those with the lowest level of development.It enables and facilitates the comparison between countries.Conducting detailed analyses for individual years gives a broader picture of what constitutes a very high, high, moderate or low level of PE/VC market development in Europe.The following Figure 2 presents the division in 2015.

Figure 2 .
Figure 2. The map of Europe with an indication of the level of PE/VC market development in Europe based on the Hellwig synthetic index measure, in 2015

31 October 2018 doi:10.20944/preprints201810.0749.v1 previous
years has been adapted to the new criteria.Joining most recent data to the analysis, where part of factors were calculated on slightly different basis, would deprive the possibility of making comparisons with previous years.Considering the above findings, for the study there were initially proposed 37 indicators determining the level of PE/VC market development (creating a potential set of features) divided into Structure of PE/VC investments due to the company development phases.The statistical data were gathered based on EVCA (Invest Europe) Yearbooks (Yearbook 2016) and reports with dataset on all European countries (Yearbook Dataset 2015), as well as, Eurostat database such as patent applications to the European patent office (Patent applications 2016), and human resources in science and technology -HRST(Human resources 1995(Human resources   & 2016)).In order to solve the problem of variable weighing, there was made the assumption on the same importance of each analysed feature.In the next stage of the study, the character of each traits was determined, yearbooks published by Invest Europe, have a new structure of calculations and only part of data for Preprints (www.preprints.org)|NOTPEER-REVIEWED|Posted:distinguishingamongthemstimulants(adiagnosticvariable where a higher value means better situation of the object) and destimulants (where a higher value means worse situation of the object), taking into account the substantive meaning of individual features.They were marked with the letters [S] and [D] respectively.It was assumed, that in some cases the higher value means deterioration (weakening) of the level of PE/VC market development.Thus destimulants were:• share of PE/VC investments financed by public entities (the higher the level of PE/VC market development makes it more independent from state funds);• share of domestic PE/VC investments of total PE/VC investment (the developed PE/VC market should attract foreign capital.)Themarket,which is financed only by domestic capitals, is a closed market, which may affect its slower growth);• share of PE/VC investment in agriculture (this sector is relatively low innovative and not technology driven in comparison with others).The differences and correlations between individual variables were verified in the study and diagnostic variables were selected, reducing the original set of features by the following indicators:X3, X4, X6, X8, X9, X13, X14 (see table1).The remaining variables were used in the Hellweg synthetic index assessment of the level of PE/VC market development in Europe.From among mentioned indicators, there were finally included 30 variables in the study.Table1below presents a list of variables, with an indication of which were included in the study.

Table 1 .
Variables defined for the Hellwig method after initial verification, with the specification of stimulant/ destimulant The value of PE/VC investment taken from aggregate tables for European countries (not individual country 213 tables).Such a choice results from the fact that the data included in collective summaries are more comparable. a

Table 2 .
The values of the Hellwig synthetic index measure of PE/C market development for European countries in 2010-2015

Table 3 .
Descriptive characteristics of synthetic index measures describing the level of PE/VC market development in European countries in 2010-2015

Table 4 .
The rules of grouping European countries based on the criteria used in Hellwig method

Table 5 .
The hierarchy of European countries due to the level of PE/VC market development based on the

Preprints (www.preprints.org) | NOT PEER-REVIEWED | Posted: 31 October 2018 doi:10.20944/preprints201810.0749.v1 factors
reach slightly lower values.However, in that group more PE/VC funds support projects concerning modern technologies.The third group includes countries where the level PE/VC market of development is assessed as sufficient/moderate.It includes mainly Poland, the Czech Republic, Italy, Spain and Finland.Also Romania and other Central and Eastern European countries (CEE) have appeared several times in this group.In the case of G3 group, the situation is not as stable as in the G1.A relatively strong displacement occurs in the rankings, depending on the year.This situation is influenced by the fact that in the case of countries from that group, investment values and other indicators are not significant, thus each positive signal from the market (small investment growth, increase in the number of patents or participation in the high-tech sector even by a unit) strongly affects the value of the synthetic indicator of a given country.Hence, countries that are on the border of clusters relatively often change their position within the group.As for the characteristics described in the above tables, the countries of this group show average values.This group is characterized by a greater interest of investors in projects in the growth phase.The last group G4, with the lowest rating of the level PE/VC market development in Europe, consists mainly of the following countries: Bulgaria, Greece, Ukraine, Romania and Hungary.These countries (with the exception of Hungary) are at the last places of the International Innovation Index for European countries.Due to the low maturity of the PE/VC market, they were characterized by a significant share of domestic capital and increased investments in companies in the early stages of development.The level of employment in science and technology in these countries, and hence the number of patent applications in the European Patent Office, were lower here than in the other countries.In this group there was a strong focus of investors on a small number of industries/sectors in a given year.

preprints.org) | NOT PEER-REVIEWED | Posted: 31 October 2018 doi:10.20944/preprints201810.0749.v1 (
Their impact strongly affected the PE/VC market in Europe, that only five countries out of the 25 managed to achieve the size of private equity investment at least as before the crisis in 2007.Investment value The conducted analysis using the Hellwig method allowed to determine the ranking of European countries in terms of the level of PE/VC market development, which reveal some significant differences in the functioning of the PE/VC market between European countries.Further detailed analysis of the designated groups of European countries allowed to determine the characteristics for countries qualified to such clusters, with a specific level of PE/VC market development.In the part of Central and Eastern Europe, both the industry structure and the share of individual types of investors in the total amount of PE/VC investments vary less than in other European countries.In Western European countries, the financing is stable and almost all sectors of the economy achieves PE/VC capital, although to different extent.The value of investments in the Central and Bąk 2016) Bąk A. 2016.Porządkowanie liniowe obiektów metodą Hellwiga i TOPSIS -analiza porównawcza (translation: Linear ordering of objects using Hellwig and TOPSIS methods -a comparative analysis).In Taksonomia 26 Klasyfikacja i analiza danych -teoria i zastosowania, Prace Naukowe Uniwersytetu Ekonomicznego we Wrocławiu.Uniwersytet Ekonomiczny we Wrocławiu, Wroclaw, no 426, p. 23.(Bąk 2013) Bąk A. 2013.Metody porządkowania liniowego w polskiej taksonomii -pakiet PLLOLD (translation: Linear ordering methods in Polish taxonomy -PLLOLD package).In Taksonomia 20.Klasyfikacja i analiza danych -teoria i zastosowania, Prace Naukowe Uniwersytetu Ekonomicznego we Wrocławiu.Uniwersytet Ekonomiczny we Wrocławiu, Wroclaw, no 278, p. 56.
Eastern Europe is also much lower than in other Western countries.This is most probably due to the fact that this form of financing has been operating in the Central-Eastern part of Europe since 90'.In addition, the lower level of general economic development of these countries is also reflected in the level of PE/VC market development.When it comes to financing of particular stages of enterprise development, in Central-Eastern Europe, mostly mature companies can gather financing from PE/VC funds.Newly founded enterprises, which Preprints (www.