Convergence Clubs, Institutional Hierarchy, and Crisis Asymmetry in European Economies

Abstract

This paper investigates the existence of convergence clubs and asymmetric crisis dynamics across European Union and Western Balkan economies over the period 2004–2023. Using the Phillips–Sul log-t methodology, we reject overall income convergence and identify three distinct convergence clubs characterized by persistent structural heterogeneity. A multinomial logit framework reveals that institutional quality emerges as the strongest predictor of convergence club membership, indicating a clear governance hierarchy across European economies. We further estimate fixed-effects growth models with crisis interactions to examine asymmetric responses during major macroeconomic shocks (2008–2009, 2012–2013, and 2020–2021). Results indicate significant negative crisis effects, with middle-income club economies experiencing disproportionate contraction. These findings remain robust to Driscoll–Kraay corrections for cross-sectional dependence, alternative crisis definitions, and sigma-convergence analysis. Overall, the results suggest that European income dynamics are characterized not by uniform convergence, but by club-based adjustment patterns associated with institutional capacity and crisis resilience. The findings contribute to the literature on nonlinear convergence and institutional heterogeneity in integrated economic areas.

1. Introduction

Economic convergence has long occupied a central position in growth theory and empirical macroeconomics. The neoclassical framework predicts conditional income convergence across economies, provided that structural characteristics and steady-state determinants are comparable (Barro & Sala-i-Martin, 1992, 2004). Empirical panel evidence for European economies has generally supported the presence of conditional β-convergence, although the speed of adjustment remains heterogeneous across country groups (Islam, 1995).

Within the European context, integration processes have reduced trade and financial barriers, yet persistent income disparities remain observable across both EU member states and neighboring economies. Recent empirical analyses suggest that convergence dynamics may differ between core economies, newer member states, and candidate or peripheral countries (Lalić & Trifunović, 2026b, 2026d). These differences raise the possibility that aggregate convergence results may mask underlying structural clustering.

Beyond standard β-convergence testing, the concept of convergence clubs has gained increasing attention. The Phillips and Sul (2007, 2009) log-t methodology allows for heterogeneous transitional dynamics and endogenous club formation, thereby relaxing restrictive assumptions of identical steady states. Evidence from various regional applications indicates that economies may converge within subgroups while diverging at the aggregate level.

At the same time, institutional quality has emerged as a key conditioning factor in growth processes. The institutional economics literature emphasizes that governance quality, rule of law, and regulatory effectiveness influence capital accumulation, productivity, and macroeconomic stability (Acemoglu et al., 2001; Rodrik et al., 2004). In the European setting, institutions may not necessarily accelerate convergence mechanically, but they may stabilize adjustment paths and reduce volatility (Lalić & Trifunović, 2026d).

The role of systemic crises adds an additional dimension to convergence dynamics. The global financial crisis, the sovereign debt crisis, and the COVID-19 shock generated asymmetric output contractions across European economies, suggesting that convergence speed may vary across structural regimes (European Commission, 2022). Whether such shocks reinforce divergence or accelerate catch-up within specific clusters remains an open empirical question.

This study examines whether European income convergence is characterized by endogenous convergence clubs, whether these clubs exhibit a systematic institutional hierarchy, and whether major systemic crises generate asymmetric adjustment across them. Its specific contribution is to integrate three dimensions that are typically examined separately: endogenous club identification through the Phillips–Sul methodology, institutional differentiation across the resulting convergence regimes, and club-specific responses to major crisis episodes. The analysis therefore moves beyond predefined regional groupings and conventional aggregate convergence tests by allowing heterogeneous transition paths to determine the club structure endogenously and subsequently examining its institutional and crisis-related characteristics. While the study builds on our earlier research on European income convergence and institutional conditioning (Lalić & Trifunović, 2026a, 2026b, 2026c, 2026d), the endogenous identification of convergence clubs and the joint analysis of their institutional hierarchy and asymmetric crisis responses constitute the distinct contribution developed here.

The remainder of the paper is structured as follows. Section 2 reviews the literature on convergence theory, convergence clubs, and institutional determinants of growth. Section 3 describes the data and variables. Section 4 outlines the empirical methodology. Section 5 presents the main results and robustness tests. Section 6 discusses the implications. Section 7 concludes.

2. Literature Review

The question of income convergence has remained central to growth theory and empirical macroeconomics for decades. Within the neoclassical framework, economies are expected to converge toward their steady-state income levels conditional on structural characteristics such as savings rates, human capital accumulation, and population growth (Barro & Sala-i-Martin, 1992, 2004). Empirical testing of β-convergence, particularly through panel methods that account for country-specific heterogeneity, has provided substantial support for conditional convergence within relatively homogeneous groups of economies (Islam, 1995). However, the magnitude and speed of convergence have proven sensitive to model specification, sample composition, and estimation techniques.

Subsequent research has questioned the assumption of a single steady state for all economies. Theoretical contributions incorporating multiple equilibria and threshold effects suggest that countries may converge within structurally similar groups while diverging across broader samples (Azariadis & Drazen, 1990; Durlauf & Johnson, 1995). This perspective laid the groundwork for empirical investigations of convergence clubs, where heterogeneity is treated as an intrinsic feature of development rather than as econometric noise.

The methodological breakthrough in this strand of literature was provided by Phillips and Sul (2007), who introduced a time-varying factor model and the log-t convergence test. Unlike traditional approaches that impose identical steady-state assumptions, the Phillips–Sul framework allows for heterogeneous transitional dynamics and endogenous club formation. Empirical applications have demonstrated that full-sample convergence may be rejected even when subgroups of countries exhibit significant convergence patterns (Phillips & Sul, 2009). This methodology has been increasingly applied in studies of European integration, revealing persistent clustering between core economies, new member states, and peripheral regions.

Beyond institutional approaches, an important strand of the convergence literature emphasizes distribution dynamics and spatial dependence as key determinants of heterogeneous growth trajectories. Quah (1996) argues that long-run convergence cannot be fully understood through average growth regressions alone, but requires analysing the evolution of the entire income distribution. Similarly, Rey and Janikas (2005) highlight the importance of spatial interactions and regional spillovers in shaping convergence outcomes. Empirical evidence provided by Ertur et al. (2006) demonstrates that spatial dependence significantly influences regional convergence across Europe.

Within the European context, convergence has been influenced not only by market integration but also by institutional harmonization. The institutional economics literature emphasizes that governance quality, regulatory effectiveness, and rule of law shape investment incentives, productivity growth, and macroeconomic stability (Acemoglu et al., 2001; Rodrik et al., 2004). North (1990) earlier argued that institutions define the “rules of the game,” thereby structuring long-term development trajectories. Empirical contributions have reinforced the view that institutional quality is strongly associated with income levels and growth performance (Acemoglu & Robinson, 2012).

The empirical literature on European convergence has progressively shifted from testing uniform β-convergence toward acknowledging structural and institutional heterogeneity across country groups. Early evidence suggested that convergence within the European Union was observable under conditions of economic integration and policy coordination, particularly among structurally similar economies (Crespo Cuaresma et al., 2008). However, subsequent analyses indicated that convergence speed and stability vary across time and institutional contexts, especially following major macroeconomic disturbances (Borsi & Metiu, 2015; Próchniak & Witkowski, 2013, 2016). These findings imply that convergence is neither automatic nor uniform, but contingent upon macroeconomic stability and structural alignment.

Within transition and post-transition economies, real convergence appears conditional upon institutional consolidation and policy credibility. Empirical evidence suggests that improvements in governance quality, regulatory effectiveness, and macroeconomic discipline are associated with stronger and more stable income dynamics (Kaufmann et al., 2011; Rodrik et al., 2004). Institutional weaknesses, by contrast, tend to amplify volatility and slow adjustment processes (Imbs, 2007; Klomp & de Haan, 2009). Recent contributions further demonstrate that regulatory quality moderates the relationship between financial development and economic performance, particularly in heterogeneous institutional environments (Ullah et al., 2024). Similarly, institutional governance has been linked to economic resilience, environmental performance, and structural competitiveness within integrated regions (Albahouth & Tahir, 2025; Ionașcu et al., 2025; Ristanović et al., 2025).

The Western Balkans represent a distinct case within the European integration framework, characterized by gradual institutional harmonization and incomplete structural transformation. Evidence indicates that income convergence in the region remains conditional upon sustained institutional reforms and macroeconomic stabilization mechanisms (Bartlett & Prica, 2016; Stanišić, 2016; Uvalic, 2019). Foreign direct investment and trade integration have contributed to growth dynamics, yet their effects appear mediated by governance capacity and policy consistency (Estrin & Uvalic, 2016). These findings reinforce the view that convergence is embedded within institutional trajectories rather than determined solely by market integration.

Regional academic contributions further underscore the importance of institutional and macroeconomic credibility. Analyses of competitiveness indicators in Western Balkan economies highlight structural constraints linked to institutional capacity (Anufrijev et al., 2026). Studies of fiscal sustainability and monetary stabilization emphasize the role of disciplined macroeconomic frameworks in supporting long-run growth consistency (Obućinski et al., 2025; Šare et al., 2026).

Recent empirical contributions focusing more directly on convergence dynamics provide additional evidence of persistent structural heterogeneity within European economies. For instance, Šuškavčević et al. (2026) document pronounced income dispersion patterns across EU member states following the global financial crisis, highlighting the uneven nature of post-crisis adjustment. Similarly, Obućinski et al. (2026) find that unemployment convergence dynamics remain phase-dependent, with stronger adjustment occurring during crisis periods and more moderate convergence during recovery phases.

Research on cross-border cooperation and regulatory alignment within the European context suggests that institutional harmonization remains uneven across peripheral and core regions (Bussoli & Fraccalvier, 2025; Fejes, 2025). While these studies do not uniformly apply identical econometric frameworks, they collectively point toward persistent structural and institutional asymmetries that shape convergence outcomes across European economies.

More recent empirical contributions in European contexts increasingly integrate institutional conditioning into convergence analysis. Evidence suggests that institutional volatility and regulatory instability produce heterogeneous growth responses across development stages (Lalić & Trifunović, 2026b, 2026c, 2026d). Institutional quality has also been associated with green competitiveness, resilience, and macroeconomic stability in post-2004 EU member states (Ristanović et al., 2025; Santos, 2025). These findings support the interpretation that institutions operate not only as level determinants of income, but also as conditioning mechanisms influencing convergence speed and stability.

Despite these advances, several issues remain insufficiently explored. First, much of the literature examines either income convergence or institutional determinants in isolation, rather than combining endogenous club formation with panel-based institutional conditioning. Second, the interaction between crisis episodes and club-specific convergence dynamics has received limited empirical attention. Third, the role of institutional heterogeneity within identified convergence clubs—rather than across the full sample—remains underdeveloped.

Addressing these gaps requires an empirical framework that allows for heterogeneous transitional dynamics while explicitly incorporating institutional and macroeconomic controls. By combining club convergence techniques with panel estimations that account for governance quality, regulatory stability, and crisis effects, a more nuanced understanding of European income dynamics can be achieved without imposing restrictive homogeneity assumptions.

3. Data and Variables

The empirical analysis is conducted on an annual panel dataset covering 32 European economies over the period 2004–2023. The time span captures multiple macroeconomic regimes, including pre-crisis expansion, the global financial crisis, the sovereign debt crisis, the COVID-19 shock, and subsequent recovery dynamics.

The sample is structured into three regionally coherent groups reflecting differences in historical integration paths, levels of economic development, and institutional maturity. The EU Core group includes Austria, Belgium, Denmark, Finland, France, Germany, Ireland, Italy, Luxembourg, the Netherlands, and Sweden. These economies represent early-integrated EU members characterized by advanced production structures and comparatively stable institutional frameworks. The EU New group comprises Poland, the Czech Republic, the Slovak Republic, Slovenia, Hungary, Romania, Bulgaria, Croatia, Lithuania, Latvia, Estonia, Cyprus, Malta, Portugal, Spain, and Greece. This category captures post-2004 Central and Eastern European members together with Southern European economies that experienced later institutional consolidation and more heterogeneous convergence trajectories. The Western Balkans group consists of Serbia, Montenegro, North Macedonia, Albania, and Bosnia and Herzegovina, representing non-EU economies or accession candidates with more diverse institutional structures and incomplete convergence processes. This classification follows the grouping adopted in the accompanying dataset documentation and aligns with comparative regional approaches commonly employed in European convergence research.

Macroeconomic data are obtained from the World Bank’s World Development Indicators database, ensuring full cross-country comparability across the entire sample, including Western Balkan economies for which alternative European statistical sources provide limited coverage. The dataset includes real GDP per capita measured in constant 2015 U.S. dollars (World Bank indicator NY.GDP.PCAP.KD), GDP growth, foreign direct investment inflows expressed as a percentage of GDP, tertiary education attainment, and inflation. Institutional indicators are drawn from the Worldwide Governance Indicators (WGI) database, which provides annual measures of governance quality across six dimensions: Voice and Accountability, Political Stability and Absence of Violence, Government Effectiveness, Regulatory Quality, Rule of Law, and Control of Corruption. To reduce dimensionality and mitigate multicollinearity, these six indicators are combined using Principal Component Analysis (PCA). The first principal component explains approximately 89.5% of the total variance and is used to construct a composite institutional quality index. The resulting index is standardized to have a sample mean of zero; therefore, positive values indicate above-average institutional quality relative to the sample, whereas negative values indicate below-average governance performance.

Institutional quality is summarized using Principal Component Analysis (PCA) applied to the six Worldwide Governance Indicators dimensions. All variables are standardized prior to estimation. The first principal component explains approximately 89.5 percent of the total variance and exhibits uniformly positive and similarly sized loadings across all dimensions (see Table 1), indicating that it captures a broad common governance factor rather than being driven by a single institutional component. This component is retained as the composite institutional index used throughout the empirical analysis.

Table 1. PCA Loadings for Institutional Index.

Variable	Loading (PC1)
Voice and Accountability (VA)	0.417
Political Stability (PV)	0.358
Government Effectiveness (GE)	0.420
Regulatory Quality (RQ)	0.414
Rule of Law (RL)	0.424
Control of Corruption (CC)	0.413

Notes: All six Worldwide Governance Indicator (WGI) dimensions were standardized prior to PCA estimation. The first principal component explains 89.5% of total variance and exhibits uniformly positive loadings across dimensions.

Table 1 reports the loadings of each governance dimension on the first principal component.

The institutional index is employed in the multinomial logit specification explaining convergence club membership and serves as a conditioning variable in extended panel regressions. Additional structural controls include tertiary education attainment, foreign direct investment inflows, and inflation, allowing assessment of whether convergence patterns reflect broader structural and macroeconomic characteristics.

Crisis effects are incorporated through dummy variables identifying major systemic shock periods affecting European economies. The baseline crisis indicator takes the value of one during the Global Financial Crisis (2008–2009), the European sovereign debt crisis (2012–2013), and the COVID-19 pandemic (2020–2021), and zero otherwise. Interaction terms between the crisis indicator and convergence club membership are introduced to test whether systemic shocks affect convergence regimes asymmetrically. As an additional robustness exercise, the aggregated crisis indicator is decomposed into separate crisis-specific dummy variables capturing the Global Financial Crisis (2009) and the COVID-19 shock (2020), allowing the contribution of individual crisis episodes to be evaluated separately. Alternative specifications with year fixed effects are also estimated to assess the robustness of the main findings.

The selected crisis periods correspond to the principal systemic macroeconomic disturbances affecting European economies during the sample period. The years 2008–2009 capture the Global Financial Crisis, while 2012–2013 represent the European sovereign debt crisis, during which fiscal instability and financial fragmentation remained particularly pronounced across several EU member states. The years 2020–2021 capture the acute phase of the COVID-19 pandemic and its immediate macroeconomic consequences across Europe. These episodes were selected because they represent broad economy-wide shocks capable of affecting convergence dynamics across countries rather than country-specific disturbances. To assess whether the estimated crisis effects depend on the aggregation of different crisis episodes, the robustness analysis subsequently estimates separate specifications isolating the 2009 Global Financial Crisis shock and the 2020 COVID-19 shock.

For dynamic specifications, lagged growth is included to account for persistence effects. Estimation procedures are structured to address potential endogeneity and serial correlation, and diagnostic tests are reported to evaluate the consistency of the dynamic framework.

The resulting dataset forms a balanced panel of 32 countries observed over 20 years for the core dynamic estimations (N = 640), while some auxiliary specifications are estimated on slightly reduced samples due to data availability. All transformations follow standard conventions in convergence analysis and ensure cross-country comparability over time.

4. Methodology

The empirical strategy integrates convergence testing, panel regression techniques, and dynamic modeling in order to capture heterogeneous growth dynamics across European economies. Rather than assuming a uniform steady-state income path for the entire sample, the framework explicitly allows for transitional heterogeneity and endogenous clustering. The methodological approach proceeds in three interconnected stages: identification of convergence clubs, analysis of within-club growth dynamics, and assessment of crisis-related and dynamic effects.

4.1. Club Convergence Framework

The analysis begins with the identification of convergence clubs using the Phillips–Sul methodology. This approach departs from traditional β-convergence models by allowing economies to follow heterogeneous transitional paths toward potentially different steady states. Instead of imposing homogeneity ex ante, the method tests whether countries share common long-run dynamics.

Let $y_{it}$ denote real GDP per capita of country $i$ at time $t$. Following the time-varying factor representation, output can be decomposed as:

$$y_{it}={\delta }_{it} {\mu }_t$$

where ${\mu }_t$ captures the common growth component and ${\delta }_{it}$ reflects country-specific transition parameters that evolve over time. Convergence implies that the transition parameters converge toward a common value.

To evaluate this process, the relative transition parameter is constructed:

$$h_{it}={\displaystyle \frac{y_{it}}{\frac{1}{N}{{\sum }_{i=1}^{N}y}_{it}}}$$

and its cross-sectional variance is computed as:

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

If countries converge, cross-sectional dispersion in relative transition paths should decline over time. This hypothesis is formally tested using the log-t regression:

$$log\left({\displaystyle \frac{H_t}{H_{t-1}}}\right)=a+blogt+u_t$$

The null hypothesis of convergence corresponds to $b$ ≥ 0. Rejection of the null indicates absence of full-sample convergence and justifies the implementation of the club clustering algorithm. Countries are then endogenously grouped into convergence clubs based on statistically coherent transition dynamics.

This approach is particularly suitable for European economies, where integration processes may generate convergence within subgroups while divergence persists at the aggregate level.

4.2. Determinants of Club Membership

After identifying convergence clubs, the analysis examines the structural determinants of club allocation. The objective is to assess whether institutional and macroeconomic characteristics systematically differentiate economies belonging to distinct convergence regimes.

A multinomial logit model is estimated:

$$P({Club}_i=j)={\displaystyle \frac{exp({\alpha }_j+{\beta }_{1j} {Inst}_i+{\beta }_{2j} {Edu}_i+{\beta }_{3j} {FDI}_i+{\beta }_{4j} {Infl}_i)}{{\displaystyle {\sum }_{k=1}^J}exp({\alpha }_k+{\beta }_{1k} {Inst}_i+{\beta }_{2k} {Edu}_i+{\beta }_{3k} {FDI}_i+{\beta }_{4k} {Infl}_i)}}$$

where the dependent variable represents convergence club membership and one group serves as the reference category. The explanatory variables include the composite institutional index derived from PCA, tertiary education attainment, foreign direct investment inflows, and inflation.

This specification allows identification of structural features associated with higher or lower probabilities of belonging to advanced convergence clubs. The multinomial framework is particularly appropriate given the unordered nature of club categories.

To facilitate substantive interpretation of the multinomial logit estimates, model-based changes in predicted club-membership probabilities are additionally calculated for a one-standard-deviation increase in the Institutional Index, with all remaining covariates retained at their observed values.

4.3. Within-Club Growth Dynamics

Having identified the convergence clubs and their structural correlates, fixed-effects panel regressions are estimated separately across the identified regimes to characterize within-club growth dynamics. These regressions are supplementary to the Phillips–Sul convergence analysis and are not interpreted as independent tests of conventional β-convergence. The coefficient on lagged income is therefore used to describe the relationship between prior income levels and subsequent growth within the empirically identified convergence regimes.

$$g_{it}={\alpha }_i+\beta ln(y_{i,t-1})+{\epsilon }_{it}$$

where $g_{it}$ denotes real GDP per capita growth and ${\alpha }_i$ captures unobserved country-specific heterogeneity.

Extended specifications incorporate crisis indicators and interaction terms:

$$g_{it}={\alpha }_i+\beta ln(y_{i,t-1})+\gamma {Crisis}_t+\delta ({Crisis}_t\times {Club}_i)+{\epsilon }_{it}$$

This formulation allows crisis effects to vary across convergence clubs, thereby testing for asymmetric responses to systemic shocks. Country fixed effects control for time-invariant structural characteristics, while alternative specifications with year fixed effects account for common macroeconomic shocks.

Robust standard errors clustered at the country level are employed. Additionally, Driscoll–Kraay standard errors are calculated to address potential cross-sectional dependence and serial correlation, ensuring consistency under general forms of cross-sectional correlation.

4.4. σ-Convergence and Dispersion Dynamics

Beyond growth regressions, convergence is also examined through dispersion measures. σ-convergence is assessed by calculating the cross-sectional standard deviation of log GDP per capita for each club:

$${\sigma }_t=\sqrt{{\displaystyle \frac{1}{N}}{\displaystyle \sum _{i=1}^N}{(\ln y_{it}-\overline{\ln y_t})}^2}$$

A declining dispersion over time indicates convergence in income levels. To formally evaluate dispersion trends, the following regression is estimated:

$${\sigma }_t=\alpha +\theta t+u_t$$

A negative and statistically significant $\theta$ suggests sustained reduction in income dispersion. This complementary analysis allows comparison between growth-based and dispersion-based convergence measures.

4.5. Dynamic Panel Diagnostic Exercise

Income growth may exhibit persistence due to structural rigidities, investment dynamics, or institutional inertia. To account for this possibility and to address potential endogeneity between growth and initial income, a dynamic panel model is estimated using the Arellano–Bond difference GMM estimator:

$$g_{it}=\rho g_{i,t-1}+\beta ln(y_{i,t-1})+\gamma {Crisis}_t+{\eta }_i+{\epsilon }_{it}$$

The inclusion of lagged growth introduces endogeneity, as the lagged dependent variable is correlated with the error term in fixed effects models. The difference GMM estimator instruments endogenous variables using deeper lags in levels, thereby eliminating country-specific effects and mitigating simultaneity bias.

Model validity is assessed using:

• Arellano–Bond tests for serial correlation (AR(1) and AR(2)).
• Sargan over-identification tests.
• Wald tests of joint significance.

Absence of second-order serial correlation and satisfactory instrument validity provide support for the consistency of the dynamic specification.

As an additional diagnostic exercise, a difference-GMM specification is estimated to examine whether the qualitative growth and crisis patterns persist after introducing a dynamic structure. Given the sensitivity of GMM estimation to instrument validity, these estimates are treated as supplementary and are not used as a primary basis for inference. Model adequacy is evaluated using Arellano–Bond serial-correlation tests and the Sargan test of over-identifying restrictions.

5. Results

5.1. Global Log-t Convergence Test

The empirical analysis begins by testing for overall income convergence across the full sample of 32 European economies using the Phillips–Sul log-t procedure. This test evaluates whether the countries share a common long-run growth path or whether transitional dynamics remain heterogeneous over the observed period.

The estimated log-t coefficient presented in Table 2 is negative (b = −0.095), and the associated t-statistic (−7.969) is substantially below the critical value required to support the null hypothesis of convergence. Accordingly, the hypothesis of full-sample convergence across the 32 European economies is rejected.

Table 2. Global log-t convergence test.

Statistic	Value
Log-t coefficient (b)	−0.095
t-statistic	−7.969

Notes: The null hypothesis of overall convergence (b ≥ 0) is rejected at conventional significance levels.

This finding indicates that the countries do not follow a single common steady-state income trajectory during the period under consideration. Rather than exhibiting uniform convergence, the sample displays persistent heterogeneity in transitional dynamics. The rejection of global convergence does not imply generalized divergence; instead, it suggests the possibility that economies may converge within structurally similar subgroups while remaining separated at the aggregate level.

The result therefore provides empirical justification for proceeding with endogenous club formation. If convergence is not observed for the full sample, identifying internally coherent convergence clubs becomes necessary in order to understand the structure of European income dynamics. The subsequent analysis applies the Phillips–Sul clustering algorithm to determine whether distinct convergence regimes can be detected within the sample.

5.2. Identification of Convergence Clubs and Institutional Hierarchy

Following the rejection of full-sample convergence, the Phillips–Sul clustering algorithm is applied to identify internally coherent convergence groups. The procedure endogenously partitions the sample into subgroups characterized by statistically compatible transition dynamics. The results reveal the presence of three distinct convergence clubs (Table 3).

Table 3. Institutional quality and income levels by convergence club.

Club	Number of Countries	Average Institutional Index	SD Institutional Index	Average GDP per Capita
Club 1	18	0.606	0.679	39,149.55
Club 2	3	−0.186	0.764	16,870.88
Club 3	10	−0.930	0.737	9236.20
Unclassified	1	−1.0579	0.1418	9064.80

Notes: Institutional indicators and GDP per capita are averaged over the sample period. Institutional quality is measured using the PCA-based composite index. One economy did not meet the clustering criteria of the Phillips–Sul algorithm and remains unclassified. GDP per capita is reported in constant 2015 U.S. dollars (NY.GDP.PCAP.KD). The institutional quality index represents standardized PCA scores derived from the six Worldwide Governance Indicators, where positive values denote above-average institutional quality relative to the sample.

The resulting convergence clubs differ substantially from the initial regional classification adopted for descriptive purposes. While the preliminary grouping distinguishes between EU Core, EU New, and Western Balkan economies based on accession history, the Phillips–Sul algorithm identifies clubs solely on the basis of observed transition dynamics. Consequently, several economies initially classified as EU New—such as Czechia, Slovakia, and Slovenia—are grouped together with long-established EU members in the highest-income convergence club. This finding suggests that long-run growth trajectories are not fully explained by accession history or geographical grouping, but instead reflect heterogeneous economic adjustment patterns.

The Phillips–Sul clustering procedure identifies three statistically coherent convergence clubs. Club 1 comprises Luxembourg, Ireland, Denmark, Sweden, the Netherlands, Austria, Finland, Belgium, Germany, France, Italy, Malta, Spain, Slovenia, Portugal, Greece, Czechia, and the Slovak Republic. Club 2 includes Cyprus, Estonia, and Montenegro. Club 3 consists of Lithuania, Poland, Croatia, Latvia, Hungary, Bulgaria, Serbia, Bosnia and Herzegovina, North Macedonia, and Albania. Romania remains unclassified, as it does not satisfy the minimum criteria required for statistically consistent alignment with any identified convergence trajectory. Importantly, club allocation is determined endogenously by the Phillips–Sul methodology and does not mechanically correspond to predefined regional classifications, underscoring that observed convergence regimes reflect heterogeneous transitional dynamics rather than ex ante grouping assumptions.

The results reveal a clear hierarchical structure across convergence clubs. Club 1 comprises the largest group of economies and exhibits the highest average institutional quality and income levels. The positive average institutional index indicates comparatively strong governance performance, while the substantially higher GDP per capita suggests advanced economic structures and sustained development trajectories.

Club 2 occupies an intermediate position. Although its institutional index remains negative on average, it is markedly higher than that of Club 3. Average income levels are also significantly below those observed in Club 1, yet considerably above those of the lowest club. This intermediate grouping suggests a transitional convergence regime characterized by partial institutional consolidation and heterogeneous growth performance.

Club 3 displays the lowest institutional quality and the lowest average income levels within the sample. The negative institutional index indicates weaker governance structures relative to the European mean, and the income gap with respect to Club 1 remains substantial. The presence of this group supports the interpretation that institutional capacity and income levels jointly shape long-run convergence dynamics.

Importantly, the distribution of institutional quality across clubs follows a monotonic pattern consistent with the income hierarchy. Economies with stronger institutional performance are systematically concentrated in the highest-income convergence club, while weaker institutional environments are associated with lower-income clusters. This pattern suggests that club formation is not arbitrary but reflects underlying structural and governance differences.

The identification of three convergence clubs confirms that European income dynamics are characterized by subgroup-specific adjustment paths rather than uniform convergence. The existence of a clear institutional hierarchy across clubs provides a preliminary indication that governance quality may play a central role in explaining club allocation. The subsequent analysis formally examines this relationship using a multinomial logit framework.

One economy does not satisfy the minimum clustering criteria of the Phillips–Sul procedure and remains unclassified. Such cases may occur when transitional dynamics are insufficiently aligned with any statistically coherent club. The presence of a single unclassified observation does not affect the interpretation of the three-club structure identified for the remaining sample.

5.3. Determinants of Convergence Club Membership

To examine the structural determinants of convergence regime allocation, a multinomial logit model is estimated in which club membership serves as the categorical dependent variable, with Club 1 specified as the reference category.

The estimation results presented in Table 4 indicate that institutional quality is a strong and statistically significant predictor of club allocation even after accounting for within-country dependence. Relative to Club 1, the coefficient on the Institutional Index is negative and statistically significant for both Club 2 (coefficient = −3.473, country-clustered SE = 1.678, p = 0.038) and Club 3 (coefficient = −4.276, country-clustered SE = 1.490, p = 0.004). These results indicate a pronounced institutional gradient across the identified convergence regimes, with stronger institutional quality being associated with a greater relative likelihood of membership in the highest-income convergence club.

Table 4. Multinomial logit estimates of convergence club membership (Club 1 as reference).

Variable	Club 2 Coefficient	Std. Error	Club 3 Coefficient	Std. Error
Institutional Index	−3.473	1.678	−4.276	1.490
Tertiary Education	0.259	0.108	0.207	0.124
FDI (% of GDP)	0.007	0.004	−0.0003	0.004
Inflation	−0.083	0.197	0.018	0.096
Constant	−8.643	2.437	−6.338	2.850
Observations:	360
Residual Deviance:	304.855
AIC:	324.855

Notes: The dependent variable is convergence club membership, with Club 1 serving as the reference category. Reported coefficients represent log-odds relative to Club 1. Country-clustered robust standard errors are reported to account for within-country dependence across repeated annual observations. The model is estimated on 360 complete country-year observations from 31 economies classified into the three Phillips–Sul convergence clubs. Romania is excluded because it remains unclassified by the club convergence procedure. Institutional quality is measured using the PCA-based composite index derived from the six Worldwide Governance Indicators dimensions.

Human capital, proxied by tertiary education attainment, is positively associated with membership in the alternative clubs relative to Club 1. The coefficient is statistically significant for Club 2 (coefficient = 0.259, country-clustered SE = 0.108, p = 0.016), while the corresponding association for Club 3 is weaker and statistically significant only at the 10% level (coefficient = 0.207, country-clustered SE = 0.124, p = 0.096). Foreign direct investment exhibits only limited explanatory power: its coefficient is marginally significant for Club 2 (coefficient = 0.007, country-clustered SE = 0.004, p = 0.075) and statistically insignificant for Club 3. Inflation is statistically insignificant in both comparisons.

The model residual deviance equals 304.86, with an AIC of 324.86. Because the estimation uses repeated country-year observations, inference is based on standard errors clustered at the country level, thereby allowing for within-country dependence over time.

To provide a more intuitive assessment of the substantive magnitude of the institutional association, we additionally calculated changes in predicted club-membership probabilities associated with a one-standard-deviation increase in the Institutional Index (SD = 1.017), while retaining all other covariates at their observed values. The model predicts that such an increase is associated with an average rise in the probability of belonging to Club 1 from 56.9% to 90.7%, corresponding to an increase of 33.7 percentage points. Conversely, the predicted probability of Club 3 membership declines from 36.9% to 7.9% (−29.0 percentage points), while the probability of Club 2 membership decreases from 6.1% to 1.4% (−4.7 percentage points). These probability shifts provide a more intuitive representation of the strong institutional gradient identified by the multinomial logit estimates. They should nevertheless be interpreted as model-based associations rather than causal effects.

Overall, the results confirm that club membership is systematically related to structural fundamentals, particularly institutional capacity and human capital accumulation. Institutional quality emerges as the most robust predictor across specifications, reinforcing the interpretation that convergence regimes reflect persistent governance differentials rather than short-term macroeconomic fluctuations.

5.4. Within-Club Growth Dynamics

Following the identification of convergence clubs using the Phillips–Sul methodology, fixed-effects panel regressions are estimated separately for each club to examine within-club growth dynamics. These regressions are not intended to provide an independent test of conventional β-convergence. Instead, the Phillips–Sul procedure provides the primary evidence regarding convergence within the identified regimes, while the fixed-effects regressions characterize within-club growth dynamics. They are used to characterize how initial income is associated with subsequent growth within the previously identified convergence regimes and to evaluate whether growth dynamics differ across clubs.

The results presented in Table 5 indicate heterogeneous growth dynamics across the previously identified convergence clubs.

Table 5. Fixed-effects estimates of within-club growth dynamics.

Club	Coefficient (ln_GDP_lag)	Std. Error	t-Value	p-Value
Club 1	5.8275	2.3966	2.4316	0.0156
Club 2	5.6013	4.3933	1.2750	0.2076
Club 3	−1.1834	1.0535	−1.1233	0.2627

Notes: The dependent variable is GDP growth. Country fixed effects are included. Robust standard errors are clustered at the country level. The coefficient on lagged income is interpreted as a descriptive measure of within-club growth dynamics and should not be interpreted as an independent test of conventional β-convergence.

For Club 1, the coefficient on lagged income is positive and statistically significant (5.83, p = 0.0156). Under the conventional β-convergence framework, such a coefficient would be inconsistent with convergence. In the present analysis, however, the convergence properties of the club are established independently through the Phillips–Sul procedure. Accordingly, the fixed-effects coefficient is reported only as a descriptive association between prior income and subsequent growth within the already identified convergence regime and is not interpreted as evidence either for or against club convergence.

For Club 2, the coefficient remains positive (5.60) but is statistically insignificant (p = 0.208). The lack of statistical significance should also be interpreted cautiously given that Club 2 contains only three economies, limiting statistical power.

For Club 3, the coefficient is negative (−1.18) but statistically insignificant (p = 0.263). The negative but statistically insignificant coefficient suggests that no systematic relationship between initial income and subsequent growth can be identified within this convergence regime over the sample period.

Taken together, these findings indicate that growth dynamics differ across the convergence clubs identified by the Phillips–Sul methodology. Rather than serving as an independent test of β-convergence, the fixed-effects regressions highlight differences in growth persistence and adjustment patterns across structurally distinct convergence regimes.

5.5. Crisis Interaction Model

To assess whether systemic crises affected convergence regimes asymmetrically, a crisis interaction specification is estimated. The model includes a crisis dummy and interaction terms between the crisis indicator and club membership dummies. Club 1 serves as the reference group.

As shown in Table 6, the crisis coefficient is negative and highly statistically significant (−2.866, p < 0.001), indicating that crisis periods reduce GDP growth by approximately 2.9 percentage points in the reference regime (Club 1).

Table 6. Crisis effects with convergence club interactions (country fixed effects).

Variable	Coefficient	Std. Error	t-Value	p-Value
ln_GDP_lag	1.5253	1.3058	1.1682	0.2432
Crisis	−2.8659	0.2381	−12.0374	<0.0001
Crisis × Club 2	−2.0911	0.4627	−4.5198	<0.0001
Crisis × Club 3	0.0456	0.5031	0.0906	0.9278

Notes: The dependent variable is GDP growth. Country fixed effects are included. Club 1 is the baseline category. Robust standard errors are clustered at the country level.

Table 6 further shows that the interaction term for Club 2 is negative and statistically significant (−2.091, p < 0.001). This implies that economies in Club 2 experience an additional contraction during crises relative to Club 1. The combined crisis effect for Club 2 is therefore approximately −4.96 percentage points, suggesting heightened sensitivity within this intermediate convergence regime.

By contrast, as reported in Table 6, the interaction term for Club 3 is statistically insignificant (0.046, p = 0.928), indicating no measurable differential crisis effect relative to the reference group.

The coefficient on lagged income remains statistically insignificant in Table 6, suggesting that short-run crisis dynamics dominate transitional income effects in this specification.

Overall, Table 6 provides clear evidence of asymmetric crisis responses across convergence regimes, with the strongest amplification observed in the intermediate-income club.

5.6. Year Fixed Effects Robustness

To account for common macroeconomic shocks affecting all economies simultaneously, the crisis interaction model is re-estimated including year fixed effects. This specification absorbs global disturbances and isolates differential responses across convergence regimes. Whereas the baseline specification captures broader crisis periods through aggregated crisis episodes (2008–2009, 2012–2013, and 2020–2021), the robustness analysis isolates the peak years of the Global Financial Crisis (2009) and the COVID-19 pandemic (2020) in order to identify which crisis episode primarily drives the estimated asymmetric effects.

As shown in Table 7, the interaction effect for Club 2 remains negative and highly statistically significant (−2.090, p < 0.001). The magnitude is nearly identical to the estimate reported in Table 6, indicating that the amplified crisis sensitivity of the intermediate convergence regime is not driven by global time-specific shocks.

Table 7. Crisis interaction model with year fixed effects.

Variable	Coefficient	Std. Error	t-Value	p-Value
ln_GDP_lag	1.2600	1.7183	0.7333	0.4637
Crisis × Club 2	−2.0896	0.4648	−4.4954	<0.0001
Crisis × Club 3	0.0530	0.5089	0.1041	0.9171

Notes: The dependent variable is GDP growth. Country and year fixed effects are included. Club 1 is the baseline group. Robust standard errors are clustered at the country level. The standalone crisis dummy is absorbed by year fixed effects.

Table 7 further confirms that the interaction term for Club 3 remains statistically insignificant (0.053, p = 0.917), reinforcing the conclusion that lower-income regimes do not exhibit differential crisis amplification once common time effects are controlled for.

The coefficient on lagged income remains statistically insignificant in Table 7, consistent with the earlier specification.

Overall, the comparison between Table 6 and Table 7 demonstrates that the asymmetric crisis response identified for Club 2 is robust to the inclusion of year fixed effects, suggesting that the observed heterogeneity reflects structural regime differences rather than common cyclical fluctuations.

5.7. Driscoll–Kraay Robustness

As shown in Table 8, the baseline crisis effect remains negative and statistically significant (−2.866, p = 0.016), although the standard error increases relative to Table 6 due to the more conservative correction.

Table 8. Crisis interaction model with Driscoll–Kraay standard errors.

Variable	Coefficient	Std. Error	t-Value	p-Value
ln_GDP_lag	1.5253	3.6568	0.4171	0.6767
Crisis	−2.8659	1.1895	−2.4094	0.0163
Crisis × Club 2	−2.0911	0.7374	−2.8360	0.0047
Crisis × Club 3	0.0456	0.4940	0.0923	0.9265

Notes: The dependent variable is GDP growth. Country fixed effects are included. Club 1 serves as the baseline group. Driscoll–Kraay standard errors account for cross-sectional dependence and serial correlation.

Given the presence of strong cross-sectional dependence across panel units (as later confirmed in Table 9), the crisis interaction model is re-estimated using Driscoll–Kraay standard errors. This estimator is robust to heteroskedasticity, serial correlation, and cross-sectional dependence, making it particularly appropriate in macro-panel settings with common shocks.

Table 9. Pesaran CD test for cross-sectional dependence.

Test Statistic	Value
z-statistic	58.531
p-value	<0.0001

Notes: Pesaran CD test applied to the baseline crisis interaction specification. The null hypothesis is cross-sectional independence.

Table 8 further shows that the interaction effect for Club 2 remains negative and statistically significant (−2.091, p = 0.0047), confirming that the amplified crisis vulnerability of this regime is robust to cross-sectional dependence adjustments.

By contrast, the interaction term for Club 3 remains statistically insignificant (p = 0.926), consistent with earlier specifications.

Importantly, the coefficient on lagged income becomes clearly insignificant in Table 8 (p = 0.677), reinforcing the conclusion that short-run crisis dynamics dominate transitional income effects once cross-sectional correlation is properly accounted for.

Overall, Table 8 confirms that the asymmetric crisis response identified for Club 2 is not an artifact of cross-sectional dependence. The main structural finding remains statistically robust under conservative error correction.

5.8. Cross-Sectional Dependence

Before adopting robust covariance corrections, cross-sectional dependence is formally tested using the Pesaran CD test. The presence of cross-sectional correlation is particularly relevant in macroeconomic panel datasets, where economies are jointly exposed to global shocks, financial spillovers, and synchronized policy responses.

As shown in Table 9, the Pesaran CD statistic equals 58.531 and is highly statistically significant (p < 0.001). The null hypothesis of cross-sectional independence is therefore decisively rejected.

The magnitude of the test statistic indicates extremely strong cross-sectional correlation across panel units. This finding is consistent with the high degree of economic and financial integration among European economies, as well as exposure to common systemic shocks.

The results reported in Table 9 provide formal justification for the use of Driscoll–Kraay standard errors in Table 8. Given the confirmed presence of cross-sectional dependence, conventional clustered standard errors may understate true variability. The robustness checks implemented above therefore ensure that inference remains valid under correlated disturbances.

5.9. Alternative Crisis Definitions

To assess whether the identified asymmetric effects are sensitive to the definition of systemic shocks, the crisis interaction model is re-estimated using two alternative specifications: (i) a dummy capturing only the 2009 global financial crisis, and (ii) a dummy capturing only the 2020 pandemic shock. This allows the separation of financial-crisis and health-crisis effects.

As shown in Table 10a, the 2009 financial crisis had a large and highly statistically significant negative effect on growth (−6.654, p < 0.001). The interaction term for Club 2 is negative and marginally significant at the 10 percent level (p = 0.099), suggesting that the intermediate regime experienced amplified contraction during the financial crisis. The interaction for Club 3 is statistically insignificant.

Table 10. (a) Crisis interaction model: 2009 financial crisis only. (b) Crisis interaction model: 2020 pandemic shock only.

Variable	Coefficient	Std. Error	t-Value	p-Value
(a)
ln_GDP_lag	−0.2628	1.5567	−0.1688	0.8660
Crisis_2009	−6.6536	0.5054	−13.1639	<0.0001
Crisis_2009 × Club 2	−4.7548	2.8750	−1.6538	0.0987
Crisis_2009 × Club 3	−1.6819	2.0673	−0.8136	0.4162
(b)
ln_GDP_lag	3.1300	1.4060	2.2261	0.0264
Crisis_2020	−6.6445	0.7405	−8.9735	<0.0001
Crisis_2020 × Club 2	−4.0939	3.6471	−1.1225	0.2621
Crisis_2020 × Club 3	−0.4246	0.9973	−0.4258	0.6704

Notes: Country fixed effects included. Club 1 serves as the reference group.

As reported in Table 10b, the 2020 pandemic shock also generated a large and statistically significant contraction in GDP growth (−6.645, p < 0.001). However, neither interaction term is statistically significant in this specification, indicating that crisis asymmetry across convergence regimes is weaker for the pandemic shock than for the financial crisis.

Taken together, Table 10a,b indicate that the asymmetric crisis effect identified in Table 6 is primarily driven by the financial crisis episode rather than by the pandemic shock. This suggests that structural regime vulnerability may be more strongly associated with financial transmission mechanisms than with exogenous health shocks.

5.10. Sigma-Convergence by Club

To evaluate whether income dispersion declines over time within each convergence regime, σ-convergence is examined by estimating a linear time trend in the cross-sectional standard deviation of log GDP per capita within each club. A negative and statistically significant time coefficient indicates declining dispersion and thus σ-convergence.

As reported in Table 11, all three convergence regimes exhibit statistically significant negative time trends, indicating declining income dispersion over the sample period.

Table 11. Sigma-convergence trend regressions by convergence club.

Club	Year Coefficient	Std. Error	t-Value	p-Value	R2
Club 1	−0.001242	0.000431	−2.883	0.0099	0.316
Club 2	−0.005992	0.001449	−4.135	0.0006	0.487
Club 3	−0.002226	0.000879	−2.532	0.0209	0.263

Notes: Dependent variable is the within-club cross-sectional standard deviation of log GDP per capita. A negative year coefficient indicates declining dispersion (σ-convergence).

For Club 1, the year coefficient equals −0.00124 (p = 0.0099), implying gradual but statistically significant convergence among advanced economies.

For Club 2, the coefficient is larger in magnitude (−0.00599, p = 0.0006), suggesting stronger within-group convergence dynamics in this intermediate regime.

For Club 3, the coefficient remains negative and statistically significant (−0.00223, p = 0.0209), indicating that even lower-income economies experience declining dispersion within their convergence cluster.

The R² values reported in Table 11 indicate that time explains a meaningful share of within-club dispersion dynamics, particularly for Club 2.

Overall, Table 11 demonstrates that σ-convergence operates within each identified regime, even though global convergence across the full sample was rejected in Table 2. This result is fully consistent with the club convergence interpretation.

5.11. Dynamic Panel Diagnostic Exercise

As a supplementary diagnostic exercise, alternative Arellano–Bond difference-GMM specifications were estimated to examine dynamic persistence and crisis effects. Although the AR(2) tests provide no evidence of second-order serial correlation, the Sargan tests reject the null hypothesis of instrument validity across all reported specifications. The GMM estimates therefore do not satisfy all diagnostic requirements necessary for reliable inference and are not interpreted as confirmatory evidence. For transparency, the estimates and associated diagnostics are reported in Appendix A (Table A1, Table A2 and Table A3). The substantive conclusions of the study are instead based on the Phillips–Sul convergence analysis and the fixed-effects specifications, including the year-effects and Driscoll–Kraay robustness checks, which do not depend on the validity of the GMM instrument set.

6. Discussion

The empirical results provide a coherent picture of heterogeneous convergence dynamics across European economies and confirm that income convergence cannot be interpreted as a uniform process operating across the entire sample.

First, the Phillips–Sul procedure rejects full-sample convergence while identifying three distinct convergence clubs. This finding reinforces the view that heterogeneity is structural rather than transitory. The club composition aligns closely with differences in institutional maturity and long-term income levels, suggesting that convergence in Europe occurs within relatively homogeneous groups rather than across the continent as a whole. The fact that Romania remains unclassified further illustrates that transitional trajectories may not fit neatly into stable convergence regimes.

An important implication of the identified convergence clubs is that they do not replicate the initial regional classification adopted for descriptive purposes. While the preliminary grouping distinguished between EU Core, EU New, and Western Balkan economies based on accession history and institutional background, the Phillips–Sul methodology grouped countries exclusively according to their observed transition dynamics. The inclusion of several newer EU member states, such as Czechia, Slovakia, and Slovenia, within the highest-income convergence club suggests that long-run development trajectories are not determined solely by accession history. Instead, sustained institutional reforms, macroeconomic stability, and successful integration into the European Single Market appear to have enabled some newer member states to converge toward the performance of long-established EU economies. This interpretation is consistent with the empirical institutional hierarchy identified in the study: Club 1 records the highest average institutional score (0.606), while the multinomial logit results show that stronger institutional quality is systematically associated with a higher predicted probability of membership in the top convergence regime. These findings indicate that data-driven convergence clubs provide a more informative representation of European economic heterogeneity than simple regional classifications.

An additional point deserving attention is the unclassified position of Romania. Rather than indicating a limitation of the Phillips–Sul methodology, this result may reflect the country’s transitional development trajectory during the sample period. Romania experienced one of the fastest rates of income growth among European economies after EU accession while simultaneously undergoing substantial institutional and structural transformation. Such dynamics may have prevented its transition path from remaining sufficiently similar to any single convergence club throughout the entire observation period. Consequently, Romania’s exclusion from the identified clubs may itself be interpreted as evidence of heterogeneous convergence dynamics, illustrating that some economies follow transitional trajectories that cannot be consistently assigned to a stable long-run convergence regime. Future research may explore whether alternative sample periods or time-varying club membership procedures lead to a stable classification of Romania, thereby providing additional insight into transitional convergence processes.

Another consideration concerns the relatively small size of the intermediate convergence club, which contains only three economies. Although the Phillips–Sul algorithm identifies convergence clubs based solely on transition dynamics and the resulting classification should therefore be interpreted as an empirical outcome rather than an imposed grouping, the limited number of countries inevitably reduces the statistical precision of subsequent within-club fixed-effects estimations. Consequently, the estimated coefficients for Club 2 should be interpreted with appropriate caution, as they may be more sensitive to country-specific shocks and individual observations than estimates obtained for the larger convergence clubs. Nevertheless, the consistency of the estimated patterns across alternative specifications and robustness analyses suggests that the principal conclusions are not driven solely by the small size of this subgroup.

Second, the institutional hierarchy results demonstrate a strong ordering across clubs. Countries belonging to the highest-income club consistently display higher composite institutional scores, while lower-income clubs are characterized by weaker governance indicators. This reinforces the interpretation that institutions operate as conditioning factors in the convergence process. Rather than generating discrete thresholds that fully determine convergence regimes, institutional quality appears to stabilize growth dynamics and reduce macroeconomic volatility within clubs.

Third, the multinomial logit estimates indicate that institutional quality is systematically associated with convergence club membership, with stronger institutional quality corresponding to a higher predicted probability of belonging to the top convergence regime. The marginal effects confirm that institutional improvements are associated with measurable shifts in club membership probabilities. This finding suggests that institutional quality is systematically associated with differences in long-run convergence regimes. However, these estimates should be interpreted as statistical associations rather than evidence of a causal relationship, as institutional quality and economic development are likely to evolve jointly over time.

Although the multinomial logit estimates reveal a strong statistical association between institutional quality and convergence club membership, the results should not be interpreted as establishing a causal relationship. Institutional quality and economic development are likely to evolve jointly, and reverse causality remains a plausible explanation, as higher income levels may themselves contribute to improvements in governance capacity and institutional performance. Consequently, the estimated coefficients should be interpreted as predictive associations rather than causal effects. Future research could address this issue using identification strategies based on instrumental variables, natural experiments, or dynamic causal frameworks capable of disentangling the direction of influence between institutions and long-run development.

Fourth, the within-club growth regressions reveal heterogeneous transitional dynamics across the identified convergence regimes. The estimated relationship between lagged income and subsequent growth differs across clubs, indicating variation in growth persistence and adjustment patterns. These regressions are interpreted descriptively and do not constitute independent tests of β-convergence. Importantly, the Phillips–Sul results reject full-sample convergence while identifying convergence within distinct club-specific transition paths.

An important implication of these findings concerns the economic mechanisms underlying the asymmetric crisis effects. The stronger crisis sensitivity observed in the intermediate convergence club may reflect its relatively higher degree of financial integration and dependence on cross-border capital flows compared with the lower-income convergence club. Economies in Club 2 appear sufficiently integrated into European financial markets to be strongly exposed to external financial shocks, while still lacking the institutional resilience characteristic of the highest-income economies. By contrast, several economies in Club 3 were comparatively less integrated into international financial markets during much of the sample period, which may have reduced the direct transmission of the 2008–2009 financial crisis despite their generally weaker institutional environments. This interpretation is further supported by the robustness analysis, which indicates that the asymmetric effect is driven primarily by the global financial crisis rather than the COVID-19 pandemic, suggesting that financial transmission channels rather than general macroeconomic vulnerability explain the observed differences. Although these mechanisms are not directly tested in the present study, they provide a plausible economic interpretation of the estimated crisis interaction effects and represent an important avenue for future research.

The crisis interaction models introduce an additional layer of asymmetry. The negative and statistically significant crisis coefficients confirm that downturns disrupt growth trajectories across clubs. However, interaction terms indicate differential sensitivity, implying that resilience varies across institutional and income regimes. These findings are further supported by the year fixed-effects specification and the Driscoll–Kraay corrections, which confirm robustness to cross-sectional dependence and heteroskedasticity.

The Pesaran CD test confirms the presence of cross-sectional dependence, validating the use of robust estimators. Meanwhile, sigma-convergence analysis indicates that dispersion trends differ across clubs, suggesting that income inequality between groups remains persistent even when within-club convergence occurs.

The supplementary GMM exercise does not provide an independent basis for confirming the main results because the Sargan tests reject instrument validity across the reported specifications. Although the estimated coefficients are qualitatively similar to those obtained in the fixed-effects analysis and the AR(2) diagnostics do not indicate second-order serial correlation, the failed over-identification tests preclude strong inference from these estimates. The principal conclusions therefore rest on the Phillips–Sul club convergence results and the fixed-effects specifications, including the year fixed-effects and Driscoll–Kraay robustness analyses.

At first glance, the coexistence of statistically significant σ-convergence and insignificant within-club growth dynamics in Club 3 may appear contradictory. However, the two concepts capture different dimensions of the convergence process. While σ-convergence reflects a reduction in cross-country dispersion over time, the fixed-effects regressions examine the relationship between initial income and subsequent growth within each convergence regime. Consequently, declining income dispersion may occur even in the absence of a statistically significant association between lagged income and growth if the dispersion is reduced through common shocks, structural adjustment, or gradual alignment of country trajectories rather than systematic catch-up by initially poorer economies. The relatively small number of observations within individual clubs and the limited time dimension may also reduce the statistical power of the within-club regressions, particularly for Club 3. Therefore, the absence of statistical significance in the fixed-effects estimates should not be interpreted as inconsistent with the observed decline in within-club income dispersion.

These findings are consistent with the broader convergence literature emphasizing that growth-based and dispersion-based measures capture complementary rather than identical dimensions of the convergence process, and that evidence from one approach does not necessarily imply corresponding evidence from the other.

Taken together, the findings suggest that European convergence is best understood as a layered and club-based process. Institutional quality functions as a stabilizing and differentiating mechanism rather than as a simple accelerator of convergence speed. Crisis episodes amplify existing structural differences rather than reshaping convergence regimes entirely.

From a policy perspective, the results imply that institutional reforms remain central to sustained income catch-up. However, convergence policies cannot be designed as one-size-fits-all strategies. Countries in lower-income clubs require structural reforms that enhance governance quality and macroeconomic resilience, while higher-income clubs must focus on maintaining institutional stability to prevent divergence during external shocks.

The supplementary GMM exercise does not provide an independent basis for confirming the main results because the Sargan tests reject instrument validity across the reported specifications. Although the AR(2) diagnostics provide no evidence of second-order serial correlation, the failed over-identification tests preclude strong inference from these estimates. The principal conclusions therefore rest on the Phillips–Sul club convergence analysis and the fixed-effects specifications, including the year fixed-effects and Driscoll–Kraay robustness analyses.

The findings also carry broader implications for European economic policy. First, the identification of distinct convergence clubs suggests that uniform cohesion policies may not be equally effective across heterogeneous groups of countries. Instead, policies aimed at reducing regional disparities should account for differences in structural characteristics, institutional capacity, and crisis resilience across convergence regimes. Second, the results highlight the importance of sustained institutional reforms for countries seeking closer economic integration with the European Union. Although institutional quality should not be interpreted as a causal determinant of club membership, its strong statistical association with higher convergence regimes suggests that improvements in governance remain closely linked to long-run development outcomes. Finally, the results have particular relevance for EU candidate and accession countries. The finding that several newer member states have converged toward the highest-income club indicates that successful institutional modernization and macroeconomic stabilization can facilitate long-term convergence. At the same time, the persistence of multiple convergence regimes suggests that accession alone is insufficient to guarantee convergence without continued structural and institutional reforms.

The pronounced crisis sensitivity of the intermediate club calls for particular attention to financial resilience. For economies in this regime, policy priorities should include stronger macroprudential buffers, improved monitoring of cross-border capital exposures, and fiscal space sufficient to absorb external financial shocks without interrupting the longer-term convergence process.

The evidence does not support strong claims of uniform European convergence. Instead, it points to persistent structural clustering shaped by institutional hierarchy and differential crisis resilience.

7. Conclusions

This study examined convergence dynamics across European economies through a club-based framework that integrates income levels, institutional quality, and crisis asymmetry. By combining the Phillips–Sul methodology, multinomial logit estimation, club-specific fixed-effects growth models, crisis interaction specifications, and dynamic panel techniques, the analysis provides a comprehensive assessment of heterogeneous growth trajectories within Europe.

The results indicate that full-sample convergence cannot be supported. Instead, economies cluster into distinct convergence clubs characterized by different income levels and institutional profiles. Institutional quality exhibits a clear hierarchical pattern across clubs, suggesting that governance structures are systematically associated with long-run development paths. The evidence further shows that institutional variables are significantly associated with the probability of belonging to higher convergence clubs, reinforcing the view that institutional maturity is closely linked to structural positioning within the European economy.

The within-club growth regressions reveal heterogeneous transitional dynamics across the identified convergence regimes, while the Phillips–Sul results provide the primary evidence that convergence operates within clubs rather than across the full sample. Crisis episodes introduce additional asymmetries, with downturns exerting significant negative effects on growth and revealing differences in resilience across institutional regimes. Robustness checks—including year fixed effects, Driscoll–Kraay standard errors, cross-sectional dependence testing, and alternative crisis definitions—support the stability of the core findings. The supplementary GMM exercise is reported separately as a diagnostic analysis and is not used as confirmatory evidence because the Sargan tests reject instrument validity.

Overall, the evidence suggests that European convergence is not a uniform process driven by a single steady state. Instead, it reflects differentiated adjustment dynamics shaped by institutional hierarchy and varying exposure to macroeconomic shocks. Institutions appear to function primarily as conditioning and stabilizing factors rather than as automatic accelerators of convergence speed.

From a policy standpoint, the findings imply that convergence strategies must account for structural heterogeneity. Institutional strengthening remains central to sustained catch-up, particularly for economies positioned in lower convergence clubs. At the same time, maintaining institutional stability is essential for higher-income economies seeking to preserve resilience during external disturbances. Policies aimed at deepening integration and enhancing governance quality may therefore contribute to narrowing long-term disparities, but their effectiveness depends on country-specific institutional contexts.

Several limitations should be acknowledged. The analysis relies on publicly available macroeconomic and governance indicators, which may not fully capture informal institutional dynamics or structural reforms occurring within shorter time horizons. Moreover, while the club-based methodology identifies distinct convergence regimes, it does not fully disentangle causal mechanisms underlying club formation. Future research may extend the framework by incorporating sectoral productivity measures, financial development indicators, or nonlinear institutional thresholds. Future research should seek to identify the causal relationship between institutional quality and convergence club membership using research designs that explicitly address potential endogeneity and reverse causality.

The dynamic panel estimates are reported only as a supplementary diagnostic exercise and should not be used for substantive inference because the Sargan tests reject instrument validity across the reported specifications.

In conclusion, the study contributes to the broader literature on European economic integration by providing evidence that convergence unfolds within institutionally differentiated clusters rather than across a homogeneous regional space. The persistence of club structures and the asymmetric impact of crises underscore the importance of institutional maturity in shaping long-run growth trajectories.