1. Introduction

When the Eurozone members adopted the single currency, many expected to see a fast cross-country convergence in terms of income levels, productivity, and economic growth. By 2012, however, the Eurozone crisis raised questions on whether the problem could be explained by institutional factors such as inadequate regulations, the irresponsible execution of fiscal policy (e.g., the case of Greece), or whether it required a more fundamental economic explanation of conditions that underlie economic growth, income distribution, and international competitiveness.

For several decades before the introduction of the single currency, the member countries followed a clearly intended economic integration. The creation of the European Common Market (Treaty of Rome, 1957), and the formalization of the European Union (Maastricht Treaty, 1993), eliminated most institutional barriers to international trade among member and the flow of capital across member countries. The removal of cross border tariffs and quotas favored each country’s specialization in those activities in which they enjoyed a comparative advantage, and this process induced a national migration of productive resources from the relatively less efficient towards the relatively more efficient industries. Greater specialization, in turn, attained economies of scale, increased investment, employment, and better standards of living for European citizens (^{Santillán, 2015}).

The only non-explicit international trade barrier that remained in place was the use of different national currencies because it created exchange rate risk and represented bid-ask spread costs in each currency exchange transaction. However, with the adoption of the euro (1999), the uncertainty due to currency exchange rate risk was finally eliminated, and the conditions for a fully integrated economic area were consummated. In retrospective, one of the strongest arguments for monetary unification was the expectation that specialization would increase Eurozone members’ international competitiveness (^{Santilllán and Ortega, 2017}). However, according to Gräbner et al. (²⁰²⁰) two decades after the adoption of the single currency and one decade after the Subprime Mortgages crisis of 2008, the economic development of the Eurozone member countries remained “remarkably uneven”.

From the point of view of economic integration and growth, the main consequence of not having achieved an efficient productivity convergence in the Eurozone was the limited specialization achieved by member countries, and the suboptimal utilization of their potential productive capacity, hindering their ability to innovate. This, in turn, is associated with the generation of new well-paid employments and with the creation of economic value, as pointed out by Krugman (¹⁹⁹³).

In recognition that one of the most influential determinants of aggregate economic productivity in any country is labor productivity, because productive chains heavily depend on labor to deliver their products and services, this work analyzes labor-productivity convergence in the Eurozone from 1992 through 2019. This is a subject that has been consciously studied by Filippetti and Peyrache (²⁰¹³), Sonderman (²⁰¹⁴), and Ahmad Naveed, and Naz (²⁰¹⁹), as it represents a necessary condition for long-term competitiveness and sustainable growth.

Filippetti and Peyrache (²⁰¹³), suggest that labor productivity growth is closely related to technological progress and that to reduce the technology gap among Eurozone member states, labor productivity should converge. However, they explored the sources of labor productivity growth in Europe between 1993 and 2007 and found that, although labor productivity differences diminished, disparities among countries were still substantial. Sonderman (²⁰¹⁴), studied labor productivity among Eurozone countries and reported that, while capital and technology free movement should have contributed to convergence in manufacturing, telecommunications, and other information technologies, no evidence could be found at an aggregate level. Although, some indications of labor productivity convergence in agriculture, transport, and communications, as well as in non-market services were detected for the period 1970-1998, from 1999 to 2007 only non-market services converged and two another industries, construction and distributive trade, showed some signals of convergence. More recently, Ahmad, Naveed, and Naz (²⁰¹⁹) explored the effect of structural change (for instance, differing share of employment in different industries, changes in demand, trade patterns and technological progress) on labor productivity convergence in the EU from 1991 to 2009. Looking at different levels of aggregation, i.e., regions, industries, and countries (hierarchical convergence analysis), these authors found that convergence was observed at a regional level. At an industry level, convergence was strongly confirmed in some sectors (agriculture, construction and market services), but it was not present in some other sectors (manufacturing, financial services and non-market services), concluding that labor productivity convergence is heterogeneous at different levels of aggregation.

Because of the elimination of frictions to the free movement of goods, capital, and labor, and the adoption of a single currency that removed exchange rate risk, economic convergence in a broad sense should have happened among Eurozone members. As expressed by Bertola et al. (²⁰⁰¹), the abolition of “economic borders” among the EU member countries should result in welfare improvements at an aggregate level since most productive activities benefit from economies of scale and scope that could not be captured before the integration process. However, in view of the available evidence that this is not the case and, for that reason, a more detailed diagnosis is required.

This paper’s contribution to the understanding of what is the state of convergence in labor productivity among Eurozone member countries is based on the results of a dynamic panel data analysis. The main findings indicate that labor productivity of Eurozone countries, measured both in per-worker terms and in per-hour terms, slowed down significantly after 2008 for the founding members (incumbents), likely as a consequence of the Global Financial Crisis (GFC). For those countries that joined the Eurozone some years after its creation (late comers), labor productivity has continued its convergence towards that of the Eurozone incumbents. However, two decades after the adoption of the euro, the gap between these two groups of countries is still economically significant.

The rest of the paper is organized as follows, the second section presents a brief literature review on labor productivity and its determinants. The third section introduces the methodological framework used in the analysis. The fourth section reports the main results of the study. The final section presents the conclusions of the study and suggests some ideas for future research.

2. Labor Productivity and its determinants

In the spirit of the neoclassical view of Solow (¹⁹⁵⁶), as countries achieve more advanced levels of industrialization, there are decreasing returns on investment and, under the assumption of free factor mobility, there will be increasing capital flows invested in lower-income countries, producing a gradual economic convergence over time. A totally different view was proposed by Romer (¹⁹⁸⁶) and Lucas (¹⁹⁸⁸) who emphasized that physical and human capital accumulation represent the main drivers of growth and believe that, under certain conditions, divergence prevails (^{Kumar and Russel, 2002}). These authors suggest that technological change is endogenous in the sense that it results from the accumulation of human capital and investments in research and development, which produces knowledge with an increasing marginal productivity. In this case there are no diminishing returns to human capital accumulation in the more advanced countries, so there are less incentives to invest overseas, reducing the chances of convergence and, in that sense, the uneven technological levels observed across countries and over time, may be explained by the prevailing differences in human capital accumulation.

The endogenous vs. exogenous perspectives dichotomy is too rigid to capture the complexity of economic integration and labor productivity convergence. However, it delineates the field’s boundaries and frames research on the subject. Studies have followed a wide variety of approaches, each of them confirming that the complex modeling of economic integration, and labor productivity convergence among Eurozone members cannot be captured with a single lens. In what follows, we briefly discuss several reported findings that provided the necessary support for our own research design.

Rivera-Batiz and Romer (¹⁹⁹¹) proposed that the role that corresponds to increasing returns to scale is of paramount importance for regional economic integration. Productivity is associated with economies of scale in general, but with different implications depending on the characteristics of each country. However, in the case of the less developed countries of the Eurozone (e.g., Spain, Portugal and Greece), the potential benefits of eliminating economic barriers are probably less promising given the significant gap in productivity and per-capita income that prevail in those countries, relative to the more advanced economies (e.g., Germany, Netherlands). Syverson (²⁰¹¹) found that different studies in labor economics have focused on the relevance of human capital as a determinant of productivity, the productivity consequences of incentive schemes, and the influence of managerial talent and practices, among other relevant subjects. Villaverde and Maza (²⁰⁰⁸) examined aggregate productivity in Europe, considering it to be the outcome of the combined evolution of sectoral productivities and the sectoral distribution of economic activity, they concluded that: a) there is “a high degree of dispersion in productivity” across regions and across industries; b) the improvement in aggregate productivity is explained by productivity gains at a sectoral level; c) the sectors that have contributed the most to reduce productivity gaps are ‘Food, beverages and tobacco’ and ‘Fuel and power products’; d) there is a declining relationship between the “aggregate productivity of each region and its geographic location”, meaning that similar (more or less efficient) regions agglomerate in space. Vechiu and Makhlouf (²⁰¹⁰) analyze productive specialization among an enlarged sample of all 27 EU countries by sector. These authors focus on individual manufacturing activities and report the presence of diminishing productive specialization across all economic sectors but increasing specialization across manufacturing industries. One of the main consequences that the productive specialization of EU countries should bring about is the improvement of productivity as it favors the learning-curve and the creation of economies of scale, and would lead to convergence.

Most empirical studies interested in the country group convergence hypothesis have used gross domestic product per capita as the dependent variable (^{Barro & Sala-i-Martin, 1991}; ^{Friederich-Eckey & Türk, 2007}); however, other indicators have been used more recently to study convergence at different levels of aggregation (regions, countries, and industries).

However, labor productivity is likely the most interesting variable to study regional and country convergence in the EU (and more specifically, in the Eurozone, which is the focus of this research) because of its theoretical implications as it is closely related to income distribution effects, international competitiveness, technological modernization, and political consequences (for example, in terms of the economic resources allocated by the European Commission to its members, in order to promote economic integration across the region).

Studies in labor productivity convergence include O’Leary (¹⁹⁹⁹), who reports evidence of aggregate and sectoral labor productivity convergence for 11 EU countries, showing a greater degree of aggregate convergence than sectoral convergence, in between 1970 and 1990. O’Leary suggests that the existence of comparatively low productivity levels in traditional activities among the less developed EU countries can potentially contribute to a more expedite labor productivity growth in those activities that are more technologically advanced, directly contributing to a faster convergence. A concrete policy implication that derives from these findings is that poorer countries’ policies which accelerate the reallocation of labor towards higher productivity activities promote convergence.

Martino (²⁰¹⁵) studies labor productivity dynamics for many EU regions for the period from 1991 to 2007 and his results confirm a clear process of unconditional convergence in financial- and business-related services. According to the author, financial liberalization detonated in 1992 by the Maastricht Treaty probably influenced the convergence process of the financial industry, as financial institutions doing business across borders in the EU would transplant their best practices to their new operations. A similar reasoning would also apply to business-related services. However, the reported results confirm that labor productivity does not converge in manufacturing.

According to economic theory, the main determinants of productivity include the free movement of capital and labor, technological innovation based on research and development (R&D) investments, and the continuous modernization of productive plants. The literature focused on the determinants of labor productivity convergence in the Eurozone has included most of them (and some others). Table 1 summarizes eight studies that aim to explain labor productivity convergence in the region, listing their driving factors, analytical method and findings.

The studies discussed in this brief literature review suggest that the most likely determinants of labor productivity include investments in research and development, innovation, human capital skills, economies of scale, free movement of capital and labor, national and foreign direct investment. While the diversity of specific variables and empirical techniques is not conclusive, the literature provides the required framework to develop and estimate our own model of labor productivity convergence. Its results seem to support some relevant conclusions.

3. Methodology

The choice of time series methods to assess convergence has been questioned because they lack the ability to account for non-observable heterogeneity across countries. Once heterogeneity is accounted for, panel data is more suitable to test the robustness of any hypothesis (^{Pesaran, Smith & Yamagata, 2013}).

Following (^{Brooks, 2002}) notation, for a set of g variables ~ I(1) and a VAR with k lags expressed as:

to test for cointegration, the model needs to be converted into a Vector Error Correction Model (VECM), as follows:

where Π=∑i=1kβi-Ig , and Γi=∑j=1iβj-Ig , so that Π represents the long-term coefficient matrix. Since ∆yt-i = 0 and E(u)=0 , the equilibrium is expressed as follows:

These types of models are often used to test for convergence in a series but, as the information is pooled, the richness of heterogeneity is swept away. Therefore, it is preferable to use panel data to account for the dynamics across countries and time (^{Baltagi, Griffin, & Xiong, 2000}). To model labor productivity one can estimate a one-way error Panel Data Analysis model, which can be contemporaneous as in equation (1), with a lagged impact, as in equation (2), or a two-way error model with lagged impact as in equation (3):

where i=1-19 countries, and t=1992 to 2017 , αi represents the time invariant effect, λt the country invariant effect across time, and uit the stochastic term, where E(uit)=0 .

In the convergence approach, the panel data model used to represent the classical growth equation, rewritten for labor productivity to determine whether there is convergence in labor productivity, is modified following Ortega-Diaz (²⁰⁰⁶):

The estimation of equation (4) with a static Fixed Effects (FE) or Random Effects (RE) model that does not account for endogeneity would result in biased estimated coefficients, but the use of instrumental variables with the Generalized Method of Moments (GMM) of (^{Arellano & Bond, 1991}) does account for endogeneity, as in equation (5):

and

where γ=β+1 , and γ<1 .

The model relies on the assumptions that T is small and N is large; uit has finite moments, E(uit)=E(uit,uis)=0 for s≠t ; and the residuals uit are not serially correlated (although not necessarily independent in time) (^{Arellano & Bond, 1991}). The model may be extended to its multivariate form with k-1 variables, as follows:

and

where X is a vector of dimensions k×1 , and Xit* is not correlated with αi . The optimal instruments matrix will depend on whether the variables in vector Xit* are predetermined or completely exogenous. If they are predetermined in the sense that E(Xit*uis)≠0 for t<s and zero otherwise, then the valid instruments are Xi1*,...,Xis-1* . If the variables in vector Xit* are completely exogenous, such that E(Xit*uis)=0 for all t and s, then all x's in Xit* are valid instruments for all the equations. Therefore, this last estimation method is selected as the most suitable for our analysis.

4. Data

Productivity growth can be assessed in various ways. In the endogenous growth literature, the engine of economic growth is explained as a consequence of the “accumulation of human capital and knowledge generation following investments in research and development (R&D) or learning by doing” (^{Klenow & Rodríguez-Clare, 1997}).

In this research we account for several determinants of labor productivity that can be related to either private or public R&D investment, and for different types of capital investments in the economy. The literature defines two measures of labor productivity that are used for this analysis: labor productivity per hour worked (lphw), available for most Eurozone countries from 1992 through the first quarter of 2019, and labor productivity per person employed (lppe), for a similar period, both expressed in constant US dollars of 2018. The series were obtained from The Eurostat database and The Conference Board Total Economy Database™ (CBTED).

Several independent variables identified from the literature as determinants of labor productivity were used in the estimations. They were grouped into three categories:

Summarizing, the list of explanatory variables used to model labor productivity were the following:

The summary statistics of the database are included in the Appendix. (our summary statistics are presented in the Appendix)

5. Estimation results

6. Conclusions

The results of our Dynamic Panel Data Analysis assessed whether there is convergence or divergence in labor productivity among Eurozone countries. They suggest the existence of gradual convergence among all eurozone countries, with a lower rate of convergence for incumbent countries, and with a higher convergence rate for late-entrant countries. Labor productivity growth converged for all countries up to 2008, suggesting that the GFC may have deterred the economic processes that leads labor productivity growth to reach a similar level across countries, after 2008 the gap among all has not diminished. Different authors have documented that the EU (as well as the United States) economy experienced a significant decline in labor productivity growth rates since the outburst of the GFC. For example, Roth (²⁰²²) reported that labor productivity growth rates were more than halved relative to the years before the GFC (1995-2007), and recognized that the decline was puzzling considering that real interest rates were either zero or below zero, as well as the fact that it happened at the same time a revolution in information and communications technology, as well as in Artificial Intelligence. His thoroughly comprehensive work documents the attempts to explain this contradiction, and critically discusses the key role of intangibles in labor productivity growth, furthering the understanding of the puzzle.

Based on our results, productivity per hour worked and productivity per worker, convergence stopped around 2008 for the 14 original members of the Eurozone. After 2012, only the late entrants catch-up towards the average growth rate of the rest, maybe since new members were characterized by lower levels of labor productivity and technological capabilities, so a rapid improvement relative to the countries with an already advanced industrialization would be expected. Our study reinforces Filippetti and Peyrache’s (²⁰¹³) findings that the lack of convergence among all countries may be attributed to the insufficient development of technological abilities in the most backward countries, as well as to the incapacity of countries to convert their technological capabilities into labor productivity.

While the findings reported in this study reveal interesting features of the evolution of labor productivity among Eurozone countries, further research is necessary to improve the understanding of the economic forces that have determined the convergence of labor productivity growth rates. A better understanding of the dynamics of R&D, the sources of Debt and the evolution of the GCI, as well as their relationship with the labor productivity gap, is fundamental for future EU expansion plans and policies.

Although this analysis is focused on national labor productivity convergence, we hope that our findings may give support to future studies at the sub-national and industry levels. New findings may also contribute to a better understanding of why labor productivity convergence stagnated among the founding member countries of the Eurozone during the past decade, and why labor productivity growth converged for all members toward the end of our sample period.