Convergence, inequality and inflation synchronization: evidence from the Eurozone

Borowski, Jakub; Fidrmuc, Jarko; Jaworski, Krystian Article — Published Version Convergence, inequality and inflation synchronization: evidence from the Eurozone Empirica Provided in Cooperation with: Springer Nature Suggested Citation: Borowski, Jakub; Fidrmuc, Jarko; Jaworski, Krystian (2025) : Convergence, inequality and inflation synchronization: evidence from the Eurozone, Empirica, ISSN 1573-6911, Springer US, New York, NY, Vol. 52, Iss. 3, pp. 413-433, https://doi.org/10.1007/s10663-025-09646-2 This Version is available at: https://hdl.handle.net/10419/323707 Standard-Nutzungsbedingungen: Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden. Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen. 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If the documents have been made available under an Open Content Licence (especially Creative Commons Licences), you may exercise further usage rights as specified in the indicated licence. http://creativecommons.org/licenses/by/4.0/ Vol.:(0123456789) Empirica (2025) 52:413–433 https://doi.org/10.1007/s10663-025-09646-2 ORIGINAL PAPER Convergence, inequality andinflation synchronization: evidence fromtheEurozone JakubBorowski1 · JarkoFidrmuc2,3,4 · KrystianJaworski1 Accepted: 26 January 2025 / Published online: 4 March 2025 © The Author(s) 2025 Abstract This paper studies the impact of real convergence in the EU countries on inflation synchronization between these countries and the Eurozone. Inflation co-movement between the Eurozone and the EU countries serves as an important measure of the adequacy of the single monetary policy for both current and future members of the common currency area. We report three major results. First, countries with higher relative GDP per capita in the EU countries report stronger inflation co-movement. Second, the relationship between real convergence and the inflation synchronization is non-linear. Third, lower income inequality is associated with greater inflation comovement. Our findings suggest that real convergence in the EU is associated with stronger inflation synchronization between the EU countries and Eurozone and more effective common monetary policy in the long run. These results provide support for the “coronation theory” which underscores that monetary integration should follow, rather than precede, the process of real convergence. We show that for the catchingup countries with relatively high GDP per capita the value of waiting for the income gap to narrow is limited as additional convergence implies only moderate increase in inflation co-movement. Keywords Real convergence· Inflation synchronization· Monetary union· Inequality· Panel data regression JEL Classification C23· E31· E32· E42· O15· O47 1 Introduction The rising frequency of significant macroeconomic shocks has prompted a wave of empirical research on inflation synchronization. Most studies point to increasingly synchronized inflation internationally over time, with advanced economies having Responsible Editor: Jesus Crespo Cuaresma. Extended author information available on the last page of the article 414 Empirica (2025) 52:413–433 the strongest inflation co-movement. Elsayed etal. (2021) highlight a high degree of integration between the oil price inflation and CPI inflation in G7 countries and China. They also show that this relationship is time-varying and has been rising over time, especially during oil crisis and episodes of financial stress. Ha etal. (2019a and 2019b) show that inflation movements have become increasingly synchronized over time and inflation synchronization is broad-based and observed not only in developed economies but also emerging market and developing countries. Their findings point to improvements in economic policy institutions and stronger global trade linkages as factors explaining greater inflation synchronization. Szafranek (2021) shows that inflation synchronization across advanced, emerging and least developed economies strengthens along with the unification of monetary policy frameworks triggering similar policy responses, the falling independence of central banks and the launch of unconventional monetary policy by the Federal Reserve. Inflation co-movement in advanced and emerging economies is also affected by oil price shocks. He also points to the increased synchronization in business cycles as a driver of price co-movements in the EU economies. Shin and Kang (2023) show that after 2008 the importance of global factors in explaining the national inflation rates in 29 countries has remarkably increased and higher global inflation synchronization is mainly driven by rising importance of the non-commodity global factor rather than that of commodity global factor. The issue of inflation synchronization is particularly relevant for the Eurozone, as diverging inflation trajectories in a monetary union cause discrepancies in domestic real interest rates which may destabilise the monetary union (Walters 1990). These rate differentials may lead to country-specific boom-and-bust cycles or excessive monetary tightening, which would undermine the effectiveness of common monetary policy. Using a stylized two-country model of a monetary union Landmann (2012) shows that an increase in the real interest rate differentials in a monetary union is a destabilizing element in a currency area with a single nominal interest rate. He argues that the time needed for the system to converge to equilibrium depends on the effectiveness of the competitiveness channel (higher prices lead to lower net exports and reduced inflationary pressure) and the adjustment process is inherently fragile and protracted. What follows are slow-motion boom-bust cycles in the countries sharing common currency leading to desynchronized cyclical fluctuations deemed “rotating slumps” (Blanchard 2007). Therefore, the issue of inflation synchronization in the Eurozone can be seen through the lenses of optimum currency area (OCA) theory which accentuates the low incidence of asymmetric shocks as one of the key characteristics of a well-functioning monetary union (Dellas and Tavlas 2009). Empirical findings suggest that the Eurozone countries have shown a high degree of inflation interdependence. Lopez and Papell (2012) find that after the implementation of the Maastricht Treaty, inflation rates converged in twelve initial euro countries. They also show that the persistence of inflation rate differentials declined significantly after the introduction of the single monetary policy. Álvarez etal. (2021) document inflation co-movement in advanced economies and show that inflation synchronization is particularly strong among euro area countries. They associate this result with substantial trade linkages and common monetary policy shared by euro 415 Empirica (2025) 52:413–433 area member states. Magkonis and Sharma (2019) focus on transmission channels of inflation between the periphery and the core of the euro area. They show that potential inflationary or deflationary shocks in the periphery are transmitted to the core (Germany) and transmission works both ways. Given the prominence of the inflation synchronization within the OCA framework, the underpinnings and sustainability of inflation co-movement in the EU will likely remain high on the research agenda. This paper contributes to the inflation co-movement literature in the following ways. First, we focus on the long-term determinants of inflation synchronization and identify the cross-country differences in GDP per capita as a factor explaining inflation synchronization between the EU member states and the euro area. Inflation co-movement between an EU country and the euro area provides information on the alignment of the single monetary policy with the inflation cycle in that country. For a euro area country, low inflation co-movement suggests that the single monetary policy is episodically too restrictive or too expansionary, thereby increasing output volatility and reducing welfare in that country. For a non-euro area country, low inflation co-movement points to an increased risk of an inappropriate single monetary policy after joining the common currency area and giving up monetary independence. Therefore, the question of whether in the long run inflation synchronisation with the euro area is related to cross-country differences in GDP per capita deserves particular attention. Second, we analyse the evolution of inflation synchronization in the period of rising GDP per capita towards and beyond EU average. We show that the impact of real convergence on inflation co-movement is non-linear and becomes negative once GDP per capita markedly exceeds the EU average. Third, we find out that income inequality is related to inflation synchronization in the EU countries and this result highlights the role of the fiscal policy in the OCA framework. 1.1 Theoretical background Throughout this paper we use the term “income gap”, which is defined as the difference in GDP per capita between an EU country and the EU average. For catching-up countries, the income gap is negative, while for high-income countries it is positive. The income gap should not be confused with the output gap, which refers to the difference between current and potential output. Our preferred measure of the income gap is the difference in GDP per capita in PPS (purchasing power standards), which is a better measure of differences in purchasing power between countries than GDP per capita at market exchange rates. The quest for the connection between income gap and inflation co-movement is based on following premises. First, according to the new trade theory, reducing the income gap leads to higher share of intra-industry trade in total trade. Helpman (1981, 1987) integrated the Heckscher-Ohlin model (explaining inter-sectoral trade) with Chamberlin-type approach to product differentiation, economies of scale and monopolistic competition (explaining intra-industry trade). The resulting generalization of the Hecksher-Ohlin theory indicates that the redistribution of factor endowments which increases the difference in the capital-labor ratios leads to a reduction 416 Empirica (2025) 52:413–433 of the share of intra-industry trade in the total volume of trade. In other words, if the difference in capital-labor ratios is large, countries may produce significantly different groups of commodities, which results in a low share of intra-industry trade (i.e. trade in similar products with horizontally differentiated varieties or trade in vertically differentiated products distinguished by quality and price). As higher capital-labor ratio leads to a higher GDP per capita, it can be expected that the decrease in the income gap contributes to greater intensity of intra-industry trade. This hypothesis was confirmed by the results of empirical research for OECD countries (Loertscher and Wolter 1980). If trade between two economies is dominated by intra-industry trade, incidence of asymmetric shocks is lower and the convergence of business cycles is likely to be stronger (Fidrmuc 2004). Greater synchronization of business cycles, in turn, should lead to stronger inflation co-movement. Second, inflation synchronization between two economies may increase if their structures of production become more similar. The structure of production is an important determinant of the economy’s vulnerability to asymmetric shocks. If there are significant differences in the structure of value added (for example, in one country the share of agriculture in value added is relatively high and the share of market services is relatively low), the probability of asymmetric shocks is high (Thimann 2005). This conclusion was confirmed by the results of empirical studies indicating the positive impact of similarity in economic structures on the synchronization of business cycles (Fidrmuc etal. 2012; Karadimitropoulou 2018). Changes in the structure of production may be the result of sectoral differences in productivity growth rates (supply side) or sectoral differences in income elasticity of demand (demand side). The latter relationship means that changes in the structure of the economy are the effect of shifts in consumer demand that occur with the rise in income. Assuming hierarchical preferences and after the introduction of non-linear Engel curves into the general equilibrium model, Foellmi and Zweimüller (2008) show that along with the increase in income there is a monotonic decrease in employment in agriculture, a temporary increase in employment in manufacturing (in the early stages of development) and a monotonic increase in the share of employment in the services sector. This means that reducing the income gap is associated with similar trends in the production structures, which become more similar. Consequently, these developments lead jointly to the growing convergence of business cycles. Eichengreen and Gupta (2011) came to similar conclusions. They estimated polynomial regression to assess the impact of GDP per capita on the share of services in GDP in over 80 countries in 1950–2005. They identified two waves of growth in the services sector—the first in countries with a relatively low level of GDP per capita and the second in countries with a high level of income. The obtained results also indicate the non-linear relationship between GDP per capita and the share of agriculture and industry (hump-shaped) in GDP. The findings of Buera and Kaboski (2012) are also consistent with this line of reasoning. They built a theoretical model in which, as income increases, demand shifts towards more skillintensive output, which contributes to a decrease in the share of home production relative to market services. All in all, the results of theoretical and empirical studies indicate that reducing the income gap may lead to greater similarity of production structures and thus greater synchronization of business (and inflation) cycles, 417 Empirica (2025) 52:413–433 and this relationship may be non-linear. Non-linearities with respect to business and inflation cycles are documented e.g. by Crespo Cuaresma etal. (2009) and Crespo Cuaresma and Silgoner (2014). Third, reduction in the income gap is likely to be associated with changes in income inequality. While Kuznets (1955) hypothesized a reduction of inequality levels with growing aggregate income, the recent decade has been characterized by increasing levels of inequality in developed and emerging economies (Fidrmuc and Gundacker 2017; El-Shagi etal. 2020). In the model proposed by Pástor and Veronesi (2021) economic growth leads to an increase in income inequality and rise in populism as a response to globalization. Rodrik (2018) and Guiso etal. (2019) also point to globalization as a source of growing populism. Populist policies can result in expansive fiscal and monetary policies as well as in weakening credit standards. These factors can fuel a consumer credit boom (Rajan 2010; El-Shagi etal. 2020). Therefore, rise in populism may lead to weaker impact of the income gap on the convergence of economic fluctuations. Furthermore, Voinea etal. (2020) show that that households’ responses to monetary policy depend on their income and debt levels. The highest impact is found for the middle class, which is more indebted and hence more sensitive to monetary policy changes than other household types. Frost and Stralen (2018) find a positive relationship between income inequality and macroprudential policies. Guerello (2018) shows that the impact of the conventional and unconventional monetary policy on income distribution is highly heterogenous between the countries and that it shows important non-linearities. Differences in the transmission mechanism and in prudential policies are also likely to lower the international synchronization of business cycles. Therefore, rising income inequality is likely to weaken the relationship between income gap and synchronization of business cycles. Following the literature review, we formulate the following research hypotheses: HA. Reduction of the income gap (real convergence) in the EU is associated with greater synchronization of inflation cycles between EU countries and the Eurozone. HB. The relationship between income gap and inflation cycles synchronization is non-linear. Once a relatively low level of the income gap is achieved, the positive impact of its further reduction on inflation co-movement becomes negligible. HC. Income inequality is related to a lower synchronization of inflation cycles between EU countries and the Eurozone. 2 Data andmethods 2.1 Data Our dataset spans from 2001 to 2022, and this range is justified by the availability of underlying monthly inflation time series in the Eurostat database. The analysis covers most EU member states (excluding Luxemburg, Malta and Cyprus, i.e. 24 countries). The chosen sample is a compromise between the length of the data series and the balancing of the panel as for some EU member states data prior to 2001 is unavailable. 418 Empirica (2025) 52:413–433 Calculation of inflation cycle synchronization1 is performed based on Harmonised Indices of Consumer Prices (HICP) provided by Eurostat, which is a measure of inflation that is comparable across countries. To measure inflation interdependency within the European Union we used existing methods presented in the literature that utilize rolling correlation (Duarte and Holden 2003; Artis and Okubo 2009;Gächter and Riedl 2014; Belke etal. 2017). Specifically, the endogenous variable capturing the synchronization of inflation is calculated in a following way: (1) as inflation is subject to significant seasonality (e.g. prices of fruit and vegetables or due to seasonal sales), the monthly level of prices of goods (total inflation excluding services)2 first is adjusted using the X-13ARIMA-SEATS to remove any potential seasonality in the data that may skew the results, (2) then a cyclical component of inflation is isolated by de-trending the of seasonally-adjusted log-prices using the Hodrick-Prescott filter, (3) a 36-month rolling correlation between the inflation cycles in individual EU member states and the Eurozone is calculated, (4) the correlation of inflation cycles in monthly frequency is aggregated to yearly frequency via a simple average. As outlined in the introduction, we believe that reducing the income gap acts as an important factor explaining the synchronization of inflation cycles in the EU. We measure the income gap with nominal GDP per capita expressed as percentage of the EU average based on purchasing power parity, extracted from the Eurostat database. We should keep in mind that inclusion of income gap as an explanatory variable significantly limits the array of potential regressors in our model due to multicollinearity issues. As shown in the literature review in the Sect.2, the most important determinants of inflation cycle synchronization are highly correlated with income gap, e.g. intra-industry trade intensity or specialization and structure of production. Moreover, these variables are often not available for all analyzed countries, which would restrict additionally the scope of presented analysis. Therefore, several “standard” exogenous variables found in research on inflation cycle synchronization cannot be included as explanatory variables for our estimations. We have also obtained different measures used to capture inequality for the individual countries from the World Inequality Database – the Gini coefficient, T10/ B50 ratio (ratio of the top 10% average income to the bottom 50% average income) or S80/S20 ratio (ratio of total income received by the 20% of the population with the highest income to that received by the 20% of the population with the lowest income). 1 We are using the terms inflation cycle correlation, inflation synchronization and inflation interdependency interchangeably throughout the paper. 2 The alternative results, which were based on total inflation (prices of both goods and services) were generally similar, however the goodness-of-fit of the proposed models (see Sect.4) was inferior compared to the baseline approach. This is likely due to a much lower level of internationalization of services markets compared to goods markets, which limits the synchronization of service inflation cycles, and as a corollary total inflation. These results can be provided by the authors upon request. 419 Empirica (2025) 52:413–433 The other explanatory variables include also the share of imports from EU in total imports of each country, which represents the trade interactions within EU. It is calculated separately for each year based on Eurostat annual data on goods’ foreign trade. Lastly, we incorporate a variable representing the volatility of producer prices in Eurozone manufacturing, which serves as a global factor influencing inflation synchronization. This volatility measure is derived from the surveys conducted by S&P Global as part of the Purchasing Managers’ Index (PMI) for manufacturing. The PMI is widely recognized for anticipating shifts in economic and market trends and acts as a key indicator of economic performance and business conditions (S&P Global 2024). Each month, the PMI survey collects qualitative assessments from a large sample of businesses regarding changes in output prices compared to the previous month. Participants respond whether prices have “increased,” “decreased,” or “remained unchanged.” These responses are aggregated into a balance statistic ranging between 0 and 100, where values above 50 indicate rising prices and values below 50 suggest falling prices compared to the previous month. To capture price volatility, we calculated the coefficient of variation (the ratio of the standard deviation to the mean) based on PMI output prices. This was computed using a moving 3-year window, offering a dynamic measure of price volatility over time. PMI surveys offer a real-time assessment of business sentiment on output prices, and many studies highlight the link between PMI data and inflationary trends. Mokinski etal. (2015) find that PMI surveys are a leading indicator of producer price inflation, particularly in the manufacturing sector. The volatility of these output price assessments, when aggregated across countries, can be used to gauge inflationary pressures at a global scale. The descriptive statistics for all variables are shown in Table1. 2.2 Estimation strategy To investigate the relationship between the inflation cycle synchronization and income gap we constructed a fixed-effect panel model, i.e. we estimate a following regression: where Yit is capturing the synchronization of inflation cycles between the i-th EU country and the Eurozone at date t, as defined above (see Sect.3.1). The GDPpcit is the GDP per capita expressed as percentage of the EU average. We include also different measures of inequality in several specifications, denoted by ineq. The X k it represent other explanatory variables outlined in the Sect.3.1. Parameters 𝜇i corresponds to individual effects of EU member countries and 𝜖it stands for the error term. Based on aforementioned theoretical literature and empirical research on the determinants of inflation co-movement, we believe that the relationship between (1) Y it =𝛼1GDPpcit +𝛼2(GDPpcit)2 +𝛼3ineqit +∑ k 𝛼kXk it +𝜇i+𝜖it 420 Empirica (2025) 52:413–433 Table 1 Descriptive statistics Source: Own calculations Variable Year Mean SD Min Q1 Median Q3 Max Correlation of inflation cycles 2003 0.45 0.24 − 0.31 0.34 0.43 0.62 0.80 2006 0.38 0.29 − 0.41 0.15 0.43 0.54 0.86 2009 0.85 0.14 0.47 0.79 0.90 0.95 0.99 2012 0.71 0.25 0.12 0.67 0.76 0.88 0.96 2015 0.78 0.18 0.06 0.73 0.81 0.87 0.96 2018 0.88 0.08 0.66 0.85 0.91 0.93 0.98 2021 0.94 0.03 0.82 0.94 0.95 0.96 0.98 GDP per capita 2003 89.34 36.67 30.50 54.70 90.85 122.78 146.50 2006 92.09 33.91 38.60 62.33 92.95 119.30 151.70 2009 91.95 30.00 43.70 64.03 91.05 118.68 139.90 2012 92.55 28.90 46.80 69.80 83.50 121.95 135.40 2015 94.60 31.79 48.10 70.08 85.65 121.73 180.80 2018 95.45 31.11 51.50 70.73 89.30 118.15 189.90 2021 98.14 34.09 57.40 74.85 89.55 120.13 218.40 Volatility of producer prices 2003 0.02 0.00 0.02 0.02 0.02 0.02 0.02 2006 0.04 0.00 0.04 0.04 0.04 0.04 0.04 2009 0.13 0.00 0.13 0.13 0.13 0.13 0.13 2012 0.07 0.00 0.07 0.07 0.07 0.07 0.07 2015 0.02 0.00 0.02 0.02 0.02 0.02 0.02 2018 0.06 0.00 0.06 0.06 0.06 0.06 0.06 2021 0.16 0.00 0.16 0.16 0.16 0.16 0.16 S80/S20 ratio 2003 4.67 1.08 3.58 4.07 4.35 4.95 6.38 2006 4.81 1.23 3.39 3.70 4.52 5.52 7.76 2009 4.80 1.15 3.24 3.94 4.48 5.82 7.40 2012 4.85 1.09 3.44 3.95 4.68 5.69 6.63 2015 5.12 1.44 3.51 4.00 4.65 6.29 8.32 2018 4.89 1.32 3.03 4.05 4.30 5.64 7.66 2021 4.78 1.28 3.20 3.85 4.28 5.81 7.45 Gini coefficient 2003 0.45 0.05 0.34 0.42 0.46 0.48 0.57 2006 0.46 0.04 0.38 0.44 0.46 0.49 0.53 2009 0.45 0.05 0.37 0.41 0.45 0.48 0.56 2012 0.45 0.04 0.39 0.42 0.45 0.48 0.54 2015 0.46 0.04 0.39 0.43 0.46 0.49 0.53 2018 0.46 0.04 0.37 0.43 0.45 0.48 0.55 2021 0.47 0.05 0.38 0.44 0.46 0.49 0.62 T10/B50 ratio 2003 8.46 2.42 4.61 6.91 8.54 9.51 15.84 2006 8.94 1.94 5.46 7.43 8.68 10.13 12.82 2009 8.33 2.12 5.15 6.65 8.15 9.38 14.79 2012 8.30 1.88 5.98 6.91 8.02 9.56 13.17 2015 8.70 1.76 6.07 7.32 8.71 9.95 12.68 2018 8.54 1.96 5.42 7.38 8.21 9.62 13.99 2021 9.49 4.00 5.45 7.63 8.58 9.86 25.87 427 Empirica (2025) 52:413–433 importance only in the last few years. The coefficients for different measures of income inequality maintained the same sign as in the baseline estimation, although some of them lost statistical significance in some specifications (e.g. S80/S20 ratio). Generally speaking, the results obtained based before/after GFC samples do not differ a lot. The estimation results on the two subsamples are presented in Tables3 and 4, respectively. It is interesting to note that the estimates of the inflection point ( GDPpcpeak , i.e. the level of GDP per capita beyond which the inflation synchronisation stops to increase) differ significantly between the subsamples. They are much lower for the pre-GFC sample (99.9–114.5% of average EU GDP per capita) than for the post-GFC sample (120.5–136.9% of average EU GDP per capita). This might suggest that in the aftermath of significant global shocks the importance of closing the income gap for synchronisation of inflation cycles increases markedly. Such conclusion seems to be supported by the results obtained on the subsample spanning between 2003 and 2019, i.e. excluding the period of COVID-19 pandemic. The estimates of GDPpcpeak stand between 125.3 and 131.2% of average EU GDP per capita, which is lower than the range obtained based on full sample (2003–2022), i.e. 144.8–160.6% of average EU GDP per capita. This means that inclusion of the pandemic shock in the estimation sample underpins the relevance of closing the income Table 5 Estimation results without pandemic period (2003–2019) Source: Own calculations t-statistics in brackets (based on Driscoll-Kraay standard errors reflecting cross-section correlation and autocorrelation) Inflection point (% of average EU GDP per capita) *** p < 0.01, ** p < 0.05, * p < 0.1 Variables Model (1) (2) (3) (4) (5) GDP per capita 0.025 0.025 0.025 0.025 0.023 (5.969)*** (5.938)*** (5.986)*** (5.474)*** (4.884)*** Square of GDP per capita − 0.00010 − 0.00009 − 0.00010 − 0.00009 − 0.00009 (− 5.782)*** (− 5.702)*** (− 5.771)*** (− 5.479)*** (− 5.295)*** Volatility of producer prices 1.642 1.567 1.556 1.345 1.534 (1.656)* (1.598) (1.586) (1.344) (1.525) Gini coefficient − 1.323 (− 2.406)** T10/B50 ratio − 0.022 (− 2.495)** S80/S20 ratio − 0.058 − 0.057 (− 2.122)** (− 2.067)** Share of imports from EU 0.753 (1.281) Observations 408 408 408 369 369 Inflection point 129.4 131.2 131.1 129.6 125.3 428 Empirica (2025) 52:413–433 gap for increasing the synchronisation of inflation cycles. The remaining results do not differ markedly compared to the baseline specification. The coefficients for the explanatory variables maintain their signs and statistical significance as in the case of baseline results (see Table5 for details). We also tested, how exclusion of some countries impacts our results. Particularly, we excluded Czech Republic, Hungary, Poland and Romania (so called CE-4 countries) from our estimation sample. These are four Central European countries that are in the process of catching-up with more advanced economies, but still did not enter the Eurozone. The results are similar to the ones calculated for the sample including all countries. The Gini coefficient and T10/B50 lose their statistical significance, but the S80/S20 ratio maintained it. We link this result with the fact that almost all remaining countries in the sample are members of the Eurozone, with much less variance in the level of income inequality (Table6). Next, we checked whether the results are sensitive to the underlying inflation indicator used to calculate the endogenous variable of inflation synchronisation. To do so, we re-estimated all the models, but this time we used the HICP core inflation (i.e. overall index excluding energy, food, alcohol and tobacco). The results do not differ markedly compared to the baseline specification. The coefficients for the explanatory variables maintain their signs, but some of the control variables lost their statistical significance (Table7). Table 6 Estimation results on a sample excluding CE-4 countries Source: Own calculations t-statistics in brackets (based on Driscoll-Kraay standard errors reflecting cross-section correlation and autocorrelation) Inflection point (% of average EU GDP per capita) ***p < 0.01, ** p < 0.05, * p < 0.1 Variables Model (1) (2) (3) (4) (5) GDP per capita 0.011 0.012 0.012 0.008 0.007 (4.096)*** (3.994)*** (3.925)*** (2.72)*** (2.081)** Square of GDP per capita − 0.00004 − 0.00004 − 0.00004 − 0.00003 − 0.00003 (− 4.065)*** (− 4.043)*** (− 3.951)*** (− 2.846)*** (− 2.525)** Volatility of producer prices 1.974 1.976 1.978 1.670 1.802 (2.863)*** (2.87)*** (2.872)*** (2.58)** (2.818)*** Gini coefficient − 0.244 (− 0.436) T10/B50 ratio − 0.003 (− 0.365) S80/S20 ratio − 0.042 − 0.037 (− 1.764)* (− 1.529) Share of imports from EU 0.869 (1.871)* Observations 400 400 400 371 371 Inflection point 148.4 150.4 149.8 143.0 127.8 429 Empirica (2025) 52:413–433 The final robustness test involved expressing all explanatory variables in terms of EU average. The baseline specification used GDP per capita (and its square) in terms of EU average, but the remaining variables were presented in their raw form, which may lead to some mismatches. To remedy that we recalculated all variables comparing the country-specific values to the EU average. Generally, the results remained similar as in the baseline specification (Table8). The coefficients of the key variables, as well as the infection points did not vary significantly. The Gini coefficient and T10/B50 ratios, as well as the share of imports from EU maintained their respective signs but lost their statistical significance. The explanation is quite straightforward. If we see a similar, general trend among all the EU countries, which is true in the case of decrease in income inequalities, then expressing the explanatory variables as the share of EU average will result in a regressor having almost no variability across time. This likely justifies the lack of statistical significance. 4 Conclusions Inflation synchronisation between EU Member States and the euro area is an important measure for assessing the adequacy of the single monetary policy for both current and future euro area members. Weak inflation co-movement between an EU Table 7 Estimation results with core inflation as an explanatory variable Source: Own calculations t-statistics in brackets (based on Driscoll-Kraay standard errors reflecting cross-section correlation and autocorrelation) Inflection point (% of average EU GDP per capita) ***p < 0.01, ** p < 0.05, * p < 0.1 Variables Model (1) (2) (3) (4) (5) GDP per capita 0.009 0.009 0.010 0.010 0.010 (3.051)*** (3.063)*** (3.164)*** (2.234)** (2.109)** Square of GDP per capita − 0.00003 − 0.00003 − 0.00003 − 0.00003 − 0.00003 (− 2.827)*** (− 2.868)*** (− 2.869)*** (− 2.22)** (− 2.191)** Volatility of producer prices 2.529 2.532 2.538 2.791 2.820 (4.925)*** (4.917)*** (4.897)*** (5.636)*** (5.568)*** Gini coefficient − 0.306 (− 0.42) T10/B50 ratio − 0.010 (− 1.145) S80/S20 ratio 0.075 0.075 (2.182)** (2.183)** Share of imports from EU 0.175 (0.363) Observations 480 480 480 441 441 Inflection point 157.3 160.3 163.5 160.4 158.0 430 Empirica (2025) 52:413–433 country and the euro area suggests that “one size does not fit all” and that the common monetary policy may amplify output fluctuations and reduce welfare in that country. We found evidence that rising relative GDP per capita levels in the EU countries lead to stronger inflation synchronization between these countries and the Eurozone and the relationship between real convergence and inflation co-movement is non-linear. Our findings are consistent with the studies pointing to the non-linear relationship between GDP per capita and GDP structure and showing the nexus between real convergence and synchronization of business cycles. Our results have several long-term implications. First, our findings show that inflation synchronization in the EU is related to the real convergence. Assuming that – in line with the conditional convergence hypothesis—the income gap between new EU member states and the EU core continues to shrink, we should observe more synchronized inflation cycles between these states and the Eurozone. Second, for new EU member states, our results constitute an argument for seeking greater real convergence before joining the Eurozone, as a more synchronized inflation cycle means more adequate common monetary policy and lower long-term costs of monetary integration. Accordingly, these results provide some support for the “coronation theory” which underscores that monetary integration should seal the Table 8 Estimation results with explanatory variables expressed in relation to EU average Source: Own calculations t-statistics in brackets (based on Driscoll-Kraay standard errors reflecting cross-section correlation and autocorrelation) Inflection point (% of average EU GDP per capita) *** p < 0.01, ** p < 0.05, * p < 0.1 Variables Model (1) (2) (3) (4) (5) GDP per capita 0.009 0.009 0.010 0.010 0.010 (3.051)*** (3.063)*** (3.164)*** (2.234)** (2.109)** Square of GDP per capita − 0.00003 − 0.00003 − 0.00003 − 0.00003 − 0.00003 (− 2.827)*** (− 2.868)*** (− 2.869)*** (− 2.22)** (− 2.191)** Volatility of producer prices 2.529 2.532 2.538 2.791 2.820 (4.925)*** (4.917)*** (4.897)*** (5.636)*** (5.568)*** Gini coefficient − 0.306 (− 0.42) T10/B50 ratio − 0.010 (− 1.145) S80/S20 ratio 0.075 0.075 (2.182)** (2.183)** Share of imports from EU 0.175 (0.363) Observations 480 480 480 441 441 Inflection point 157.3 160.3 163.5 160.4 158.0 431 Empirica (2025) 52:413–433 real convergence process rather than be used as a convergence booster. Yet it should be noted that for the catching-up countries with relatively high GDP per capita the value of waiting is limited as additional convergence implies only moderate increase in inflation co-movement. Finally, excessive inequality may also influence inflation synchronization. Rising income inequality in countries that share a common currency or seek membership in a currency union may lead to higher long-term costs of monetary integration. This conclusion should be seen from the perspective of the OCA framework which emphasises the role of domestic fiscal policy as a potential source of idiosyncratic shocks. Funding Open Access funding enabled and organized by Projekt DEAL. This work was supported by the SGHWarsaw School of Economics. Data availability The data that supports the findings of this study is available from the corresponding author, upon reasonable request. Declarations Conflict of interest The authors report there are no competing interests to declare. 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