Labour market inclusion and economic well-being: a trajectory analysis for some European countries (1995–2019)

Abstract

The Europe 2020 strategy has been implemented since 2010 to recover from the Great Recession which has affected European Union countries. One pillar of this strategy is that economic growth should be sustainable and inclusive. Focusing on the concept of inclusiveness, a set of economic indicators observed over the 1995–2019 period in a subgroup of member countries is selected. To track the evolution of inclusive growth in each country, we propose an approach towards three-way data analysis. Using such an approach, a time trajectory showing the dynamics of labour market inclusion and economic well-being in each country can be plotted. This graphical analysis allows us to examine the extent to which economic growth has been inclusive in each country and compare the growth paths of different countries. The results show that economic growth has been heterogeneous across countries and has been coupled with a more inclusive labour market only in some countries.

1 Introduction

The Europe 2020 strategy is the European Union (EU) programme to support growth and occupation by 2020. Adopted by the European Council in 2010, it started as an intervention to overcome the structural weaknesses of the European economy after the 2008 global financial crisis. The 10-year objective was to enhance competitiveness and productivity and support a more sustainable market economy. In this context, three essential priorities regarding economic growth are pursued: smart, sustainable and inclusive.

The sectors involved in this strategy could be classified into five areas: employment, education, poverty, energy and climate change and research and development. The effects of the Europe 2020 strategy are on-going and the deadline is almost expired; a new strategy referred to “Agenda 2030” is already planned and it is predominantly based on the efficacy of institutions and sustainable development in environmental, social and economic dimensions (United Nations 2016).

This study focusses on the inclusive growth defined by the European Commission as: “How citizens and groups can interact and participate in open policy and decision making”. According to this definition, two objectives are proposed. First, to raise the employment rate for the population of 20–64 years old to 75%. Second, to remove 20 million people from poverty risk and social exclusion conditions. It is seemingly essential to supervise the employment rates through the indicator “employment rate for people aged 20 to 64 years”, which is computed as the percentage of those employed in the 20–64 year age range over the total population.

The original definition of inclusiveness has been reinterpreted as being analysed in a statistical context. Herein, the interpretation of inclusiveness as a term entail the capability to make young individuals and women participants in the production of national wealth and the decrease the levels of inequality. Thus, the following areas have been considered as the main dimensions of inclusiveness: employment, gender equal opportunities and fair income distribution (Mariani et al. 2019). In the literature, employment rates and the Gini index have been used as indicators of inclusiveness or economic growth in Bhalla (2007) and Zhuang and Ali (2010).

Given these premises, the research hypothesis of this study is to verify the presence of economic inclusive growth for eight foundation EU countries using only variables referring to the labour market and economic well-being during the last 25 years. This purpose is achievable using time trajectories represented in an easy way via a graphical approach. Similar contributions about this issue and methodology can be found in Castellano and Rocca (2017) and Tassinari and Vichi (1994).

After the Schengen Agreement of 1985 and the abolishment of internal border checks, in 1999 according to the Treaty of Amsterdam the free circulation also involved goods, services and assets. This innovation, combined with the introduction of euro currency in 2002, heightened the incentive for other countries to enter the European Union. Therefore, between 2000 and 2010, starting with the original composition, many nations (especially from East Europe) requested to join the EU and Euro area. Conversely, between 2010 and 2020, owing to the economic crisis, the European Union received numerous requests for aid from the single components to save their countries’ economy, thus leading to the adoption of some cogent economic measures. In 2013, the European Fiscal Compact was implemented as a new and stricter version of the Stability and Growth Pact. This agreement provides for the balanced budget rule, a general budget deficit not exceeding 3% of the gross domestic product and a significant reduction in the debt-to-GDP ratio for the states. Unfortunately, these actions were hosted as austerity measures that received many criticisms and increased anti-EU movement unrest in several states. The founding member countries reacted in different ways to the Fiscal Compact: in Southern Europe the countries of the PIGS group (Portugal, Italy, Greece and Spain) experienced a fall in employment rates leading to a negative climate towards the European Union; in Central Europe, Germany and France mitigated the negative effects defending these measures; while the United Kingdom (UK) asked for less binding actions for countries in the EU but not in euro currency area, thereby leading to the commencement of the Brexit process.

For these reasons, macro-economic indicators for a 25-years period (from 1995 to 2019) have been considered for eight foundation EU countries: France, Germany, United Kingdom, Ireland, Portugal, Italy, Greece and Spain. The aim of this study is to verify the presence of inclusive growth in these states by searching for similarities and differences among them via a trajectory analysis.

To apply dynamic factor analysis, in the primary step it proceeds to a reduction of the problem dimension via a principal component analysis (PCA). This technique allows the extraction of a number of latent components lower than the original variables to show, choosing the first two components in a bi-dimensional plot on a Cartesian plane. Thus, the trajectory for each country is simply shown by joining the points representing each year. The trajectory on the graph appears to be very informative both in the evolution of the country over time and in a comparative way, by plotting trajectories for more than one country on the same figure.

A fundamental issue with this technique is the choice of weights to attribute to the years in the aggregation method. Different weights can lead to deviant results. Furthermore, after choosing the weights it is possible to compute the barycentre as a point representing the synthesis of the entire time interval. In this context, the barycentre could be used as a measure of synthesis indicating the centre of the trajectory. For each unit, the average of the two coordinates is computed.

The remainder of this paper is organised as follows. In Sect. 2, a brief description of EU economic models is provided. Section 3 introduces some considerations regarding social inclusion in Europe. Section 4 provides information about the data sources and some descriptive statistics. Section 5 presents the methodology based on the dynamic factor analysis. In Sect. 6, trajectory analysis is presented to show the principal evidence. Finally, the discussion and final remarks are presented in Sect. 7.

2 Three different European economic models

To make the dissertation more efficient, it has been chosen to analyse countries according to a family of well-known economic and sociological models (Amable 2003; Burroni 2016; Sapir 2006). These models have stressed similar features among groups of European countries strictly that are related to spatial proximity. The three models are the continental, Anglo-Saxon and Mediterranean models.

The continental model is introduced by Amable (2003) grouping Austria, France, Germany and the Netherlands together. These countries are pooled by some policies inclined towards development, innovation-oriented and favouring high internal flexibility. In recent years, the mechanisms of productivity organisation have improved. Their labour market has been centred on a high level of attention for occupations with highly qualified employees to be able to cover more roles in the same firm. This has caused low worker mobility because of the lack of specialised manpower. Other similarities concern the welfare system based on insurance principles intended to reduce social disparities and maintain high trust in institutions (Scriptema 2017).

The Anglo-Saxon model, which grouping United Kingdom and Ireland together is characterised by a labour market with a dual structure: on the one hand, economic sectors with high qualifications, while on the other hand, sectors with a low level of professionalism. The high participation in the labour market is due to expedients that favour the activation of new contracts. It presents a consistent external flexibility with high mobility and short-term contracts. In addition, very low subsidies are granted for the unemployed, thus encouraging strong competitiveness among workers and self-investment in formative courses with general competencies. Furthermore, public interventions through active policies are scarce, except for high technology (Burroni 2016).

Some countries in Southern Europe could be classified as states operating with a Mediterranean economic model, and they included Portugal, Spain, Italy and Greece (Amable 2003; Regini 2015). There are many similarities between the labour market and the welfare of these countries. First, the role of the family is fundamental in this context in terms of members’ support. This facilitates the commencement of business activities at a familiar level sometimes being unable to better bear the comparison with Central and Northern Europaen firms based on investments in innovation (Burroni 2016). Public interventions to contribute to development are marginal and small: there is a low contribution of expenditure to the innovation. Notwithstanding a slight increase in the employment rate (above all the female rate), this indicator is still low compared to the average of the European Union. Moreover, an expansion of atypical employment has been registered in these countries after the 2008 economic crisis (Gialis and Leontidou 2016). Data on young unemployment are not positive, even in the case of high educational levels. Moreover, the introduction of euro currency in presence of low competitiveness has not yielded a winning strategy for these countries (Boda and Považanová 2015). Notwithstanding a long series of reforms about the labour market, they struggle to recover after the economic crisis, thus leading to their repeated requests for financial aid from EU (Burroni and Trigilia 2011).

3 Social inclusion in Europe

According to the United Nations definition, social inclusion is the process through which individuals improve their participation and self-realisation within a society, thereby reducing barriers that prevent them from fully participating in political, economic, and social life. Social inclusion is multi-dimensional and it affects different life spheres, not only economic but also political, cultural and social, and all these spheres evidently depend on each other.

Creating an inclusive society has been a key goal in the process of European integration from the onset, and the latest Great Recession put new emphasis on this objective: social inclusion became a priority in the EU 2020 Strategy, setting a common goal of taking 20 million people out of the risk of poverty by 2020.

In this study, the attention is focused on economic inclusion looking specifically at some aspects that are crucial ingredients of inclusion and are strictly connected, namely economic growth, equality and occupation. Indeed, social participation may be hindered when people lack access to material resources, including income, and employment. In view of this, the first indicator used to evaluate the ability of countries to realise social inclusion is GDP growth.

In the last decade, the Great Recession of 2009 led to a severe recession in the EU, with a fall of 4.3% in real GDP; however, this was followed by a recovery in 2010 and a further expansion in 2011. Afterwards, GDP contracted in 2012 but from 2015 to 2018 economic growth was fairly stable, between 2.0 and 2.8% per year, with a partial stoppage in 2019, when the EU-27 recorded a 1.5% increase in GDP. However, within the EU, economic growth varied considerably among member states. For instance, in 2012 only 14 member states witnessed economic expansion. Moreover, despite all the member states recording positive GDP growth since 2017, there were huge differences between countries, going from Ireland, who registered the highest annual growth rate in 2019 (5.6%), to Italy, who recorded the lowest value of 0.3%. On average, the annual GDP growth rate in the EU over the last decade (from 2009 to 2019) has been 1.6%, albeit this average hides important differences between countries as well. The average growth rate over the same period ranges from the highest level recorded in Ireland (6%) to the lowest values for Portugal and Italy, where the average growth rate was below 1%, while Greece recorded a negative value (Eurostat 2020a).

Obviously, if the aim is to evaluate citizens’ living standards and social inclusion, in addition to GDP growth, it is necessary to consider at per-capita GDP as well, which amounts on average to 31.1 thousand euro (in current prices) in the EU-27 in 2019. However, in this case, the average value covers relevant differences between countries, which range from Luxembourg, where the 2019 GDP per inhabitant has been reported to be approximately 2.6 times the EU-27 average, to around 0.5 in Bulgaria. Moreover, in the last decade, due to low GDP growth rates, Italy and Spain moved from above to below the EU-27 average, while Greece and Portugal dropped further below. In contrast, Denmark, Germany, Ireland and Luxembourg moved further ahead, thus enhancing the economic differences among older EU countries (Eurostat 2020a).

Despite the undeniable role that economic growth plays in promoting well-being and poverty reduction, to explore the drivers of social inclusion, it is also important to consider how the poorer fragments of society participate in economic growth. This is equivalent to considering how a country’s wealth is distributed among its citizens or, put differently, appraising at inequality. Some degree of inequality may be functional to economic growth in providing incentives, for instance inducing people to invest more in human capital if returns to education are high, or by providing incentives for innovation and entrepreneurship. However, higher inequality lowers growth through different channels, such as under-investment in education (and resulting poor labour productivity) by the poorest fractions of society (OECD 2014). The negative impact of inequality on economic growth may be channelled by greater political and social instability (Alesina and Perotti 1996).

In general, economic growth does not intrinsically imply that all groups of the population have access to the same economic opportunities. Although the literature on the relationship between inequality and growth is mixed (Darvas and Wolff 2016), it is well established that income inequality influences the rate at which growth facilitates poverty reduction. Reducing inequality and bringing it together with economic growth is crucial to achieve more inclusive growth, which, according to OECD (OECD 2014), is defined as “economic growth that creates opportunity for all segments of the population and distributes the dividends of increased prosperity, both in monetary and non-monetary terms, fairly across society”.

Income inequality in the EU as a whole is lower than that in the US and most emerging countries. In the last decades, also thanks to redistributive fiscal measures, net inequality measured by the Gini index after taxes and transfers has declined until the Great Recession, and it has remained stable afterwards (Bubbico and Freytag 2018). Overall, however, the reduction of inequality in Europe is mainly due a reduction of inequality across member states, and this is related to an increase in the average income in the poorer EU countries relative to the richer ones. The larger contributor to inequality in Europe is due to within-country inequality, which is increasing in most developed countries (Milanovic 2016; World Bank 2016).

Moreover, there are significant differences across EU countries with respect to intra-country inequality, even across countries that are characterised by similar development levels. More specifically, in general Mediterranean countries and the UK show higher levels of inequality compared to Nordic and continental EU countries. High within-country inequality means that segments of these countries’ populations are excluded from the wealth created at country level.

There are several factors that interact with each other besides income inequality, such as inequality in opportunities to access higher education, as well as, changes in labour market institutions or in redistributive policies. However, a key element is certainly related to labour market performance, and specifically to individuals’ employment. In fact, low occupation and labour market participation rates imply that many individuals are excluded from income-generating opportunities and have a negative impact on their living conditions. Consequently, one of the main instruments for reducing inequality and achieving inclusive growth is increasing employment, especially in the labour force segments that are more often excluded from the labour market. Equal opportunities in access to the labour market are key to reducing inequality and promoting inclusive growth. Moreover, low employment may be detrimental to economic growth potential itself, due to human capital deterioration and discouragement effects when individuals spend long periods outside the labour market (Darvas and Wolff 2016). The EU itself considers empowering people through high levels of employment a tool to attain inclusive growth. Specifically, the EU 2020 target for inclusive growth includes reaching 75% of the population aged 20–64 years in employment, with a special emphasis on women and the young (in addition to low-skilled and older workers). Indeed, although anyone may be potentially at risk of social exclusion, specific individual characteristics increase this risk. In this respect, there are considerable cross-country variations in labour market performance across member states, and low youth and female employment is particularly worrying in some European countries. In such countries, inclusive growth should particularly focus on the part of the labour force that is excluded from the growth process. As regards the youth, in 2019 the average EU-27 employment rate for young people aged 15–24 years was 33.4%, ranging from the highest value in the Netherlands (65.3%) and Denmark (55.0%) to the lowest in Italy and Greece, which recorded a lower than 20% employment rate. A similar across-country variation is observed in the employment rate of young people aged 25–29 years. A related issue is that of the young people neither in employment nor in education or training (NEET). Among young people aged 20–34, in 2019 the NEET status encompassed approximately 12.7 million young people, representing around 16.4% of this population. Similar to the previous economic indicators, data show a large variation across countries: in 2019 the NEET rate spread from below 10% in Sweden, Luxembourg and the Netherlands to over 25% in Italy and Greece (Eurostat 2020b).

The second target population for improving social inclusion are women. In the last decades, the employment rate for women has been lower than the corresponding rate for men in all EU-27 member states, and in 2019 the employment rate gap between females and males is reportedly 11 percentage points. However, female employment varies significantly across EU member states, from approximately 80% in Sweden (79.7%) to slightly more than 50% in Italy (53.8%) and Greece (51.3%) (Eurostat 2020c).

In general, low youth and female employment rates have important implications in terms of higher risk of social exclusion, with both current and long-term consequences for these segments of the population. Being out of the labour markets has negative implications both at the individual level, since it increases the risk of marginalisation and social exclusion, and at the macro-level, as it represents a loss of productive capacity for the economic system as a whole.

Overall, despite the multidimensionality of inclusion as a concept, economic growth, equality and labour market participation are crucial ingredients. They are also strictly related and interact with each other. In view of this, in the following part of this paper, the analysis will concentrate on their temporal evolution in the last decades in a selected group of EU member states.

4 An overview on preliminary statistics

The dataset used in this study has been provided by Eurostat, the statistical office of the European Union having the aim to provide high quality statistics and data on Europe. Eurostat produces European statistics in partnership with the National Statistical Institutes and other national authorities in the EU member states.

In time-series analysis, it is very important to consider a uniform interval time range for all the countries considered. For this study, the interval is from 1995 to 2019, and the only problem is represented by some missing values for some years. The adopted solution is the use of interpolation to impute these missing values. Thus, the data matrix can be treated as complete. In the case of missing values, they are replaced using a linear trend at point. The existing series is regressed on an index variable scaled from 1 to n. Missing values are replaced with their predicted values. The final dimension of the dataset is composed of 8 countries $\times$ 25 years.

Eurostat databases offer a lot of information about inclusiveness in the labour market, in particular in the section called “Labour market” data have been obtained under the “Employment and unemployment (Labour force survey)” sub-section. This domain is based on the results of the European Union Labour Force Survey (EU-LFS). Few indicators use other data sources, such as national account employment or registered unemployment. The EU-LFS is a quarterly household sample survey carried out in the member states of the European Union, the United Kingdom, European Free Trade Association countries (except for Liechtenstein) and candidate countries (Montenegro, North Macedonia, Serbia and Turkey). It is the main source of information about the situation and trends on the labour market in the European Union. The EU-LFS is organised into 12 modules covering demographic background, labour status (International Labour Organisation definition), employment characteristics of the main job, atypical work, working time, employment characteristics of the second job, previous work experience of persons not in employment, search for employment, main labour status (self-perceived), education and training, labour market situation one year before the survey and income. The survey’s target population consists of all persons in private households, although the variables related to labour market, education and training are only collected for persons aged 15 years or older covering all economic sectors.

In addition to data from the Labour Force Survey, data on GDP and the Gini Index are collected. The complete list of the analysed variables is presented in Table 1.

Table 1 List of the analysed variable

Information about Gross Domestic Product is available in the section called “National accounts”. National accounts are a coherent and consistent set of macroeconomic indicators, which provide an overall picture of the economic situation and are widely used for economic analysis and forecasting, policy design and policy making. Eurostat publishes annual and quarterly national accounts, annual and quarterly sector accounts as well as supply, use and input-output tables, which are each presented with associated metadata. The domain consists of main GDP aggregates: main components from the output, expenditure and income side, expenditure breakdowns by durability and exports and imports by origin. GDP at market prices is the result of the production activities of resident producer units. GDP income components and other income measures are only available at current prices, because purely monetary flows cannot be decomposed into a price and volume components. However, they may be converted to “real terms” by applying an appropriate deflator. National accounts aim to capture economic activity within the domestic territory.

Data regarding the Gini index are available thanks to EU Statistics on Income and Living Conditions (EU-SILC) survey. These data are in the section called “Income and living conditions”. The “Income and living conditions” domain covers five topics: people at risk of poverty or social exclusion, inequality, income distribution and monetary poverty, living conditions and material deprivation, which are again structured into collections of indicators on specific topics. The EU-SILC results are produced according to relevant international classification systems. The statistical units involved are households and household members. The EU-SILC target population in each country consists of all persons living in private households.

Once the variables have been identified, it is necessary to verify whether they are all directed in the same way. Regarding this study, one of the considered issues is inequality; the variable strictly connected with this issue is the Gini index, which is oriented in a negative way. The higher the Gini index, the lower the equality, for this reason it is necessary to reverse this variable by computing the complementary value to 100.

Eight countries are selected for this study: France and Germany belong to the group of Central European countries, United Kingdom and Ireland represent the Anglo-Saxon area, while Portugal, Italy, Greece and Spain are grouped under the Mediterranean area. These countries are selected because their time series are complete. The aim of this paper is to verify the presence of inclusiveness during the last 25 years across Europe not only considering at single country, but also proving the similarity of this behaviour in countries belonging to the same local area. The eight countries are obviously very different in terms of population. Thus, factor analysis is performed by applying a weight as a normalisation factor. This factor is represented by the population of the countries.

Table 2 Descriptive statistics for GDPpc, 1995–2019

In Tables 2, 3, 4, 5 and 6, descriptive statistics are shown for all variables involved in the analysis. The most common tendency and variability indices are displayed including the compound annual growth rate (CAGR). The CAGR is an indicator measuring the annual growth of the considered variables over a specific period of time, and it is frequently used in financial issues expressed as a percentage. GDPpc connotes the GDP per capita, which is the ratio between the GDP and the population, the values in Table 2 show that all countries present the smallest values in the first year of the time series and the largest value for 2019, except for Italy and Greece which have had their maximum values in 2007. Ireland has the highest GDPpc values in terms of mean and median. It is also the country with the maximum range, underlining the great development of this indicator over the entire period.

Table 3 contains the descriptive statistics for the employment rate, all values are contained in the interval (57.7–79.2%). As already underlined for GDPpc, all countries show the smallest values in the first year of the time series. The maximum of the time series is in 2019 for all countries except Ireland (2007) and Spain (2012). Greece has the smallest mean (and median), while the country with the highest values on average is the United Kingdom (or Germany, if median is considered). Although the countries start from different values, they converge at a mean of approximately 70%, except for Greece.

Table 3 Descriptive statistics for employment rate, 1995–2019

The values for female employment rate values displayed in Table 4 show a similar trend to employment rate but with the lowest values. The countries in the Mediterranean area have very small values compared to other areas. Italy is the country with the minimum absolute value (42.5% in 1995) and also on average (50.3%), followed by Greece and Spain (with 54.4% and 60.2% respectively). The only country in this area with a high female employment rate is Portugal with values similar to those of the top countries such as the United Kingdom and Germany, that have average values close to 70%. Spain also has the maximum range and maximum CAGR.

Table 4 Descriptive statistics for female employment rate, 1995–2019

Young employment rate trend (Table 5) considerably differs from the previous rates because this indicator does not present minimum values at the beginning of the series. Except for France, all countries show the lowest values at the end of the series compared to 1995. the United Kingdom and Greece present the minimum values for 2019. As already seen for GDPpc, Ireland has highest values in absolute terms and in terms of range, but it reaches its maximum in 2007 and a CAGR index of − 0.06%. Coherently with the female employment rate, Greece and Italy suffer the worst position with average values approximately 30%. The United Kingdom is the most virtuous country with a mean and median value of 61%, despite a decrease of up to 56.6% in 2019.

Table 5 Descriptive statistics for young employment rate (15–24 years), 1995–2019

Table 6 shows the descriptive statistics for the distribution of the complement of the Gini index to 1 over the 1995–2019 period by country. AS the complement of the Gini index to 1 measures the extent to which income is evenly distributed within a country, such a measure can be seen as an indicator of the degree of equality in income distribution.

Table 6 Descriptive statistics for the complement of the Gini index to 1, 1995–2019

There is no common minimum and maximum in time trend; some countries, such as Greece, Spain and Ireland, reach the bottom at the beginning of the series, while other countries, including Germany and Italy, do so at the end of the series. By considering average values, the highest values are reached by the two Central European countries (i.e., France and Germany) with values approximately 71%. However, Portugal represents the worst situation with an average of 64%. Regarding the CAGR Index, there are very low values for this indicator.

5 Three-way data approach based on principal component analysis

In this study, a set of variables for a subgroup of European countries is observed over the 1995–2019 period. These data form a multivariate time array ${\mathbf {X}}$ (D’Urso 2000; Kiers 2000; Rizzi and Vichi 1995), the structure of which is

$$\begin{aligned} {\mathbf {X}}\equiv \left\{ x_{ijt}: i=1,\ldots ,I; j=1,\ldots ,J; t=1,\ldots ,T\right\} \end{aligned}$$

(1)

where i is a statistical unit (i.e. a country), j is one of the observed variables and t is an occasion (i.e. a year within the 1995–2019 period). Such three-way data can be rearranged to obtain time trajectories (Coppi and Zanella 1978; Coppi 1986; D’Urso 2000), thereby displaying the paths of the countries over time on a J-dimensional space.

Rizzi and Vichi (1995) point out that re-arranging ${\mathbf {X}}$ as a pooled two-way data set is useful for data analysis, and described alternative strategies to represent ${\mathbf {X}}$ as a large two-way matrix. The choice of a specific strategy essentially depends on the aim of the analysis. Rizzi (1989) applies PCA to a specific two-way representation of ${\mathbf {X}}$ to reduce dimensionality and obtain the so-called principal component matrices. To synthesize most of the common information contained in three-way data, Vichi (1990) proposes the factorial matrices analysis whereby a set of factorial matrices is determined; as shown by Rizzi and Vichi (1992), the first factorial matrix is equivalent to the compromise matrix of the STATIS procedure (Escoufier 1987). Castellano and Rocca (2017) used dynamic factor analysis (Coppi and Zanella 1978; Coppi 1986; Federici and Mazzitelli 2005) to break down the total variability in three-way data into three components capturing different facets of data variability.

The strategy we use to re-arrange ${\mathbf {X}}$ comprises two steps. In the first step, the observed values of the J variables on all I units in t are selected from the multivariate time array ${\mathbf {X}}$, thus obtaining an $I\times J$ matrix which is called “frontal slice” (Rizzi and Vichi 1995; D’Urso 2000):

$$\begin{aligned} {\mathbf {X}}_{..t}\equiv \left\{ x_{ijt}: i=1,\ldots ,I; j=1,\ldots ,J; t=1,\ldots ,T\right\} \ \ \ \left( t=1,\ldots ,T\right) . \end{aligned}$$

(2)

Frontal slice ${\mathbf {X}}_{..t}$ is an $I \times J$ matrix including J variables observed on I units in t, with $t=1,\ldots ,T$, Consequently the multivariate time array ${\mathbf {X}}$ can be seen as a set of T slices. In the second step, slices are stacked on top of each other to obtain the $\mathbf {{\widetilde{X}}}$ matrix with $I\cdot T$ rows and J columns, as shown in Fig. 1.

Fig. 1

Representation of ${\mathbf {X}}$ as a matrix consisting of slices stacked on top of each other

The generic row of $\mathbf {{\widetilde{X}}}$, denoted by ${\mathbf {x}}_{it}$, contains the observed values for unit i in t:

$$\begin{aligned} {\mathbf {x}}_{it}\equiv x_{i1t},\ldots ,x_{iJt}. \end{aligned}$$

(3)

Considering that countries are the I units in this study, the matrix displaying the time trajectory of country i is obtained by selecting the J-dimensional vectors ${\mathbf {x}}_{it}$, with $t=1,\ldots ,T$, from $\mathbf {{\widetilde{X}}}$ (D’Urso 2000):

$$\begin{aligned} \mathbf {{\widetilde{X}}}_{i}\equiv \left\{ {\mathbf {x}}_{it}: t=1,\ldots ,T\right\} . \end{aligned}$$

(4)

A time trajectory $\mathbf {{\widetilde{X}}}_{i}$ can be achieved for each country i, with $i=1,\ldots ,I$, and then such trajectories can be compared to detect the dissimilarities among countries. D’Urso (2000) compares the time trajectories of different statistical units by using a geometric setting in which each unit i is located on T parallel J-dimensional spaces. However, a comparison between time trajectories is easier when the synthesis of the information in $\mathbf {{\widetilde{X}}}$ is carried out via PCA (Jolliffe 2002) to reduce the number of variables J.

The aim of applying PCA to a data set with J variables is to reduce its dimensions by transforming the original J variables into new Q variables, with Q less than J. Such new variables are obtained in a way that ensures the loss in statistical information is minimised for each Q (with $Q=1,\ldots ,J-1$), as measured by the proportion of total variance that is not explained by the Q new variables. These new Q variables referred to as PCs, are uncorrelated with each other by construction. A PC, indicated by ${\mathbf {y}}$, is given by the linear combination ${\mathbf {y}}=\sum ^{J}_{j=1}a_{j}{\mathbf {x}}_{j}=\mathbf {{\widetilde{X}}}{\mathbf {a}}$, where ${\mathbf {x}}_{j}$ is the jth column of $\mathbf {{\widetilde{X}}}$ and ${\mathbf {a}}=\left\{ a_{1},\ldots ,a_{J}\right\}$ is a vector of coefficients (Jolliffe and Cadima 2016). The elements of ${\mathbf {a}}$ are chosen to maximize the variance of ${\mathbf {y}}$, which is

$$\begin{aligned} Var\left( {\mathbf {y}}\right) =Var\left( \mathbf {{\widetilde{X}}}{\mathbf {a}}\right) ={\mathbf {a}}^{T}\mathbf {\Sigma }{\mathbf {a}}, \end{aligned}$$

(5)

where $\mathbf {\Sigma }$ represents for the variance-covariance matrix of $\mathbf {{\widetilde{X}}}$. To find the vector ${\mathbf {a}}$ that maximises ${\mathbf {a}}^{T}\mathbf {\Sigma }{\mathbf {a}}$, the constraint that ${\mathbf {a}}$ is a unit-norm vector (i.e. ${\mathbf {a}}^{T}{\mathbf {a}}=1$) is commonly imposed. Once this is done, the problem can be solved by maximising the function $L\left( {\mathbf {a}}\right) ={\mathbf {a}}^{T}\mathbf {\Sigma }{\mathbf {a}}-\lambda \left( {\mathbf {a}}^{T}{\mathbf {a}}-1\right)$, where $\lambda$ is a Lagrange multiplier (Jolliffe and Cadima 2016). After differentiating with respect to ${\mathbf {a}}$ and setting the first derivative to ${\mathbf {0}}$, we obtain

$$\begin{aligned} \mathbf {\Sigma }{\mathbf {a}}=\lambda {\mathbf {a}}. \end{aligned}$$

(6)

Equation 6 shows that ${\mathbf {a}}$ is an eigenvector of $\mathbf {\Sigma }$ and $\lambda$ is the respective eigenvalue. Given Equations 5 and 6, the variance of ${\mathbf {y}}$ is equal to $\lambda$. Choosing the greatest eigenvalue of $\mathbf {\Sigma }$, denoted by $\lambda _{1}$, the corresponding eigenvector ${\mathbf {a}}_{1}$ gives the linear combination with the largest variance ${\mathbf {y}}_{1}=\mathbf {{\widetilde{X}}}{\mathbf {a}}_{1}$, i.e. the first PC. The second PC can be obtained by using the same approach with the additional constraint that the two eigenvectors must be orthogonal, that is ${\mathbf {a}}^{T}_{1}{\mathbf {a}}_{2}=0$. Because the variance-covariance matrix $\mathbf {\Sigma }$ has J real eigenvalues, J orthonormal eigenvectors can be defined and therefore J uncorrelated PCs can be created (Jolliffe and Cadima 2016). As the target of PCA is to reduce of the number of variables, only Q PCs (with $Q<J$) are held. When PCA is applied to $\mathbf {{\widetilde{X}}}$ and only the first two PCs are held, we obtain a two-dimensional plane in which the time trajectory of each unit is depicted in the space spanned by the first two PCs. The advantage of such an approach is that the time trajectory of a country can be displayed by connecting its PC scores, calculated for each year in the period considered, in a Cartesian plane.

6 Evidence from trajectory analysis

As mentioned in the Introduction, data refer to five macroeconomic indicators of employment and well-being for eight European countries from 1995 to 2019. In particular, the five considered indicators are:

• the GDP per capita (GDPpc);

• the complement of the Gini index to 1, where the Gini index is calculated using the equivalent disposable income (Gini);

• the total employment rate (Empl);

• the young employment rate (15–24 years) (Young);

• the female employment rate (Female).

Fig. 2

Cartesian plan in weighted factor analysis

Through the graph displayed in Fig. 2, it is possible to note that the two components are strictly related to two sub-groups of indicators: the first component is identified by GDPpc and Gini and it is named “Well-being”, while the second one is correlated with the three employment rates and is named “Employment”.

In the same two-dimensional plan, it is possible to visualise a couple of coordinates for each year of each country representing the two components obtained by the weighted factor analysis. The union of these coordinates draws a single trajectory for each country defining the route over the time between well-being and employment.

However, when all countries are represented in the same Cartesian plane, each quarter of the plot displays group of countries in common situations. Four areas of inclusion have been detected using the naming of the two axes. For example, in the first quarter, countries with high values of well-being and employment are displayed, thus, they could be named countries with active inclusion. The second quarter is for countries with high values of well-being but low values for employment, they can be defined as resilient inclusion countries. In the third quarter, countries with difficult situations are plotted. They have low values for both well-being and employment, therefore they are defined as poor inclusion countries. Finally, in the fourth quarter it is possible to find countries with an intermediate position given by low values of well-being and high values for employment. Given these parameters, they are defined as countries with prospective inclusion. Figure 3 plots all the countries in the same graph using a bubble chart representing the barycentre. It could be useful to detect intersections among countries by positioning them in the four defined quarters.

Fig. 3

Bubble chart for all countries (1995–2019)

The aerogramme in Fig. 3 represents a static point of view based only on the barycentre of the countries and it does not consider the trend of the entire time-series: the dynamic aspect is better represented by the trajectory analysis. Therefore, using the previous definition of the four quarters, France appears to be a resilient inclusion country, even if it has been moving towards active inclusion in recent years. Germany and Ireland could be considered as countries with active inclusion: however, trajectories show that Ireland has only actually entered this area in recent years, while Germany is leaving it. For many years, Italy has appeared as a country with resilient inclusion, but its trajectory is now in the poor inclusion area: in opposite, Greece is in a situation of poor inclusiveness. Spain is in a poor inclusion area, even if it is moving in the next quarter where Portugal is positioned: they could be defined as countries with prospective inclusion and the same definition is possible for the UK.

The bubble chart and trajectories clearly explain what has happened in the eight selected European countries from 1995 to 2019 about the citizens’ economic well-being (which, in this paper, depends on the GDP and the existing inequality in income/wealth distribution) and the employment rate (which, herein, is strongly related to female and youth employment). They underline the relevance of welfare policies and policies in favour of the inclusion of women and young people in the labour market in the face of changes in economic trends, in particular after the global financial and economic crisis involving all European countries after the failure of the Lehman Brothers Bank in September 2008.

The richest countries, such as France and Germany confirm their high citizens’ well-being but data related to the analysed period allow to show very different trajectories based on the diverse reasons creating these positive performances. In France, where GDPpc increases by approximately $30\%$ during the analysed period, the employment rates are not positive for a considerable part of the considered time interval and put French citizens in the resilience inclusion area. Only in the last few years, has data shown an improvement in the job market allowing the insertion in the active inclusion areas to maintain a good level of citizens’ well-being. This was related to the welfare policies established in the new millennium: new laws helped families, and for those with more children, the new “allocations” system strongly helped French citizens to maintain their quality of life even if the data concerning the labour market were not so good. Thus, data concerning the number of jobless women and young people improved in a context where the well-being decreased less than in Germany and in the last year increased and represented the best of all analysed cases. In contrast, its data related employment remained very lower than that of Germany.

In Germany, where the GDPpc increased by approximately $37\%$ during the considered period, the employment rates concerning women and young people became positive in the new millennium: during the 1990s, German employment data were affected by the high number of jobless people living in the former Eastern Germany lands and after there were some problems related to the initial negative economic effects of the birth of the Eurozone (Economic and Monetary Union, EMU). The latter put Germany in the resilient area and obliged Schroeder’s government to establish policies that reduced the welfare budget and had good effects, moreover, in Merkel’s governments years, for the employment. However, in the new millennium, the welfare state progressively decreased its positive effects on German citizens’ quality of life: until 2004. it allowed German families to remain in a positive economic well-being even if the negative economic trend reduced employment and consumption, and the high interest rates related to the arrival of the Euro reduced investments. In the following years, while the employment rates became the best (among the analysed countries) the level of economic well-being strongly decreased and became the same of the half of the 1990s and, even if it remained positive was in the active inclusion area, and new laws improved the minimum wage, it arrived at a very low level, far from the value existing before the 2008 financial crisis.

Concerning the British area, notable in the UK, GDPpc increased by approximately 43% in the 1995–2019 period. The low level of welfare policies (compared to the EU average) influenced citizens’ well-being in a context where the employment rates were always largely positive. In a labour market offering many opportunities also for women and young people, a relevant part of the inhabitants did not enjoy their lives because the average quality of the latter was generally low. In a few years, data allowed the UK to be placed in the active inclusion area: the normal condition was in fact represented by the prospective inclusion area. There were no significant changes concerning the level of citizens’ economic well-being even if, in the worst years, jobless people increased by only 2–3%. Thus, from the 1990s to the first years of the new millennium, employment rates increased and citizens’ well-being decreased. However, the following years showed that there was no trade-off: citizens’ well-being increased even if the employment rates remained stable. In addition, a particular exception was represented by the 2012–2016 year when the post 2008 financial shock years finished thanks to the good reaction of the English economic system: the relevance of the tertiary (in particular the City) facilitate the recover of job opportunities and also temporarily increased well-being. Thereafter, the flexibility of the labour market and the increase in the cost of living in the main English town continued to maintain low citizens’ well-being, and the welfare system did not help workers who did not have good professional skills.

In Ireland, where the GDPpc increased by approximately $170\%$ during the analysed period, the inclusion strongly varied and the citizens’ well-being revealed evidence of the best improvement among the studied countries. The expansive policies (in particular thanks to favourable taxation for foreign enterprises) and the effects of the new treaties for a durable peace between the Eire and Northern Ireland allowed the former to pass from the poor inclusion area to the prospect one and, moreover, to the active one: the government policies progressively created new job opportunities involving women and young people too. Even if the welfare system was not significantly improved, the Irish social context benefited from the low cost for accommodation and food; thus, Irish citizens enjoyed their increasing real wages, in particular compared with the English ones. While the latter only improved for the high-specialised workers (in particular the white collar), in Eire the improvement of salaries was generalised. In addition, it is important to consider the positive psychological effects of the progressive improvement of the quality of life of Irish families starting from a level that was inferior to the English one and favoured migration flows toward England. The new and better earnings apparently favoured consumption growth which added to new investments related to new fiscal policies: so Eire was the only country classified as “PIIGS” with high citizens’ well-being in the new millennium. During the second half of the 1990s, employment rates increased, but well-being remained stable. In the first years of the new millennium, data showed that well-being increased and then decreased while the employment rates improved. The trade-off continued after the 2008 financial crisis when employment rates were strongly reduced even if they remained positive. Finally, in recent years, data on the number of job opportunities and quality of life started to grow together: citizens’ well-being progressively became higher than in Germany and at the same level as France.

Furthermore, the figure and the trajectories allowed to analyse the different conditions of the Iberian countries, that is Portugal and Spain, during the study period. Both countries showed an improvement in employment rates and passed from the poor inclusion area to the prospective one, albeit they followed different trajectories. In Portugal, where the GDPpc increased by approximately $36\%$ during the analysed period, only half of the 1990s women and young people registered negative results concerning their employment. In contrast, in Spain this last progressively increased but it entered the positive area only after 2005. Citizens’ well-being in Portugal the lowest (considering the analysed countries) in the 1990s and it remained very low until 2005 even though the employment rates increased and favoured small growth in the citizens’ consumption. The citizens’ well-being remained low because the government’s choice of low real wages and low taxation to increase the appeal of Portugal for new enterprises operating in the industrial sector and services: Barroso’s era and the related European investments for the building of new infrastructure evidently increased the demand. New fiscal policies had to face the respect of the Eurozona (EMU) criteria concerning public debt and deficit, however, after the great financial crisis of 2008, the reduction of the budget for welfare policies did not strongly reduce employment rates. In recent years, new policies in favour of the welfare and allowing a low taxation for European retired people who decided to transfer their residence in Portugal changed the conditions: the employment rates remained stable but the citizens’ well-being progressively increased and arrived at the minimum level of the active inclusion area.

Data put Spain, where the GDPpc increased by approximately $41\%$ during the analysed period, in the poor inclusion area until 2006: the employment rates progressively increased as well as the citizens’ well-being thanks to the great development of the building sector and the creation of new infrastructure which allowed Spanish entrepreneurs to make great businesses. However, while the growth of the employment rates continued, the citizens’ well-being was reduced because the government had to respect the Eurozona obligation and to cut the welfare budget. The quality of life after 2006 remained superior to in the 1990s even though the global financial crisis slowed the improvement of employment rates. The inclusion of women and young people in the labour market remained more or less stable, while the citizens’ well-being arrived at the minimum when Spain had to apply hard rules to remain in the EMU. In recent years, as in the case of Portugal, citizens’ well-being progressively increased, but it was lower than in Portugal and far from the active inclusive area because the real wages remained low and the growth of job opportunities was limited. Furthermore, the analysis of the Spanish case was complicated because regions registered great differences concerning the data used, in particular the Catalonia: thus, the trajectories represented an average of very different values (Fig. 4).

Fig. 4

Trajectory for the analysed countries from 1995 to 2019

The Italian case is the most complicated to analyse because data are always the average between two very different social and economic areas, that is the regions of the North and Centre and those of the South. The North and Centre are the richest and most developed. Southern regions have low employment rates and underestimated real wage data. However, Fig. 3 and trajectories allowed to resume the effects of the economic, labour and welfare policies which entered into force in Italy, where the GDPpc increased by $8\%$ (with the top result, 17%, registered in 2007). During the nineties, Italy passed from a poor inclusion area to a resilient one. However, in the new millennium fluctuations were registered, thereby putting the country again in the poor inclusion area particularly in recent years. The national employment rate remained the lowest among the analysed countries. For women and young people, access to the labour market remained difficult, in particular in the regions where there was a lack of structures helping women with children (e.g. nurseries, kindergartens, and full-time compulsory education). In addition, for young people the labour market continued to offer low-paid jobs. During the second half of the 1990s, citizens’ well-being increased, arriving at the top early in the new millennium. However, the employment rates remained stable. They progressively increased in the following years while the citizens’ well-being decreased but remained positive with the exception of the years immediately following the adoption of Euro when inflation grew and real wages reduced as well as the welfare budget. The economic conditions improved in 2006 but the arrival of the 2008 financial crisis stopped the economic growth: the Italian economy progressively paid the effects of the economic efforts to allow Italy to remain in the EMU after the general sovereign debt crisis of the “PIIGS”. After the crisis, data reveal evidence the growth of the employment rates and the reduction of citizens’ well-being. This last period progressively replaces Italian country in the poor inclusion area even though the employment rates registered a good increase. However, as the data show two different economic areas, it is very difficult to explain trajectories. When Italy entered the EMU and the effect of the privatisation of a relevant part of public enterprises in fact allowed an improvement of the GDP in its Northern regions but this did not entail an equivalent increase in the entire Italian labour market. Notably, positive employment rates during the first years in the Eurozone when the decrease in interest rates on financial market permitted to increase job opportunities; meanwhile, the reform of the welfare system (particularly the pensions) reduced citizens’ well-being. The improvement of the labour market continued after the economic crises of 2008, but data concerning real wages remained negative, particularly for women and young people in the South. Moreover, the reduction of real wages and the cut of public expenditure which were very important, particularly regarding the social and economic equilibrium of the southern regions, reduced citizens’ well-being. The employment rates in Northern Italy, where secondary and tertiary sectors maintained good revenues and workplaces, were different from those in the South, where the financial crisis and the reduction of public intervention strongly influenced the local labour market and favoured the emigration of young people. The final average illustrated that Italy had the lowest level of employment rates concerning women and young people, while the level of citizens’ well-being was the lowest (but other countries, e.g. Spain and the UK, had better employment rates). Finally, data concerning the last years put Italy in the poor inclusion area as Greece, but the trajectories indicated more negative perspectives for the future: data on Greece, where the GDPpc increased by 20% during the analysed period (with the top result, approximately 51%, registered in 2007), in fact illustrated growing trajectories in recent years.

The Greek case clearly shows the strong effect of the economic crisis on the country, the poorest country in the Eurozone (EMU) and the only one that has been remained in the poor inclusion area throughout the analysed period. The data registered relevant improvements concerning both the employment rates and citizens’ well-being, but their real levels remained low even when economic performances and national debt improved and allowed Greece to enter the EMU in 2002. Greek citizens’ real economic and social conditions were partially hidden until the Great Recession following the 2008 financial crisis: the Greek economy was unable to support such a strong currency as the Euro and it was very difficult for the government to respect the EMU criteria concerning the national debt; thus, real data concerning this were reduced and did not illustrate the actual Greek debt position toward the financial world. When this was discovered in 2010, new European policies to resolvethe problem of the real Greek debt and deficit did not help the Greek economy; the Troika decisions (EU, ECB and IMF) strongly increased the number of jobless people in the public administration and, simultaneously, reduced the welfare system. The employment rates of women and young people remained stable while the citizens’ quality of life decreased (even when it remained better than in the 1990s). When the general economic trend improved. the citizens’ well-being was also enhanced, particularly in the last years, while the employment rates did not register a significant increase.

7 Conclusions

Inclusiveness is one of the most important objectives of the Europe 2020 strategy to sustain occupation and growth. In the year that this agenda expires, this contribution tries to verify whether the expected results are still ongoing or have already been achieved for some European countries. To reach this purpose, the original definition of inclusiveness has been reinterpreted in a statistical context as “the capability to make young and women participants to the production of national wealth and the decrease of inequality”.

Considering the last 25 years, 5 macroeconomic indicators have been considered for 8 EU countries: France, Germany, United Kingdom, Ireland, Portugal, Italy, Greece and Spain to verify the presence of inclusive growth and search for similarities and differences through a trajectory analysis. Using this approach, three-way data can be rearranged to obtain the so-called multivariate time trajectories displaying the path of each country over the years on a bi-dimensional space. Consequently, the evolution of a country over time is plotted in an informative and comparative way.

A bi-dimensional Cartesian plane shows that the two components are strictly related to two sub-groups of indicators: “Well-being” and “Employment”. The first component is identified by the GDPpc and Gini, while the second is correlated with the three employment rates. Based on the quarter of the plan where the barycentre of a single country is located, EU countries have been grouped into four categories. France and Germany are active inclusion countries, but the perspectives are better for the former, while the latter risks to pass to the prospective inclusion area; Germany improved its employment rates and lost a great part of its citizens’ well-being, while France confirmed the latter and registered few increase its in employment rates. Spain and Portugal are prospective inclusive countries: both of them present low levels of well-being and their employment rates progressively increased during the analysed period. However, the improvement started before in Portugal and the perspectives are better; for Spain, a regional analysis could permit a better evaluation of the existing differences. In the British area, employment rates are positive but the UK citizens’ well-being is limited by low welfare policies, while in Ireland this issue has been overtaken by using expansive policies and favourable taxation for foreign enterprises. Thus, Ireland could be considered as an active inclusion country and it is also the country with the longest trajectory; which could be interpreted as a signal of change and development. In contrast, the UK remains in the prospective inclusive area even if its employment rates are positive. Italy and Greece are in a situation of poor inclusiveness: the perspectives seem better for the latter, but in the Italian case (which has indicated the worst situation for employment rates) only a regional analysis can allow to veritably distinguish the different economic conditions between the Northern and the Central and the Southern area. Notably, both registered their best GDPpc in 2007, while the other analysed countries attained this in 2019; which clearly negatively influenced the analysed data and the perspectives of their employment rates and citizens’ well-being.

In conclusion, the situation regarding inclusiveness appears to be highly heterogeneous among countries. There is no common direction for these European countries towards inclusiveness. Considering the bubble chart, some countries with a more solid economic situation, such as Germany and France, or in a development phase, such as Ireland, tend to move close to the selected dimensions of inclusiveness; however, considering the trajectories followed in the last years, Germany could change. However, the Mediterranean area countries remain far from inclusiveness owing to the influence of a complex internal economic phase; nonetheless, Spain is in the prospective inclusion area, while Italy and Greece are in the poor one.

Data concerning the evolution of female and young people’s employment rates are less heterogeneous. Even if significant differences exist between the best cases in Germany and the UK and the worst cases in Italy and Greece, women everywhere have increased their accession to the labour market and the best results are very recent (the oldest case in 2016). Conversely, data concerning young people show a reduction (sometimes very strong as in the Italian case) and the minimal values are in the last years (only France represents an exception), while most of the best results are attained in the 1990s (only France, Portugal and Spain obtained them after but always before 2010).

Future works could approach different aspects of inclusiveness using other indicators that are not necessarily limited to the economic area. Moreover, a similar analysis could be applied to other territories within Europe.