Convergence and Divergence Tendencies in the European Union: New Evidence on the Productivity/Institutional Puzzle

Abstract

The World Bank (WB) has described the European Union (EU) as a convergence machine, and the real and institutional convergence has been achieved for a long period of time, and EU’s cohesion policy, alongside the Recovery and Resilience Facility (RRF), remains crucial for driving reforms and fostering investments that promote growth. But, in the last two decades this convergence machine has stopped working, and the convergence process has turned in the divergence. The divergence process poses a great risk for the smooth functioning of the EU, and it increases vulnerability of the EU to negative economic shocks. Productivity and institutional convergence are a necessary precondition for the smooth functioning of the EU, reducing differences in standards of living, increasing resilience, and achieving environmental sustainability. In the present paper, we will apply log t-test over the period 2003–2023 to investigate the formation of productivity and institutional convergence clusters. Our goal is to identify which countries belong to the poor productivity/institutional clubs, and to provide the necessary policy implications. Results indicate the existence of multiple steady states, which means that EU is vulnerable to external economic shocks

1. Introduction

The European Union (EU) integration process is a large, extremely complex process, the greatest endeavor in the globalization era of economic and political unification. But the more complex the project is, the greater is risk that it will fail. The EU started as a small, successful, and manageable project, but constant enlargement has made it very difficult to achieve institutional, productivity, and income convergence, which is stressed as a necessary precondition for further EU integration. Institutional convergence, which refers to the convergence of economic rules and policies, should have been fostered by the EU enlargement process.

In the aftermath of the financial crisis, the EU has been affected by several correlated shocks, which have led to banking and debt crises in some of EU countries (Pérez-Moreno et al. 2020). The EU has been described as a “convergence machine” by the World Bank (WB) (Indermit and Raiser 2012), but since the 2008 financial crisis, the “convergence machine” has stopped working, which led to a north-south divide in the EU (Landesmann 2015). The gap is increasing between the more productive North and the inert South (Gopinath et al. 2017). The north-south divide does not refer only to productivity and income, it also refers to the institutional divide. In contrast, North and Western European countries are members of high-quality institutional clubs, and South-Eastern European countries are members of low-level institutional clubs (Glawe and Wagner 2021a). The Central and Eastern European countries seem caught in the middle-income trap (Staehr 2015) and the poor institutional trap (Glawe and Wagner 2021a). The EU has experienced a productivity slowdown since the late 1990s, mainly because of the decline in Total Factor Productivity (TFP) and capital deepening (Escribá-Pérez and Murgui-García 2019). Not only that the productivity in the EU slowed down, but the international position of the EU has been unfavorable since the United States (US) has experienced high growth rates since the late 1990s. Institutional quality is central for the productivity challenge in the EU (Rodríguez-Pose and Ganau 2022).

In recent years, the COVID pandemic and war in Ukraine have completely changed the global environment. These challenges place significant pressure on countries, necessitating continuous technological advancement that involves redesigning production models to be more efficient, competitive, and environmentally sustainable. The global lockdown during the COVID pandemic led to a historic peak in CO₂ emissions (IEA 2022), causing record levels of carbon dioxide, methane, and nitrous oxide in the atmosphere in 2021 (WMO 2019). Technological progress, based on innovations will lead to a carbon-free future, by cutting CO₂ emissions (Castrejon-Campos et al. 2022). Technological progress will enable a more effective green energy transition. Sustainable development across all regions is crucial for economic prosperity, social well-being, and the EU’s overall competitiveness. Over recent decades, EU policies, especially cohesion policy, have greatly helped to reduce the development gaps between different regions.

Achieving sustainable development across all regions is crucial for economic prosperity, social well-being, and the EU’s competitiveness. Over recent decades, EU policies, especially cohesion policy, have greatly helped to reduce the development gaps between different regions. The EU’s cohesion policy, alongside the Recovery and Resilience Facility (RRF), remains crucial for driving reforms and fostering investments that promote growth. The growth that lacks cohesion will intensify concentration trends, leading to greater territorial and social divisions. Those who are marginalized may cultivate resentment and discontent toward the democratic system and the foundational values of the EU, which will increase the vulnerability of the EU, and decrease its resilience. Lack of cohesion will significantly decrease the probability of achieving environmental sustainability and increase the probability of falling apart of the EU.

The importance of institutions for the productivity and long-term economic growth has been stressed out in both theoretical and empirical literature, stating that the institutional quality is equally important, or outweighs traditional factors, including technology, in explaining the differences in income per capita among countries (North 1981; Knack and Keefer 1995; Hall and Jones 1999; Acemoglu et al. 2001, 2005; Acemoglu and Robinson 2012; Rodrik et al. 2004). The absence of institutional convergence in short term, i.e., the institutional divergence among EU countries, will likely make countries with the low level of institutional quality more exposed to the shocks, which will make entire EU vulnerable to the shocks (Pérez-Moreno et al. 2020). In the long term, institutional divergence will lead to divergence in productivity, per capita income, and in overall standard of living, which will substantially increase risk of falling apart of the EU (Pérez-Moreno et al. 2020). The institutional divergence within the EU would result only in conditional convergence, at best, which will result in high dispersion between the national levels of income per capita, in the long run (Blackburn et al. 2006). The trend of institutional divergence has been stressed by many researchers, especially recently, as a constant feature of the EU, instead of an institutional convergence process. As already mentioned, institutional divergence trends have been the main characteristics of the EU, rather than the institutional rapprochement, which has been verified by applying the sigma, or beta convergence tests. This kind of analysis neglects the possibility of existing multiple steady states.

This paper focuses on identifying multiple steady states, i.e., convergence clubs. This study offers several contributions to the literature on the multiple steady states regarding productivity and institutional quality within the EU. The present study is among the first to study multiple productivity and institutional clubs within the EU, by using Phillips and Sul’s (2007, 2009) methodology. Our goal is threefold. Our first goal is to provide evidence which will enable us to determine whether the EU is vulnerable to external economic shocks. The existence of the multiple productivity and institutional convergence clubs is considered as evidence of vulnerability to external economic shocks, which could, in long term, cause the falling apart of the EU. Our second goal is to identify which countries are members of the high productivity/institutional quality convergence clubs, and which countries are underperforming, and whether productivity and institutional clubs are formed mainly based on geographic region. And our third goal is to identify the factors that explain the formation of productivity convergence clubs across the EU. Answering these three questions is important for policymakers, enabling them to identify specific policies for particular countries to achieve environmentally and economically sustainable development, which will decrease the Union’s vulnerability to external economic shocks, and its dependance on polluting energy sources.

This paper is organized as follows. Section 2 discusses the existing literature and gives some theoretical background. Section 3 provides information on the model specification, applied methodology and the data. Section 4 contains the empirical results and discussion. Section 5 is the conclusion of the paper.

2. Theoretical Background

The present study is focused on institutional quality and its impact on productivity growth. The methodology focused on identifying the multiple steady states is relatively new within economic theory, which is why the economic literature is deficient with research focused on productivity and institutional convergence clubs. Especially literature focused on the TFP convergence clubs. In this section we will start with the briefly presentation of the findings of the general literature on importance of the institutional quality for the productivity growth, then we will focus on the research on the productivity and institutional convergence within the EU.

The characteristic of the EU is institutional divergence during and after the financial crisis. Regarding productivity, since the mid-1990s, productivity growth in the Eurozone has consistently lagged behind that observed in other advanced economies. Since 2004, the Member States in Central and Eastern Europe have continued to experience relatively strong productivity growth. In contrast, in the former EU-15 countries, productivity has remained almost stagnant, barely above zero. Nonetheless, there is productivity convergence between the former socialistic countries that joined the EU in 2004, on the one hand, and the core EU countries, on the other hand.

There is wide consensus in economic literature that institutional quality is a necessary precondition for economic and productivity growth. Institutional quality, measured by the EFI is stressed as an important factor which accelerates the economic growth, for the small, transitioned country (such as Bosnia and Herzegovina), and for the EU members (Croatia) (Borović 2014a, 2014b).

On the one hand, the high-quality institutions are a necessary precondition for increasing countries productivity and efficiency, and on the other hand, country’s ability to adopt superior technology developed elsewhere also depends on the quality of institutions (Acemoglu et al. 2005; Giuseppe and Scarpetta 2003; Havik et al. 2008; Mc Morrow et al. 2010). The productivity in the EU is affected by the quality of institutions directly, and indirectly, through increased short and long-term returns of human capital and innovations (Rodríguez-Pose and Ganau 2022). To increase productivity, local and national governments within the EU should make an additional effort to increase institutional quality, with a focus on corruption (Ganau and Rodríguez-Pose 2019; Rodríguez-Pose and Ganau 2022; Égert 2017). For the former socialistic countries that joined the EU in 2004, institutional quality is vital for long-term productivity growth (Borović et al. 2020). For the five European countries (France, Germany, Italy, Spain, and the United Kingdom) and the US, long-term productivity growth depends on high-quality institutions, especially on market efficiency (Calcagnini et al. 2021).

Institutional quality is stressed as an important factor in speeding up productivity growth, as well as boosting productivity convergence between the former socialistic countries that joined the EU in 2004, on the one hand, and the core EU countries on the other hand (Borović and Radicic 2023). For the OECD, private governance, market liberalization, and competition are vital for increasing productivity growth, and for creating productivity convergence (Giuseppe and Scarpetta 2003). The impact of the regulations on the productivity growth of the EU, and on their absorptive capacity is sector-specific, according to Mc Morrow et al. (2010). In the case of manufacturing, the market regulations are boosting productivity growth, while it is the opposite for the market services. Productivity convergence between the EU and the US, with an emphasis on institutional quality, has been confirmed by Mc Morrow et al. (2010), and Inklaar et al. (2008). Productivity convergence within the EU has been confirmed by Radicic et al. (2023), Bournakis (2012), and Männasoo et al. (2018).

A study conducted by Beyaert et al. (2019) focused on stochastic institutional convergence of the Eurozone for the period from 2008 to 2018. Their results suggest that within the Eurozone institutions do not converge. The same conclusion goes for the smaller sub-groups. Similar results were obtained by Pérez-Moreno et al. (2020). They were investigating institutional convergence within the euro area for the sub-periods during and after the financial crisis. Their findings show that the institutions diverge within the euro area. More specifically, during the financial crisis there was a sigma-divergence, with nonsignificant sigma divergence for the period after the crisis. They conclude that there is an increasing institutional gap between the core European countries and the European periphery. In contrast to previous research, Schönfelder and Wagner (2019) have confirmed the institutional β convergence within the EU and the pretendant countries. The convergence is mainly the result of the pretendant countries. Convergence refers to the area of product market and business regulation, while there is β divergence in the area of rule of law within the first twelve euro-area members (Schönfelder and Wagner 2019). Regarding the σ convergence, the authors stressed that the cross-country variance in all aspects of institutional development is reduced only if the EU aspirants are included.

The previous studies were focused on the β and σ convergence, neglecting the possibility of existing multiple steady states. The study conducted by Glawe and Wagner (2021a) applied the Phillips and Sul’s (2007) log t-test over the period 2002 to 2018. Their results confirm the existence of multiple institutional clubs which are formed mainly based on the geographic region. The same conclusion goes for the income per capita clubs. The literature regarding productivity clubs is rather scarce. Kijek et al. (2023) identified the three productivity clubs, across European regions, with the regional innovation systems as an explanation for the multiple steady states. Mendez (2020) has identified three productivity clubs within the developed countries, and five convergence clubs within the developing countries, with a huge gap between the bottom clubs and mean, with a continuous divergence trend. Study carried by Basel et al. (2020) was focused on the multidimensional index of development for the 1996–2015 period. The study sample covers 102 countries, with results indicating the existence of four clubs. Study conducted by Harb et al. (2024) focuses on the TFP convergence clubs covering 155 NUTS regions. Their results indicate that the high productivity club consists mostly of “old” EU members, while some south regions are at high risk of falling in the “productivity trap”. The EU was characterized by two distinct convergence clubs, regarding the GDP per-capita, for the period 1980–2004 (Apergis et al. 2010). The authors have stressed out that for these two convergence clubs, the proximate determinants of GDP per-capita are highly heterogeneous. For the 17 countries of Latin America, for the 1990–2014 period, four convergence clubs were identified, regarding GDP per-capita (Barrios et al. 2019).

3. Methodology and Data

3.1. Productivity and Institutions

To measure productivity, we will use the TFP which is described as the portion of output that is not explained by the number of inputs used in production (Comin 2010). The notion that growth is driven by factor accumulation combined with “something else”, broadly referred to as technical progress or the “Solow” residual, continues to dominate the thinking within the profession. The TFP difference between the poor and rich countries is stated as a main reason behind the difference in income per capita (Hall and Jones 1999; Klenow and Rodríguez-Clare 1997; Gallardo-Albarrán and Inklaar 2021). Solow (1957), along with authors like Griliches (1987, 1994, 1996) and Nelson (1973, 1981), acknowledged that TFP is a problematic concept and that its calculation involves certain challenges. Nowadays, there seems to be widespread agreement that both the concept and measurement of TFP pose significant issues (Felipe and McCombie 2020; Sickles and Zelenyuk 2019). The interpretation of the TFP as a measure of efficiency growth or the rate of technical progress (or cost reduction) is problematic. At most, TFP serves as a measure of distributional changes (Felipe and McCombie 2020). To calculate the TFP, we follow Hall and Jones (1999), and according to Felipe and McCombie (2020), the calculated TFP is measured dollars per worker, which means that TFP growth is growth of the dollar wage. Accordingly, the relative TFP levels of the two countries will also be the ratio of two values measured in dollars per worker. As mentioned, we follow procedure, proposed by Hall and Jones (1999) which is based on the standard Cobb-Douglas production function:

$$Y=K^{\alpha }{\left(AH\right)}^{\beta },$$

(1)

This is standard notation, Y stands for Gross Value Added (GVA), k stands for countries capital volume, H stands for the human capital, and α and β represent the marginal products for the capital and labor, respectively, where α + β = 1. The data on the H are based on the estimations of the return to education in the Mincerian wage regression (Mincer 1974), and on the average years of schooling. The marginal product of the capital, α, is calculated based on the marginal product of the labor, which is based on the share of the compensation of employees in the GVA, as done in Radicic et al. (2023). Equation (1) can be rearranged in per capita terms as:

$$y={\left(k\right)}^{{\displaystyle \frac{\alpha }{1-\alpha }}}hA ,$$

(2)

This is standard notation of the Cobb-Douglas production function in per capita terms, where y stands for the GVA per employee, k stands for the capital output ratio (K/Y), and h stands for the human capital per employee. The TFP is calculated based on the Equation (2):

$$TFP={\displaystyle \frac{y}{k^{\frac{\alpha }{1-\alpha }}h}} ,$$

(3)

We obtain capital volume by applying the perpetual inventory method (PIM):

$$K_t=I_{t-1}+(1-\delta )K_{(t-1)}$$

(4)

where I stands for investments, and δ stands for depreciation. For the purpose of this research, we will set the depreciation at 0.06 as done in McQuinn and Whelan (2007), Burda and Severgnini (2008), McGuinness (2007), Borović and Radicic (2023), and Radicic et al. (2023). The initial capital is calculated for the year 2002, which is the first year of our analysis, and we have applied the US Bureau of Economic Activity (BEA) procedure, as done in Burda and Severgnini (2008), Borović and Radicic (2023), and Radicic et al. (2023):

$$K_0=I_0{\displaystyle \frac{1+\delta }{g+\delta }}$$

(5)

where K₀ stands for the anchor capital, I₀ stands for the investments in the initial year, and g stands for a ten-year annual average output growth rate (Bernanke and Garkaynak 2001). The linear depreciation method will enable the initial capital to be fully depreciated in 1/δ years:

$$K_t=\left(1-t\delta \right)K_0+\sum _{i=0}^{t-1}\left(1-t\delta \right)I_{t-i}$$

(6)

In this way the current capital stock is the weighted sum of initial capital value, K₀, and intervening investment expenditures, with weights corresponding to their undepreciated components (Burda and Severgnini 2008). When calculating the capital volume, the capital in use is what belongs in the production function, not capital in place (Solow 1957). The data on capital utilization are available only for the manufacture. In this paper, we follow Solow (1957), and we have corrected the numbers from Equation (6) by the fraction of the labor force unemployed in each year. The main assumption is that the labor and capital always suffer unemployment to the same percentage, which Solow admits being wrong. But in the case where there is no actual data, this assumption is closer to the truth, than taking no action at all (Solow 1957).

The WGI-s are used extensively in economic literature as a measure of institutional quality (Pietrucha and Żelazny 2020; Glawe and Wagner 2021a, 2021b; Badalyan et al. 2016; Schönfelder and Wagner 2019; Borović and Radicic 2023). To measure the quality of the institutions we will use the WGI (Kaufmann et al. 2010):

1.

WGI1—Voice and Accountability;

2.

WGI2—Political Stability and Absence of Violence/Terror;

3.

WGI3—Government Effectiveness;

4.

WGI4—Regulatory Quality;

5.

WGI5—Rule of Law;

6.

WGI6—Control of Corruption;

The WGI are designed in standard normal distribution, with mean zero, standard deviation of one, and running from approximately −2.5 to 2.5, with higher values corresponding to better governance (Kaufmann et al. 2010). For the purpose of this research, we will use the WGI3, WGI4, WGI5, and WGI6. The WGI3, government effectiveness, refers to the quality of the public and civil services, and their independence from political pressure, the quality of policy formulation and implementation and the credibility of the government’s commitment to such policies (Kaufmann et al. 2010, p. 4). The WGI4, regulatory quality refers to the to the ability of the government to formulate and implement sound policies and regulations that permit and promote private sector development (Kaufmann et al. 2010, p. 4). The WGI5, rule of law, refers to the extent to which agents have confidence in and abide by the rules of society, and in particular the quality of contract enforcement, property rights, the police, and the courts, as well as the likelihood of crime and violence (Kaufmann et al. 2010, p. 4). And WGI6, control of corruption, refers to the perception of the extent to which public power is exercised for private gain, including both petty and grand forms of corruption, as well as “capture” of the state by elites and private interests.

3.2. Econometric Specifications

As mentioned in the introduction, we will apply the log t-test for the decomposition of a panel for institutions/productivity (y_it) developed by Phillips and Sul (2007, 2009) to identify multiple steady states. The methodology proposed by Phillips and Sul (2007, 2009) indeed introduces an innovative approach for identifying subgroups or “convergence clubs” within a larger dataset. Their approach addresses situations where the entire set of economies or units may not be converging toward a common steady state, but where subsets of units (clubs) are converging within themselves. Tho logic behind the log t test is to take relative transition paths for each unit (e.g., country), which represents an individual trajectory for each unit (e.g., country) relative to the cross-sectional average, and then regress the logarithm of the variance of these paths over time.

The log t-test assumes that economies converge at similar rates. However, when there is significant heterogeneity in the growth patterns of the countries, the test results may become less reliable. If economies within a group are heterogenous regarding their initial level of development, or they follow substantially different growth paths, the test’s sensitivity could result in incorrectly rejecting convergence or misclassifying convergence clubs. This occurs because the model may not accurately reflect diverse growth behaviors, leading to faulty conclusions about whether the economies are converging or diverging.

For the starting point of this procedure, Phillips and Sul (2007, 2009) proposed the following nonlinear dynamic factor model:

$${logy}_{it}=g_{it}+x_{it}t$$

(7)

where g_it stands for the systematic components and x_it comprises the idiosyncratic time path. We can rearrange the Equation (7) as:

$${logy}_{it}=\left({\displaystyle \frac{g_{it}+x_{it}}{{\mu }_t}}\right){\mu }_t={\delta }_{it}{\mu }_t$$

(8)

where δ_it stands for the time-varying idiosyncratic component and μ_t represents a common trend component. On the one hand, the economic interpretation of the δ_it is that it describes the transition path of each economy, while μ_t describes the equilibrium growth path that is common to all economies (Mendez 2020). On the other hand, statistically idiosyncratic component, δ_it measures how far is individual economy (logy_it) from the common trend (μ_it). According to Phillips and Sul (2007, 2009), the dynamics of the idiosyncratic component (δ_it) can be described in the following way:

$${\delta }_{it}={\delta }_i+{\displaystyle \frac{{\sigma }_i{\xi }_{it}}{\log \left(t\right)t^{\alpha }}}$$

(9)

where δ_i varies only across economies, and ξ_it is iid(0,1) across economies, that is weakly dependent over time. The heterogeneity parameter is described with the σ_i, for σ_i > 0. To achieve convergence, all economies should shift to the same transition path:

$$\underset{t\to \infty }{\lim }{\delta }_{it}=\delta \wedge \alpha \ge 0$$

(10)

Phillips and Sul (2007, 2009) have defined a relative transition parameter, h_it, in order to test the convergence hypothesis from Equation (10):

$$h_{it}={\displaystyle \frac{{logy}_{it}}{\frac{1}{N}\sum _{h=1}^N{logy}_{it}}}={\displaystyle \frac{{\delta }_{it}}{\frac{1}{N}\sum _{i=1}^N{\delta }_{it}}}$$

(11)

This transition parameter removes common trend component (μt) from the Equation (8), by dividing the observed variable by its cross-sectional mean in each year (Mendez 2020). The convergence hypothesis from the Equation (10) can be rearranged as:

$$H_t={\displaystyle \frac{1}{N}}{\sum }_{i=1}^N{\left(h_{it}-1\right)}^2\to 0$$

(12)

This is valid only in the long run, when t→∞. From the Equation (12), the convergence is achieved when H_t→0, or when h_it→1. From an economic standpoint, this means that the convergence will occur when cross-sectional variance (H_t) tends to zero, or when the relative transition parameter (h_it) tends to unity (Mendez 2020). For the empirical testing of the convergence hypothesis, Phillips and Sul (2007, 2009) have proposed the following log-t regression model:

$$log\left({\displaystyle \frac{H_1}{H_t}}\right)-2log\left\{log\left(t\right)\right\}=a+blog\left(t\right)+{\epsilon }_t;$$

$$for t=\left[rT\right],\left[rT\right]+1,\dots ,T with r>0$$

(13)

where [rT] stands for the initial observation, and for the time span less or equal to 50 years, Phillips and Sul (2007, 2009) suggest setting r = 0.3. From the Equation (13), the coefficient b indicates whether ratio of cross-sectional variance (H₁/H_t) is increasing or decreasing. When b is positive (negative), it indicates that the cross-sectional variance (H_t) is inclined to be smaller (larger) than the initial cross-sectional variance (H1). Statistically significant and positive (negative) coefficient b suggests convergence (divergence) among the cross-sectional units of the sample (Mendez 2020). When b is not significantly different from zero, but the t-statistic is above the threshold value, we cannot rule out the possibility of convergence (Phillips and Sul 2009, p. 1168). From the Equation (13), the relative convergence (convergence in growth rates) is achieved when 0 ≤ b < 2. Absolute convergence (convergence in levels) is achieved when b ≥ 2, and the convergence speed is calculated as b/2. The statistical significance of the coefficient b is based on one-sided t test:

$$t_b={\displaystyle \frac{\widehat{b}-b}{S_b}}⟹N\left(\mathrm{0,1}\right)$$

(14)

When t_b < −1.65, the null hypothesis of convergence is rejected. The rejection of the null hypothesis for overall convergence suggests that the local convergence clubs are more likely to exist. Phillips and Sul (2007, 2009) have proposed the data driving clustering algorithm which is based on the logic that countries are ranked, based on their performance by grouping the top-performing economies together. Then log t-test is applied to subgroups to test for the convergence. If the test results in convergence, this group constitutes a convergence club. If convergence is not found, the algorithm removes the worst-performing economy from the group and re-tests the remaining economies for convergence. This process continues until a subgroup of economies that exhibits convergence is identified, forming the first convergence club. Once the first convergence club is formed, the algorithm then moves on to the remaining economies that were not part of the initial club. The same procedure is applied to these economies to determine if they form another convergence club. This process repeats, identifying additional clubs, until no further clubs can be formed. After multiple convergence clubs are identified, the algorithm checks whether any of the clubs can be merged. This is done by testing if combining clubs’ results in a valid convergence group, using the log t-test. The algorithm consists of five steps1:

7.

Cross-sectional ordering;

8.

Core group formation;

9.

Sieving individuals for new club members;

10.

Recursion and stopping rule;

11.

Club merging.

3.3. Data

To measure productivity, we will use the TFP, and to measure institutional quality we will use the WGI. The data on the TFP are collected from AMECO database, Pen World Table (PWT) database (see (Feenstra et al. 2015) and https://www.rug.nl/ggdc/productivity/pwt/ (accessed on 20 April 2024)), and from the Conference Board database. The data on the WGI are collected from the World Bank. Data, their description, and sources are presented in

Table 1. Variables description and sources.

Variable	Description	Source
Y	GVA, Current prices, million purchasing power standards (PPS, EU27 from 2020)	EUROSTAT (2024)
I	Gross Fixed Capital Formation, Current prices, million purchasing power standards (PPS, EU27 from 2020)	EUROSTAT (2024)
L	Thousands of persons employed, expressed in 106
β	Marginal product of labor, expressed as share of the compensation of employees in GVA	EUROSTAT (2024)
α	Marginal product of capital, α = 1 − β	Authors calculation
h	Human capital index, based on years of schooling and returns to education	PWT 10.01
K	Capital volume	Authors calculation
k	Capital output ratio, K/Y	Authors calculation
y	GVA per employee Y/L	Authors calculation
δ	Depreciation rate	Set at 0.06
g	10-year output growth rate	Authors calculation
β	Marginal product of labor, expressed as share of the compensation of employees in GVA	EUROSTAT (2024)
α	Marginal product of capital, α = 1 − β	Authors calculation
h	Human capital index, based on years of schooling and returns to education	PWT 10.01
K	Capital volume	Authors calculation
k	Capital output ratio, K/Y	Authors calculation
y	GVA per employee Y/L	Authors calculation
δ	Depreciation rate	Set at 0.06
TFP	Total Factor Productivity	Authors calculation
WGI3	Government Effectiveness	The World Bank (2024)
WGI4	Regulatory Quality	The World Bank (2024)
WGI5	Rule of Law	The World Bank (2024)
WGI6	Control of corruption	The World Bank (2024)
WGI	Mean of the WGI3-WGI6	Authors calculation
TFP	Total Factor Productivity	Authors calculation
WGI3	Government Effectiveness	The World Bank (2024)
ICT	Growth in capital services provided by ICT assets (change of the natural logarithm)	The Conference Board Total Economy Database (2024)
R&D	Research and development as a percentage of GDP	EUROSTAT (2024)
OPN	Country openness, calculated as a percentage of sum of imports and exports of goods and services in GDP	The World Bank (2024) Authors calculation
EDU	Growth in labor quality (change of the natural logarithm)	The Conference Board Total Economy Database (2024)
PTNT	Patent applications, residents	The World Bank (2024)
FDI	Foreign direct investment, net inflows (% of GDP)	The World Bank (2024)

.

Our analysis is conducted on 27 EU countries for the time period 2002–2023. Our sample consist of following countries: Austria (AUT), Belgium (BEL), France (FRA), Germany (GER), Italy (ITA), Luxemburg (LUX), Malta (MLT), Netherlands (NET), Denmark (DEN), Ireland (IRE), Grece (GRE), Portugal (POR), Spain (SPA), Austria (AUS), Finland (FIN), Sweden (SWE), Cyprus (CYP), Czechia (CZE), Estonia (EST), Hungary (HUN), Latvia (LAT), Lithuania (LIT), Poland (POL), Bulgaria (BUL), Slovakia (SLO), and Slovenia (SLV). Descriptive statistics are presented in

Table 2. Descriptive Statistics.

Variable	Obs	Mean	Std. dev.	Min	Max
TFP	567	8.653	0.646	6.893	10.642
WGI	567	1.071	0.592	−0.239	2.176
WGI3	567	1.076	0.599	−0.364	2.347
WGI4	567	1.159	0.443	−0.052	2.040
WGI5	567	1.074	0.608	−0.266	2.125
WGI6	567	0.975	0.786	−0.441	2.459
h	567	1.162	0.099	0.802	1.369
R&D	564	0.230	0.630	−1.427	1.316
ICT	567	14.566	7.225	−5.250	59.040
OPN	568	4.701	0.464	3.816	5.974
EDU	567	83.536	3.814	67.6	91.4
PTNT	506	6.336	2.078	0.000	10.804
FDI	567	1.836	1.826	−6.679	6.800

Source: Authors’ calculation.

.

All variables are in logs, except for the institutional quality variables. The highest score is achieved in WGI4 (Regulatory Quality), and lowest score is achieved in WGI6 (Control of corruption), which also has the highest variation among the institutional quality variables, which means dispersion between the countries. The highest variation between the countries is regarding the ICT, EDU, PTNT, and FDI, respectively. While there is very small dispersion regarding human capital variable (h), and trade openness. Compared to Glawe and Wagner (2021a), there have been no changes in institutional quality variables in the last four years. In Figure 1 and Figure 2 we present the TFP and institutional quality variables for a full sample. We follow Glawe and Wagner (2021a), and present the variables for the EU14 (AUT, BEL, DEN, FIN, FRA, GER, GRE, IRE, ITA, LUX, NET, POR, SPA, and SWE), EU13 (BUL, CRO, CYP, CZE, EST, HUN, LAT, LIT, MAL, POL, ROM, SVK, and SVN), and GIIPS (GRE, ITA, IRE, and SPA).

Regarding the average TFP, Figure 1 shows constant growth over the last two decades, with small drawbacks in the years of financial crisis. What is interesting, is that during the COVID pandemic, there was no decline in overall productivity. Regarding the institutional quality variables, Figure 2, there have been no significant changes compared to Glawe and Wagner (2021a). In Figure 3 we present the TFP for the EU14, EU13, and GIIPS.

There have been no significant changes compared to Glawe and Wagner (2021a) regarding the institutional quality variables, presented in Figure 4. For the EU13, the WGI6 is constantly around 0.5, affecting the overall WGI6 for the whole sample to be lower than the other institutional quality variables. Comparing the EU14 and GIIPS, it is clear that the decline of the institutional quality variables for the EU14 has been driven by the decline of the institutional quality variables within the GIIPS group.

As shown in Figure 5, for the EU14 and GIIPS we observe constant decline in average WGI, while for the EU13 the average WGI follows the inverted U shape pattern, which is reflected in overall EU performance, presented in Figure 2 and Figure 4.

4. Results and Discussion

The first step is to apply the log t-test on TFP and institutional quality measures across 27 EU countries for 2002–2023. The results of the log t-test are presented in

Table 3. Results of the log t-test.

TFP			WGI4
b	SE	T-stat	b	SE	T-stat
0.593	0.131	−4.537	−1.445	0.167	−8.655
TFP EU14			WGI4 EU14
b	SE	T-stat	b	SE	T-stat
−0.847	0.107	−7.932	−1.361	0.247	−5.511
TFP EU13			WGI4 EU13
b	SE	T-stat	b	SE	T-stat
−0.434	0.101	4.335	−1.715	0.149	−11.505
TFP GIIPS			WGI4 GIIPS
b	SE	T-stat	b	SE	T-stat
−2.272	0.304	−7.471	−1.588	0.428	−3.704
WGI			WGI5
b	SE	T-stat	b	SE	T-stat
−0.912	0.022	−31.578	−0.857	0.052	−16.386
WGI EU14			WGI5 EU14
b	SE	T-stat	b	SE	T-stat
−1.061	0.118	−8.950	−1.311	0.091	−14.433
WGI EU13			WGI5 EU13
b	SE	T-stat	b	SE	T-stat
−0.969	0.14	−6.922	−0.465	0.066	−6.962
WGI GIIPS			WGI GIIPS
b	SE	T-stat	b	SE	T-stat
−1.172	0.265	−4.419	−1.471	0.1824	−8.065
WGI3			WGI6
b	SE	T-stat	b	SE	T-stat
−0.848	0.144	−5.881	−0.698	0.041	−16.758
WGI3 EU14			WGI6 EU14
b	SE	T-stat	b	SE	T-stat
−0.796	0.079	−10.013	−0.885	0.094	−9.795
WGI3 EU13			WGI6 EU13
b	SE	T-stat	b	SE	T-stat
−1.011	0.311	−3.251	−0.603	0.146	−4.112
WGI3 GIIPS			WGI6 GIIPS
b	SE	T-stat	b	SE	T-stat
−1.197	0.236	−5.068	−0.631	0.241	−2.614

Source: Authors’ calculation.

.

When analyzing the results of the log t test for the productivity and for the institutional quality measures, the hypothesis of overall convergence is rejected. What is interesting, that even for the subsamples, the hypothesis of overall convergence is always rejected. In this case there are two possibilities. The first possibility is absolute divergence, and the second possibility is the existence of convergence clubs. In the second step we will apply the clustering procedure proposed by Phillips and Sul (2007). Results of the clustering procedure are presented in

Table 4. Final club classifications.

TFP
Clubs	Countries	b	T-stat
Club1 (14)	AUT BUL CZE DEN GER IRE ITA LAT LIT LUX MAL POL ROM SWE	−0.211	−1.488
Club2 (7)	BEL CYP EST FRA NET POR SVN	0.025	0.122
Club3 (6)	CRO FIN GRE HUN SPA SVK	0.022	0.299
WGI
Clubs	Countries	b	T-stat
Club1 (14)	AUT BEL CZE DEN EST FIN FRA GER IRE LAT LIT LUX NET SWE	−0.035	−0.509
Club2 (2)	POR SVN	−1.706	−0.711
Club3 (9)	CRO CYP GRE ITA MAL POL ROM SPA SVK	−0.001	−0.002
Not convergent group (2)	BUL HUN	−1.121	−1.671
WGI3
Clubs	Countries	b	T-stat
Club1 (15)	AUT CZE DEN EST FIN FRA GER IRE LAT LIT LUX NET POR SVN SWE	0.107	0.7305
Club2 (4)	BEL CYP MAL SPA	0.046	0.109
Club3 (4)	CRO CYP GRE ITA MAL POL ROM SPA SVK	0.102	0.201
Club4 (3)	GRE POL ROM	−1.089	−1.199
Not convergent group (1)	BUL		-
WGI4
Clubs	Countries	b	T-stat
Club1 (14)	AUT BEL CZE DEN EST FIN FRA GER IRE LAT LIT LUX NET SWE	−0.205	−1.106
Club2 (9)	CRO CYP ITA MAL POL POR SPA SVK SVN	0.113	0.263
Club3 (4)	BUL GRE ROM HUN	0.253	0.336
WGI5
Clubs	Countries	b	T-stat
Club1 (17)	AUT BEL CRO CZE DEN EST FRA GER IRE LAT LIT LUX NET POR ROM SVN SWE	−0.09	−0.447
Club2 (6)	CYP HUN MAL POL SPA SVK	−0.406	−1.367
Club3 (2)	GRE ITA	0.291	−1.178
Not convergent group (2)	BUL FIN	−0.780	−10.031
WGI6
Clubs	Countries	b	T-stat
Club1 (15)	AUT BEL CZE DEN EST FIN FRA GER IRE ITA LAT LIT LUX NET SWE	−0.064	−0.498
Club2 (10)	CRO CYP GRE MAL POL POR ROM SPA SVK SVN	−0.186	−1.065
Club3 (2)	BUL HUN	0.443	3.041

Source: Authors’ calculation.

. We present only final clubs for the whole sample. The final club classifications for the subsamples (EU14 and EU13) are in the Appendix A.

Regarding the TFP, high productivity Club1 mostly consist of core European countries, while some of these countries are former socialistic countries (BUL, LAT, LIT, POL, and ROM), and low productivity Club3 consist mostly of countries from South-East Europe (SE), which is line with Harb et al. (2024). The coefficient b is negative, with T stat above the threshold, which means that Club1 is weakest convergence club (Phillips and Sul 2007). High performing Club1 identified by Harb et al. (2024) is also characterized by relatively weak convergence (positive b coefficient, but statistically insignificant). The coefficient b for Club2 and Club3 is positive, but statistically insignificant, which according to Phillips and Sul (2007), also means weak convergence. The coefficient b is less than 2 for all three clubs, which means weak convergence at a very slow pace (1.25% for Club2, and 1.1% for Club3). Results for the final club classifications for the subsamples are in the Appendix A. If we analyze only EU 14, from

Table A1. Results of the log t-test.

TFP EU14
Clubs	Countries	b	T-stat
Club1 (5)	AUT GER IRE ITA LUX	−0.223	−1.628
Club2 (5)	BEL DEN FRA NET SWE	−0.011	−0.054
Club3 (4)	FIN GRE POR SPA	−0.070	−0.775
WGI EU14
Clubs	Countries	b	T-stat
Club1 (6)	DEN FIN GER LUX NET SWE	−0.282	−0.682
Club2 (2)	AUT BEL	−1.632	−1.594
Club3 (2)	FRA IRE	−1.120	−1.130
Club4 (2)	GRE ITA	−2.492	−1.365
Not convergent group (2)	POR SPA	−2.596	−1.992
WGI3 EU14
Clubs	Countries	b	T-stat
Club1 (8)	AUT DEN FIN GER IRE LUX NET SWE	−0.272	−0.639
Club2 (2)	BEL FRA POR SPA	0.951	2.516
Club3 (2)	GRE ITA	1.048	0.286
WGI4 EU14
Clubs	Countries	b	T-stat
Club1 (6)	DEN FIN GER LUX NET SWE	−0.205	−1.106
Club2 (3)	AUT BEL IRE	−0.123	−0.165
Club3 (2)	POR SPA	2.486	0.931
Club4 (2)	GRE ITA	−1.585	−0.291
Not convergent group (1)	FRA
WGI5 EU14
Clubs	Countries	b	T-stat
Club1 (5)	AUT DEN LUX NET SWE	−0.899	−1.466
Club2 (5)	BEL FRA GER IRE POR	0.295	0.987
Club3 (2)	GRE ITA	−2.291	−1.178
Not convergent group (2)	SPA FIN	−1.801	−9.006
WGI6 EU14
Clubs	Countries	b	T-stat
Club1 (6)	DEN FIN GER LUX NET SWE	−0.298	−0.882
Club2 (5)	AUT BEL FRA IRE ITA	−0.256	−1.138
Club3 (2)	GRE POR SPA	−0.379	−0.716

Source: Authors’ calculation.

, there are three TFP convergence clubs, with negative coefficient b, with T stat above the threshold, which means weak convergence. For the EU 13 countries, from

Table A2. Final club classifications, EU13.

TFP EU13
Clubs	Countries	b	T-stat
Club1 (10)	AUT GER IRE ITA LUX	0.022	0.158
Club2 (3)	CRO HUN SVK	3.171	3.456
WGI EU13
Clubs	Countries	b	T-stat
Club1 (6)	CYP CZE LAT LIT MAL SVN	0.995	0.781
Club2 (5)	CRO HUN POL ROM SVK	0.141	0.694
Not convergent group (2)	BUL EST	−1.034	−5.092
WGI3 EU13
Clubs	Countries	b	T-stat
Club1 (7)	CYP CZE EST LAT LIT MAL SVN	0.604	0.478
Club2 (2)	CRO HUN	−0.154	−0.091
Club3 (2)	POL SVK	−0.811	−0.289
Club4 (2)	BUL ROM	−0.940	−0.236
WGI4 EU13
Clubs	Countries	b	T-stat
Club1 (4)	CZE EST LAT LIT	0.135	0.272
Club2 (6)	CRO CYP MAL POL SVK SVN	0.356	0.562
Club3 (3)	BUL HUN ROM	0.795	1.575
WGI5 EU13
Clubs	Countries	b	T-stat
Club1 (11)	CRO CYP CZE HUN LAT LIT MAL POL ROM SVK SVN	0.000	0.001
Not convergent group (2)	BUL EST	−0.734	−5.911
WGI6 EU13
Clubs	Countries	b	T-stat
Club1 (11)	BUL CRO CYP CZE LAT LIT MAL POL ROM SVK SVN	0.176	0.973
Not convergent group (2)	EST HUN	−2.662	−16.488

Source: Authors’ calculation.

, there are two TFP convergence clubs. The first Club consists of ten countries, with positive, and insignificant b coefficient, which means weak convergence. The second Club consists of three countries (CRO, HUN, SVK), with statistically significant coefficient b above 2, which means strong, absolute convergence. Kijek et al. (2023) has identified three TFP clubs for the EU regions for the 2008–2018 period. Kijek et al. (2023), identified three TFP clubs, where high productivity Club3 is strongest convergence club, with positive and statistically significant b coefficient, and convergence speed at 15 percent. The coefficient b is less than 2, reflecting relative convergence. Mendez (2020) identified three clubs for the developed countries, and four clubs for the developing countries. In contrast to Kijek et al. (2023) and Harb et al. (2024), productivity clubs at country level are characterized by weak convergence among all units within those clubs compared to much stronger convergence among all units within regional clubs.

Regarding the WGI, the first club consists of 14 countries, and as in the case of the TFP, most of these countries are core European countries (EU14-10 countries, EU13-5 countries). Compared with the high productivity Club1, 9 countries from the high institutional quality Club1, are also members of the high productivity Club1. Countries from the low institutional quality Club2 and Club3 are members of the low productivity Club2 and Club3. The coefficient b is negative for all three clubs, with negative T stat, above the threshold, which means weak convergence. Reported b coefficient in Glawe and Wagner (2021a) was insignificant and negative for Club1, while it was positive, and still insignificant for Club2, Club3, and Club4. Up until 2018 there were four clubs, with one divergent group of two countries (Glawe and Wagner 2021a). According to Glawe and Wagner (2021a), Club1 is made up of seven countries, Club2 is made up of 4 countries, Club3 is made up of eight countries, Club4 is made up of six countries. In the last four years there has been a consolidation of the first two clubs, and of the last two clubs. Results from Table A1 suggest that for the EU 14, there are four convergence clubs, with one not convergent group (POR and SPA), with negative b coefficient, with T statistics above the threshold, which means very weak convergence among all units within these clubs. When analyzing the overall WGI for the EU 13, results from Table A2 suggests existence of two clubs, with one not convergent group (BUL and EST), with insignificant, and positive b coefficient, indicating weak convergence.

Regarding the WGI3, the first club consists of 15 countries, where most of these countries are also members of the high institutional quality Club1 (WGI), and high productivity Club1 (TFP). While members of the low institutional quality clubs are also members of the low institutional quality clubs (WGI), and low productivity clubs (TFP). The coefficient b is positive, but statistically insignificant for the first three clubs, which indicates weak convergence. The b coefficient for Club4 is negative, with negative T stat, above the threshold, which indicates weak convergence. The speed of convergence for the first three clubs is 36.5%, 5.5%, and 10%, respectively. Compared with Glawe and Wagner (2021a), the clusterization has been more pronounced in the last four years. Up until 2018, all b coefficients have been positive, reflecting stronger convergence. Analysis of the EU 14, from Table A1, reveals the existence of three clubs. Club1 is weakest among these three clubs, with negative b coefficient, with T statistics above the threshold. Club2 is strongest, with a positive and statistically significant b coefficient, which means relative convergence with speed of 47.5%. The b coefficient for Club3 is positive, but insignificant, indicating weak convergence. Regarding EU 13, there are four clubs, and the b coefficient is positive and insignificant only for Club1. The b coefficient for Club2, Club3, and Club4 is negative, but the T statistics are above the threshold, which means weak convergence among all units within these clubs.

Regarding the WGI4, Club1 consists of 14 countries, and like in previous cases, they are mostly members of the previous high institutional quality clubs (Club1 WGI, and WGI3), and high productivity Club1 (TFP). The b coefficient is negative for the Club1, with negative T stat, above the threshold, which indicates weak convergence. For Club2, and Club3, the b coefficient is positive, but statistically insignificant, with speed of convergence at 13 and 16.5% respectively. In the last four years there has been a consolidation of the first two clubs, and of the last two clubs, since the reported number of clubs (3) is less than five reported clubs in Glawe and Wagner (2021a). The b coefficient is positive for all five clubs, which indicates stronger convergence (Glawe and Wagner 2021a). For the EU 14, the clustering algorithm confirms the existence of the four clubs, and one divergent group (FRA). The b coefficient is positive and insignificant only for Club3. The rest of the clubs have negative b coefficient with T statistics above the threshold, which means weak convergence among all units within these clubs. When analyzing the WGI4 for the EU 13, analysis reveals existence of three clubs, where Club1 consists of countries which are members of high productivity Club1 and previous high institutional quality clubs. The b coefficient is positive for all three clubs, but statistically insignificant, reflecting weak convergence.

Regarding the WGI5, Club1 consists of 17 countries, where most of these countries are also members of the high institutional quality Club1 (WGI, WGI3, and WGI4), and high productivity Club1 (TFP). While members of the low institutional quality clubs are also members of the low institutional quality clubs (WGI, WGI3, and WGI4), and low productivity clubs (TFP). The b coefficient is positive only for Club3, with negative T stat, above the threshold, which indicates weak convergence among all units within all three clubs. Glawe and Wagner (2021a) have reported four clubs with one diverging group (three countries). The b coefficient is negative only for Club4, which indicates stronger convergence (Glawe and Wagner 2021a). Regarding the WGI5, the EU 14 countries from Table A1, are characterized by three clubs, with one divergent group (SPA, FIN). The b coefficient is positive, but statistically insignificant only for Club2, while it is negative with T statistics above the threshold reflecting weak convergence among all units within these clubs. WGI5 for the EU 13, from Table A2, indicates existence of one club (11 countries), and not convergent group (BUL, EST).

We have identified three clubs for WGI6. The b coefficient is positive and statistically significant only for the low institutional quality Club3, with average speed of convergence at 22%, reflecting relative convergence. The b coefficient is negative for the first two clubs, with negative T stat, above the threshold, which means weak convergence. Glawe and Wagner (2021a) reported five clubs with all b coefficients being positive, reflecting stronger convergence. For EU 14, there are three clubs, all three with negative b coefficient, and with T statistics above the threshold reflecting weak convergence among all units within these clubs. Regarding WGI6, from Table A2, similarly as for the WGI5, there is only one club (11 countries), and one non convergent group (EST, HUN). For Club1, the b coefficient is positive, but statistically insignificant, reflecting weak convergence among all units within the club. The number of identified final clubs in this survey is always below the number of identified final clubs in Glawe and Wagner (2021a).

We will only present the graphs of the transition curves for the TFP, WGI, WGI3, WGI4, WGI5, and WGI6. The transition curves between clubs and the individual paths within each club of each subsample are in the Appendix A. Regarding the transition paths displayed in Figure 6, productivity divergence between Club1 and Club2 has been increasing continuously since 2011. Club 3 is constantly at 50% of the average of Club2, and since the financial crisis, Club2 and Club3 have almost the same, downward slope.

The transition path for Club1 is above the EU average, and it is upward, while transition path for the Club2 is downward, closing to the EU average. The transition path for Club3 is downward, and below the EU average. The only high productivity club is Club1, but with the weakest convergence. Mendez (2020) identified three clubs for the developed countries, regarding the aggregate efficiency (the TFP) with no sign of convergence. For the developing countries, Mendez (2020) identified four clubs, again, without signs of convergence. When analyzing EU 14, from Figure A1, the transition paths reveal a similar pattern as on Figure 6. There are clearly separating tendencies between Club1 on one hand, and Club2 and Club3 on the other hand, with clubs two and three showing a similar downward slope. For the EU 13, Figure A2 reveals two clubs without any sign of convergence.

Relative transition paths are displayed in Figure 7.

Regarding Club1, IRE, LUX, and MAL are high above club average, while rest of the countries converge around Club1 average. Regarding Club2, BEL, FRA, and NET are starting above the Club2 average, and in time, they decline, and close on the Club2 average. Estonia starts below the club average, but in time converge to the Club2 average. Regarding Club3, only FIN and SPA are above average, with a constant slope. Rest of the Club3 countries relative transition paths are on, or below average, and in time they converge on Club3 average. For the EU 14, out of countries who belong to the Club1, only Ireland and Luxembourg are above club average, while rest of the countries converge around Club1 average. For the Club2, all countries are grouped around Club2 average. The same conclusion goes for Club3. For the EU 13, only Cyprus and Malta are systematically above the average, while rest of countries group around Club1 average. For Club2, all countries are converging to the Club2 average, with a downward tendency. The transition paths for the WGI are presented in Figure 8.

High institutional quality Club1 has an upward transition path, with a constantly increasing gap with the other two clubs. Club2 and Club 3 are below the average, with constant, or downward transition path. The countries that belong to clubs whose transition curves are above average and upward sloping are on a high institutional growth path (Glawe and Wagner 2021a). Countries that are member of a high institutional quality Club1 are on a high institutional growth path. Countries whose relative transition paths are below the cross-section mean and have a stagnating and declining tendency caught in a poor institutional trap (Glawe and Wagner 2021a). Which means that countries that belong to Club2, and Club3 are caught in a poor institutional trap. Compared with Glawe and Wagner (2021a), we have identified three clubs, with one diverging group, while Glawe and Wagner (2021a) have identified four clubs, with two clubs above average, with upward transition paths, and two clubs below average with downward transition paths. For the EU 14, Club 1 is systematically above the average, while Club 4 is constantly below average with a downward slope. Countries that belong to Club 4 are in a poor institutional trap. Countries that belong to Club 2 and Club 3 are stuck in a bad institutional equilibrium (Glawe and Wagner 2021a). For the EU 13, there are two clubs, with Club1 above the cross-sectional average, and Club 2 below the cross-sectional average, without a sign of convergence. Relative transition paths are presented in Figure 9.

Regarding the high institutional quality Club1, most countries are above average with stagnating relative transition paths, and steep upward relative transition paths characterize those countries below average. Regarding Club2, relative transition paths for both countries have a stagnating tendency. For Club3, countries which are above average, their transition paths are steep downward, while countries which are below or at the cross-section average, their transition paths are constant, or with upward slope. For the EU 14, almost all countries which are member of the Club1 have an upward slope. For clubs two and three, countries converge around the average with constant slope. And for Club4, countries have a downward slope. Regarding the EU 13, only Check Republic, Latvia and Lithuania, from Club1, have a upward slope, while rest of the countries are experiencing constant or negative slope. From the Club2, only Croatia and Romania, which are below the average, are experiencing the upward slope, while the rest of the club is experiencing the downward slope.

Transition paths for the WGI3, WGI4, WGI5, and WGI6 are presented in Figure 10. Compared with Glawe and Wagner (2021a), Club1 consists of countries that are members Club1, and Club2 from Glawe and Wagner (2021a). While Club2, and Club3 countries are members of Club3, and Club4 from Glawe and Wagner (2021a).

For all four institutional quality variables, only countries that belong to high institutional quality Club1 are on a high institutional growth path, where only WGI3 Club1 has positive b coefficient, with average speed of convergence at 35.15%. while countries that belong to Club2, and Club3, for all four institutional quality variables, are caught in a poor institutional trap. Regarding Club2, for the WGI3, these countries are diverging from the high institutional quality Club1 since the aftermath of the financial crisis, and they have dropped below the cross-section average in the middle of the last decade. It is safe to say that these countries have also been caught in a poor institutional trap, since 2015. Glawe and Wagner (2021a) have also identified only one high institutional quality Club1, on a high institutional growth path, for all four institutional quality variables, while rest of the clubs are caught in a poor institutional trap or stuck in a bad institutional equilibrium. When analyzing EU 14, countries that belong to high institutional quality Club1 are on a high institutional growth path for all four institutional quality variables. Countries that belong to Club2 are experiencing constant slope, around, or below the cross-sectional average. While countries that belong to clubs three and four are caught in a poor institutional trap. For the EU 13, only countries that belong to high institutional quality Club1 are on a high institutional growth path, while countries that belong to other clubs are caught in a poor institutional trap.

In the next step, we will estimate the ordered probit model which will enable us to identify the factors that explain the formation of productivity convergence clubs across the EU. The Ordered Probit Model is a type of regression used for a dependent variable that is ordinal, meaning its categories follow a natural order but do not have numerically meaningful differences between them. In this model, the categories are ranked (such as “low”, “medium”, “high”), but the gaps between the rankings are not clearly defined in terms of size or value. In our case the dependent variable is club membership, described as the group or club to which a country belongs, showing that the country is part of a subset of economies that exhibit similar patterns of convergence or development over time. Clubs are ranked as first (Club1), second (Club2), and third (Club3). While the ordered probit model is effective for analyzing ordinal data, it has limitations such as assumptions about linearity, normality, and threshold interpretation.

The ordered probit model will be estimated with marginal effects (at means values), which are calculated as a mean marginal effect for each explanatory variable. We will estimate two models. Model 1 will include the mean WGI, while model 2 will include individual WGIs. Results of the ordered probit model are presented in

Table 5. Results of the ordered probit model, marginal effects (ey/ex), Model 1.

Dependent Variable Final Club	Model 1
	Coefficient		Margins for the Clubs
WGI	−0.417 *** (0.137)	1	0.626 *** (0.106)
		2	−0.174 ***
			(0.058)
		3	−0.584 ***
h	−0.926 ** (0.498)	1	0.822 ** (0.374)
		2	−0.374 **
			(0.224)
		3	−1.267 **
ICT	−0.018 ** (0.007)	1	0.206 ** (0.089)
		2	−0.103 **
			(0.047)
		3	−0.346 ** (0.157)
R&D	0.295 ** (0.132)	1	−0.052 ** (0.023)
		2	0.027 ** (0.013)
		3	0.092 ** (0.042)
OPN	−0.289 ** (0.125)	1	0.552 ** (0.463)
		2	−0.120 ** (0.230)
		3	−0.403 ** (0.793)
FDI	0.016 (0.027)	1	−0.011 (0.038)
		2	0.006 (0.021)
		3	0.021 (0.068)
/cut1	−4.363 (0.364)
/cut2	−3.606 (0.957)
Log pseudolikelihood	AIC	BIC
−559.288	1134.576	1169.256

Notes: Robust standard errors in brackets. All variables are expressed in logs. Pseudo R² = 0.2328. * Significance at 10%; ** significance at 5%; ***significance at 1%. Source: Authors’ calculation.

and

Table 6. Results of the ordered probit model, marginal effects (ey/ex), Model 2.

Dependent Variable Final Club	Model 2
	Coefficient		Margins for the Clubs
WGI3	−1.526 *** (0.305)	1	0.754 *** (0.269)
		2	−0.854 ***
			(0.181)
		3	−1.297 *** (0.494)
WGI4	−1.003 *** (0.334)	1	0.935 *** (0.283)
		2	−0.483 ***
			(0.228)
		3	−1.680 *** (0.623)
WGI5	−0.930 ** (0.376)	1	0.793 ** (0.299)
		2	−0.409 **
			(0.221)
		3	−1.424 ** (0.634)
WGI6	−0.029 (0.256)	1	0.023 (0.178)
		2	−0.012 (0.131)
		3	−0.041 (0.381)
EDU	−0.139 *** (0.018)	1	9.332 *** (1.211)
		2	−4.820 *** (1.174)
		3	−16.767 (2.601)
OPN	−0.430 *** (0.182)	1	0.602 *** (0.541)
		2	−0.828 *** (0.455)
		3	−2.879 *** (1.209)
PTNT	−0.119 *** (0.037)	1	0.270 *** (0.041)
		2	−0.199 *** (0.046)
		3	−0.579 *** (0.106)
/cut1	−14.475 (1.703)
/cut2	−13.571 (1.695)
Log pseudolikelihood	AIC	BIC
−435.9238	889.8475	927.8863

Notes: Robust standard errors in brackets. All variables are expressed in logs. Pseudo R² = 0.2584. * Significance at 10%; ** significance at 5%; ***significance at 1%. Source: Authors’ calculation.

. We have applied the backward stepwise approach, in order to deal with multicollinearity, which resulted in the reduced model. Graphs of the conditional marginal effects are in the Appendix A.

When comparing the outcomes of Model 1, and Model 2 using Akaike’s information criterion (AIC), Bayesian information criterion (BIC), and log pseudolikelihood, it is evident that Model 2 is better than Model 1, nonetheless, both estimations yield the same results. Human capital is the most important driver for club membership. An increase in the human capital index from Model 1, by 1 percent, on average, increases countries’ probability of being members of the high productivity Club1 by 0.8 percent. An increase in the growth in labor quality from Model 2, by 1 percent, on average, increases countries’ probability of being a member of the high productivity Club1 by 9.3 percent, which is in line with Kijek et al. (2023). These results are in line with the economic theory and with empirical evidence. Human capital is a necessary precondition for innovation creation. On the other hand, human capital speeds up productivity growth by enabling the absorption of superior technology, developed in the technologically most advanced economies, and thus, helps decrease the productivity gap between the technology leader and following countries (Nelson and Phelps 1966). Institutional quality variables in both models are also important for club membership. An increase in the mean WGI, from Model 1, by 1 percent increases countries’ probability of being a member of the high productivity Club1 by 0.626 percent. On the other hand, an increase in WGI3, WGI4, and WGI5, from Model 2, by 1 percent increases countries’ probability of being members of the high productivity Club1 by 0.754, 0.935, and 0.793 percent, respectively. These results also align with the economic theory and empirical evidence. The differences in productivity between countries are mainly driven by the differences in institutions and government policies (Hall and Jones 1999). Next to the human capital, institutional quality impacts a country’s ability to absorb technology developed at the technological frontier (Giuseppe and Scarpetta 2003; Havik et al. 2008; Mc Morrow et al. 2010; Borović and Radicic 2023). Trade openness of the countries has been identified as an important factor determining the club membership. An increase in trade openness of 1 percent increases countries’ probability of being members of the high productivity Club1 by 0.55 and 0.6 percent, respectively for Model 1 and Model 2. Increasing trade openness will lead to increased flow of the capital, goods, and services, which will increase domestic competition and innovations through increased venture capital supply. The number of patent applications is also an important factor for clubs’ formation. An increase in patents applications of 1 percent increases countries’ probability of being members of the high productivity Club1 by 0.27 percent. All variables are affecting the TFP as predicted by economic theory, except for the R&D. An increase in share of the R&D expenditure in the GDP of 1 percent decreases countries’ probability of being members of the high productivity Club1 by 0.052 percent. Possible explanation could be reduced marginal return to the R&D in the advanced regions, while less advanced regions gain more from the increased R&D (Männasoo et al. 2018). Burda and Severgnini (2008) were analyzing the TFP convergence for the German states, and they have also reported the diminishing returns to the R&D. Our results are in line with those of Männasoo et al. (2018) and Burda and Severgnini (2008), an increase in share of the R&D expenditure in the GDP of 1 percent increases countries’ probability of being members of the Club2 and Club3 by 0.027 and 0.092 percent.

5. Conclusions

In the present paper we investigated the presence of productivity and institutional convergence clubs by applying the Phillips and Sul (2007, 2009) methodology. The main idea is that the existence of different productivity and institutional clubs means a systematic divide in the EU, which makes the EU more vulnerable to external shocks. We have used the WGI as an indicator for institutional quality, and the TFP as a measure of productivity. We recognize that the TFP is a problematic concept and that its calculation involves certain challenges. Nonetheless, our results offer insight into EU productivity development. Our sample covers 27 EU countries for 2002–2023.

We have identified three productivity clubs, and for institutional quality, we have also identified three convergence clubs for the mean WGI, with one non convergent group. For the TFP, and for the mean WGI, members of the high institutional and quality Club1, and high productivity Club1 are mostly members of the EU 14, with few countries that have joined EU in 2004. And members of the low institutional quality Club3, and low productivity Club3 are mostly located in SE Europe. This conclusion goes for all institutional quality variables. We have identified that members of the high institutional quality Club1 are mostly members of the high productivity Club1. This conclusion also goes for all institutional quality variables, but not for the subsamples. Similarly to Kijek et al. (2023) and Harb et al. (2024), we have identified existence of productivity convergence clubs, with members of the high productivity clubs are mostly located in western and northern Europe, while low performing clubs are located in SE Europe. In our case, Italy is a member of the high productivity Club1, which is in line with Kijek et al. (2023), yet Harb et al. (2024) identified Italian regions as low performing.

The productivity divergence process between Club1 and Club2 started in the aftermath of the financial crisis, while countries that belong to the low performing Club3 were constantly diverging with a downward slope, risking reminding trapped in productivity trap. The divergence between the clubs one and two became more profaned during the COVID pandemic. Where high performing countries were able to overcome these negative shocks and to stay on a high productivity path, while other countries failed. The war in Ukraine will definitely have more severe consequence for the EU convergence and it will test the Unions cohesion to the maximum. Same conclusion goes for the subsamples.

In the case of the institutional quality variables, development of the WGIs did not change compared to Glawe and Wagner (2021a), but what is different is the number of the final clubs that we have identified, which is less than the number of clubs identified by Glawe and Wagner (2021a). This could be consequence of the alternative post-clustering algorithms applied by Glawe and Wagner (2021a).

The transition path for the institutional WGI mean is similar, and different compared to Glawe and Wagner (2021a). We have identified one club being on the high institutional growth path, with two clubs being caught in the poor institutional trap, without any sign of convergence. Glawe and Wagner (2021a) have identified two clubs on the high institutional growth path, and two clubs being caught in the poor institutional trap. These differences could be consequence of the alternative post-clustering algorithms. Or it could be consequence of the COVID pandemic and war in Ukraine, since Glawe and Wagner (2021a) data are covering 2002–2018. We believe that COVID pandemic and especially war in Ukraine is a main cause for the weak institutional convergence. A similar conclusion goes for the subsamples, and for the individual institutional quality variables.

Our analysis reveals that the human capital is the most important factor explaining club membership, with institutional quality variables in second place. Country’s openness, ICT capital and number of patents are also very important factors explaining formation of productivity clubs in the EU. Institutional quality has both direct and indirect impact of club’s formation. First, it impacts productivity directly, and secondly, it impacts productivity through increased human and ICT capital, which is in line with Rodríguez-Pose and Ganau (2022).

Our results indicate that the EU is highly vulnerable to external shocks. This is confirmed not just by the existence of a divide between the high performing north-west and the low performing south-east, but by the increasing divergence between clubs, which often starts in the aftermath of the crisis. Secondly, analysis reveals that club formation is based mainly on geographic region, with precise specification of which countries are high performing, and which countries are low performing. The financial crisis, COVID pandemic, and war in Ukraine have “shocked” the EU, and even more intensified already existing differences in productivity and in the institutional quality. We have stressed that institutional quality determines the club membership, directly and indirectly. We have identified that within the EU is achieved growth without cohesion. Which means inability to achieve environmental sustainability and balanced and sustainable growth of all EU members.

Our analysis has several policy implications. First, to improve institutional quality, it is essential to prioritize regions that are falling behind, particularly those at risk of entering a productivity trap, which could further hinder their development. The Catching-up Regions Initiative offers a suitable framework to support these lagging areas. However, to improve its effectiveness, the initiative needs to be restructured, with more strategic allocation of funding. In recent years, the initiative has primarily focused on regions in Eastern Europe, often overlooking those in Southern Europe. Second, simply increasing financial support to underdeveloped regions is unlikely to yield results without a comprehensive strategy that addresses regional deficiencies impeding Total Factor Productivity (TFP) growth. Third, fostering interregional cooperation between high-performing regions and those lagging behind, especially in innovation and R&D, is recommended. This would boost productivity in lower-TFP regions through technology transfer, entrepreneurship, and knowledge sharing. Finally, in countries where many regions exhibit low productivity, a well-coordinated, multi-level intervention involving both regional and national authorities may be the most effective way to improve productivity.

As it is already stated, institutional quality is at the heart of the productivity challenge in the EU (Rodríguez-Pose and Ganau 2022), and that the regional Cohesion Policy should be redesigned in order to bring interventions across multiple areas within a unified framework (Harb et al. 2024). The policy makers should focus on designing institutions of high quality on the local, regional, and national level. The EU Cohesional Policy should be focused on the institutional divergence, not only on the regional level, but on the country level as well, especially on the countries that lags behind, with respect to the existing development differences between the states. Harb et al. (2024) states that some regions lack infrastructure, while others lack R&D, which should be considered when designing cohesion policies. We are simply putting institutional quality first, because if policies are not designed to increase transparency and accountability, and to decrease corruption, equally for all EU members, then returns on human and physical capital will be severely diminished, along with any possibility for innovations. This will jeopardize the environmental sustainability, the green transition, and common economic long-run growth among the EU members, which will lead to differences in standards of living and increase possibility of falling apart of the EU. Without technological advancements there can be no efficient transition to green energy. Without technological progress, which is based on innovations, there can be no carbon-free future. Uneven growth will exacerbate concentration trends, deepening territorial and social divides. Those left behind may develop resentment and dissatisfaction with the democratic system and the core values of the EU, which would weaken the EU’s stability and reduce its resilience. A lack of cohesion will greatly reduce the likelihood of achieving environmental sustainability and increase the risk of the EU fracturing. Ensuring sustainable development across all regions is critical for economic growth, social well-being, and the EU’s overall competitiveness. Cohesion policies should be focused on regional and on national level, with institutional quality in its center, while respecting different levels of economic development of its member states.

As a suggestion for future research, this research can be continued on a regional level, with regional variability (DiPasquale 2022; Mussida and Parisi 2017) in focus, comparing formations of productivity and institutional clubs on NUTS level, by expanding present study with non-economic factors, such as political instability or social capital, and Sustainable Development Goals. This will enable us to fully understand the sever economic consequences of the war in Ukraine on the EU cohesion.