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The convergence process is generally regarded as the implication of neoclassical growth theory (Solow, 1956). The assumption of diminishing returns to reproducible capital leads to convergence across countries and regions. Units with relatively lower initial capital to labour ratios experience technology transfers and capital flows from those with higher ratios. As a consequence, the income level converges across countries and regions. Baumol (1986) and Barro (1991) define convergence as catching-up process in time series of output differences. The deviations between two countries have ten- dency to narrow over time. If yi, t > y j, t, then E y i,tþT - y j,tþT jIt < y i,t - y j,t ð3:1Þ for some T, where I t denotes the information set as of time t. There are two key concepts of convergence. The first one assumes that units starting from high level of income exhibit lower income growth than units beginning with low-income levels. Since this process is measured by coefficient of regression, it is named β-convergence (Barro & Sala-i-Martin, 1992). The second one assumes the decreasing dispersion of income across units. Since the dispersion is measured by standard deviation or coefficient of variation, it is called σ-convergence. The existence of σ-convergence means that dispersion of the cross-sectional distribution of income decreases over time. The faster growth of poorer economies, which implies in β-convergence process, is showed by negative coefficient of regression between the income growth rate and its initial level, named as the growth-initial level regression. Quah (1993) and Friedman (1994) argued that negative β coefficient in growth-initial level regression does not necessarily imply a reduction in dispersion. It is proved that existence of β-convergence is necessary, © The Author(s) 2023 T. Kijek et al., Innovation and Regional Technological Convergence, SpringerBriefs in Regional Science, https://doi.org/10.1007/978-3-031-24531-2_3 25 26 3 Regional Technological Convergence: Patterns and Determinants but not sufficient, condition of σ-convergence. This is because random shocks appears during convergence processes between economies. The studies on convergence initially were based on cross-sectional data. In that case the specification of growth regression includes the initial level of income and the income growth rate between the last and first period. The verification of conver- gence using this kind of analysis does not confirm the existence of convergence understood as a process. Considering only the first and last period of time interval, ignoring the intermediate periods, can lead to erroneous conclusions. To avoid this problem, the regression for panel data is used. Another advantage of panel data appliance is correction for the omitted variables problem existing in cross-sectional studies (Stock & Watson, 2011). Another important issue of convergence is the distinction of unconditional and conditional convergence. The unconditional convergence assumes that characteris- tics of economies, which affect steady-state income levels, are the same for all units. As a result, the growth-initial level regression does not include other explanatory variables besides initial level income. The growth equation in a general form is as follows: ln y it y i,t - 1   = α þ β ln y i,t - 1
 þ u it , ð3:2Þ where y it is income of the ith economy in time t, u it has mean zero, finite variance σu2 and is independent over t, and i, α and β are parameters. Otherwise, if country-specific characteristics cause differences in steady-state income levels, these factors should be controlled in the regression. The regression augmented with variables, such as rates of physical and human capital accumulation and population growth, has the following form: ln y it y i,t - 1   = α þ β ln y i,t - 1
 þ γZ it þ u it , ð3:3Þ where Z it is a vector of variables affecting the growth rate and γ represents a vector of parameters. The negative sign of β in the augmented regression indicates the conditional convergence. The conditional convergence assuming differences in the steady state for each economy is to some extent similar to club convergence. It also does not assume one equilibrium-level for all economies, but it takes a multiple equilibrium for groups of countries. The existence of different equilibria is the effect of sharing the same initial position or other attributes by group of countries. The development of the concept of club convergence can be attributed to Baumol (1986), but its continued formal extension is mainly an outcome of the efforts of Durlauf and Johnson (1995). According to Galor (1996), the difference between conditional convergence and club convergence is that in the case of conditional

5 Contents 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 2 Innovation and Regional Development . . . . . . . . . . . . . . . . . . . . . . . . 5 2.1 Spatial Aspects of Innovation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 2.2 Knowledge-Based Foundations of Regional Development . . . . . . . . 10 2.3 Policy Framework of Innovation-Driven Regional Development in the European Union . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 3 Regional Technological Convergence: Patterns and Determinants . . . 2 3.1 Theoretical Background and Types of Convergence . . . . . . . . . . . . 25 3.2 Role of TFP in Measuring Technological Convergence . . . . . . . . . . 28 3.3 Innovation as a Source of Technological Convergence . . . . . . . . . . 37 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41 4 Empirical Analysis of Technological Convergence in the European Regional Area . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47 4.1 Data and Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47 4.2 Spatial Distribution of TFP Across the EU Regions . . . . . . . . . . . . 54 4.3 Analysis of Regional Technological Convergence . . . . . . . . . . . . . . 59 4.4 Impact of Innovation Activities on Processes of Regional Technological Convergence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73 5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79 vi

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