Intergenerational mobility fosters innovation in Europe

Abstract

The circumstances into which individuals are born can place fundamental constraints on their future economic opportunities^1–5, leading to a mismatch between talent, education and occupation. One major determinant of this inequality of opportunity is the absence of intergenerational educational mobility². Here we extend existing knowledge on intergenerational mobility by presenting The European Atlas of Spatially Disaggregated Intergenerational Mobility (EUROPE-IGM-ATLAS), a panel database comprising indicators of intergenerational mobility for European subnational regions. In doing so, we make two contributions. First, we extend existing knowledge on the development of intergenerational mobility in European regions. The EUROPE-IGM-ATLAS reveals several spatiotemporal trends that characterize the changing geography of opportunity in Europe. For example, we show that observed increases in intergenerational mobility primarily stem from improvements in educational achievements among individuals from families at the lower end of the educational distribution, with fewer changes in rank across the educational spectrum. However, these increases are not uniformly distributed. Regions with a high degree of educational inequality also exhibit lower levels of intergenerational mobility, implying the co-existence of inequality both within and between generations. Second, we use this database to provide evidence on the relationship between intergenerational mobility and innovation. We provide large-scale time-series evidence that European regions with higher intergenerational mobility achieve higher innovation outcomes, one important driver of economic growth. Subsets of results further indicate that this relationship is nonlinear and that distinct mechanisms operate in major innovation hubs.

The EUROPE-IGM-ATLAS reveals spatiotemporal trends that characterize the changing geography of opportunity in Europe and its relationship with regional innovation.

Main

The circumstances into which individuals are born can place fundamental constraints on their future economic opportunities^1–5, leading to a mismatch between talent, education and occupation. One major determinant of this inequality of opportunity is the absence of intergenerational mobility of education. If socioeconomic circumstances outside of an individual’s control constrain their educational opportunities, they may not be able to acquire a level of education commensurate with their abilities². In turn, intergenerational immobility (that is, persistence) of education contributes to the reproduction of economic inequalities if the unachievable educational pathways are positively related to future earnings trajectories^3–5.

Although the decades-long debate in both academia and the policy sphere has largely focused on the individual consequences of inequality^6–12, a more recent strand of research addresses the potential negative implications of intergenerational persistence for aggregate long-run growth and development^13–16. With the misallocation of talent resulting from intergenerational persistence limiting individual productivity to a level below an individual’s productivity potential, aggregate productivity is also likely to be negatively affected. However, owing to a lack of adequate data, the empirical question of how improvements in intergenerational mobility over time affect economic growth and development at a broader scale remains open¹⁷.

In this Article, we present the EUROPE-IGM-ATLAS database. This database extends existing knowledge on intergenerational mobility of education and its relationship to economic development in two ways. First, building on a recently developed procedure¹⁴, we are able to measure changes over time in effective intergenerational mobility by transforming cohort-linked measures into time series indicators, thereby resolving one of the major challenges in estimating the economic implications of intergenerational mobility over time^1,16,18. Second, to demonstrate the value of our database in empirical research, we apply it to studying one channel potentially driving the relationship between intergenerational mobility and economic growth, namely innovation. Consequently, our analysis also contributes findings to the emerging literature investigating subnational variations in social mobility across economics, sociology and geography, thereby generating insights across European countries and regions^14,19–22.

Using harmonized microdata at the subnational level, we first draw the geography of intergenerational mobility of education in Europe and construct comparable descriptive indices for three birth cohorts over the second half of the twentieth century. We then transform these cohort-linked measures into composite annual measures of effective intergenerational mobility for each region, based on weighted contribution profiles over the lifecycle. Specifically, our EUROPE-IGM-ATLAS database comprises regional annual measures of intergenerational mobility of education, educational inequality and average education from 1985 to 2025 (details on the procedure and a full description of the available indices are provided in the Methods) for 225 microregions (Nomenclature of Territorial Units for Statistics 2 (NUTS 2)) or 108 mesoregions (NUTS 1) within 36 countries. These indices permit cross-national comparisons between regions, as well as a complementary analysis of how intergenerational mobility in Europe has evolved over time. The EUROPE-IGM-ATLAS database therefore offers a valuable resource for studying various potential regional implications of past intergenerational mobility.

We then use our database in combination with patent data to analyse the mobility–innovation nexus. Previous suggestive evidence shows that intergenerational mobility is correlated with innovation^23–25, that parental background and the local environment have an important role in the opportunity structure that determines who becomes an inventor^26,27, and that financial constraints based on parental background may harm economic growth by delivering inefficiencies in the allocation of talent and idea production²⁸. Our approach enables us to examine one direction of the relationship between intergenerational mobility and innovation while mitigating concerns about reverse causality. In particular, the observed association is shaped by younger cohorts entering the labour market and accumulating experience, as older cohorts gradually withdraw from the workforce¹⁴.

Our analysis provides large-scale longitudinal evidence that the positive relationship between intergenerational mobility and innovation holds across European regions over time, while exhibiting marked heterogeneity within major historically entrenched innovation hubs. These results hold even after we control for the broader structure of educational opportunities by including differences in average education and educational inequality across cohorts and regions. Further analyses suggest that the observed relationship may be nonlinear in nature, with the largest innovation gains arising at low to intermediate levels of mobility.

Geography of intergenerational mobility

When we apply our estimation procedure (Methods), the EUROPE-IGM-ATLAS reveals several spatiotemporal trends that characterize the changing geography of inequality of opportunity in Europe. We find that observed increases in intergenerational mobility primarily stem from improvements in educational achievements among individuals from families at the lower end of the educational distribution, with fewer changes in rank across the educational spectrum. At the NUTS 1 level, and for the cohorts born in 1940–1959, 1960–1979 and 1980–1999, educational persistence between generations (as measured by the slope coefficient of a regression capturing the degree of association between parental years of education and the education of their children) decreased by 0.104 (from 0.459 to 0.355; paired t-test, t-statistic = 5.959, P < 0.001; 95% confidence interval (CI) = 0.070–0.139; n = 117 NUTS 1 regions) between the oldest and youngest cohorts, on average, indicating that mobility increased over the second part of the twentieth century.

However, returns to education fluctuate over time and across economies, meaning that greater educational attainment, while valuable in itself, might not automatically translate into improved economic well-being. Thus, we introduce an additional mobility indicator that accounts for these nuances. The change in mobility as measured by standardized persistence, which specifically captures alterations that affect the relative positions of families within the localized distribution of education, exhibits a minor, statistically insignificant shift (an average decrease of 0.015, from 0.415 to 0.400; paired t-test, t-statistic = 1.157, P = 0.250, 95% CI = −0.011–0.042; n = 117 NUTS 1 regions). This result is consistent with findings from other world regions^17,29,30.

However, these increases in mobility are not uniformly spatially distributed. Figure 1 illustrates the geography of intergenerational mobility of education in Europe at the regional level, using the cohort-level measures. To offer a more nuanced understanding, the figure connects intergenerational mobility, measured by the slope coefficient (persistence), to educational inequality, measured by the coefficient of variation in years of schooling for each region and cohort pair. This figure, which presents the terciled distributions of these two measures, can broadly be understood to be the ‘Great Gatsby’ map for Europe, in the spirit of Corak’s popularized graph⁴ widely known as the Great Gatsby curve.

Fig. 1. The geography of intergenerational mobility and educational inequality in Europe.

a–c, The bivariate distribution of intergenerational mobility (persistence; as measured by the slope coefficient) versus educational inequality (measured by the coefficient of variation for education) for the 1940–1959 (a), 1960–1979 (b) and 1980–1999 (c) cohorts. Higher slope coefficient values indicate higher levels of intergenerational persistence (that is, immobility). The axes indicate terciles, and the results are reported at the NUTS 1 level with the addition of Ukraine and Türkiye. The use of terciles demonstrates relative changes in position between the three periods. Sources: European Social Survey (ESS) 2002–2023; European Commission (Eurostat/GISCO), under a CC BY 4.0 licence; and ESRI, Garmin International, US Central Intelligence Agency (The World Factbook) and the National Geographic Society. Shapefiles were modified to include non-NUTS regions (Supplementary Fig. 4).

Regions with lower levels of intergenerational mobility (that is, higher levels of persistence) tend to also exhibit a relatively high degree of educational inequality, implying the co-existence of inequality both within and between generations. The Pearson correlation between intergenerational persistence and inequality in years of education across all cohorts is substantial; 0.62, 0.47 and 0.41 at the country (P < 0.001, n = 114), NUTS 1 (P < 0.001, n = 351) and NUTS 2 (P < 0.001, n = 674) levels, respectively (average estimates of persistence and standardized persistence for each cohort and country are shown in Supplementary Tables 1 and 2). Notably, country borders are clearly visible in Fig. 1, indicative of geographical discontinuities in intergenerational mobility and educational inequality. This suggests that factors that act at the country level have an important role in determining intergenerational mobility and educational inequality. The estimates also reaffirm the differences between Central and Northern Europe versus Southern and Eastern Europe, with the former having higher mobility and lower inequality, and the latter having lower mobility and higher inequality^17,29. These differences largely persist over time. The figure also reveals a notable degree of heterogeneity in intergenerational mobility within countries.

Furthermore, after transforming the cohort-level measures into composite annual measures of effective mobility using weighted contribution profiles over the lifecycle (Methods), we find that educational inequality has not substantially converged between European countries since 1985, despite relative improvements within countries over time. Between 1985 and 2020, the relative dispersion (or the ratio of the s.d. to the mean multiplied by 100) of educational inequality decreased by 2.7 and 6.8 percentage points at the cross-country level and NUTS 1 regional level, respectively (Extended Data Fig. 1). Conversely, we find evidence of a greater degree of convergence in intergenerational persistence at the country level than between regions. As Fig. 2 illustrates, over the past four decades, the relative dispersion of persistence decreased by 3.6 and increased by 0.96 percentage points at the cross-country level and NUTS 1 regional level, respectively. This regional heterogeneity underscores the importance of using this variability at the subnational level to investigate the link between intergenerational mobility and economic performance.

Extended Data Fig. 1. Distributional Changes in Educational Inequality in Europe.

Extended Data Figure 1 depicts how effective educational inequality, weighted according to the profile I weights, has changed in Europe from 1985 to 2020. Panel (A) illustrates effective educational inequality at the country level, measured by the coefficient of variation for education, in its annualized form (n = 1,296). Panel (B) illustrates the first and last observation of effective educational inequality at the NUTS 1 level (n = 107). Based on the annualized measures of effective educational inequality, Panel (A) demonstrates that educational inequality has not converged between European countries since 1985 despite relative improvements within countries over time. Further, though inter-regional disparity at the NUTS 1 level decreased, Panel (B) demonstrates this is driven by a subset of countries, with many proximate to the 45-degree line. Source: ESS 2002-2023, profile I weights are derived from life-cycle labour participation profiles, see Methods for details.

Fig. 2. Distributional changes in persistence in Europe.

a,b, Depiction of how effective persistence, weighted according to profile I cohort-participation weights (Methods), has changed in Europe over the past four decades, from 1985 to 2020. a, The effective persistence at the country level in its annualized form. n = 1,296. b, The first and last observation of effective persistence at the NUTS 1 level. n = 107. a, On the basis of the annualized measures of effective persistence, persistence has not converged between European countries since 1985. b, However, the dispersion of persistence has decreased comparatively more than at the regional level. Source: ESS 2002–2023; profile I weights are derived from life-cycle labour participation profiles (Methods).

Intergenerational mobility and innovation

In this section, we test the relationship between effective intergenerational educational mobility and innovation. To maximize subnational variation in our measures of intergenerational educational mobility, we conducted the analysis at an augmented NUTS 1 level that incorporates NUTS 2 distinctions in cases in which the NUTS 1 region corresponds to an entire country (Methods). The baseline sample (n = 233,057 observations) that we used to construct the annualized regional indices at the augmented NUTS 1 level for this application (n = 137 regions, year t = 1992 to 2020 for regions encompassed by the former Warsaw pact and 1985 to 2020 for all other regions; Methods) excludes first-generation migrants to avoid bias arising from selective international migration to high-mobility or high-innovation areas. To measure the level of regional innovation, the dependent variable, we used the inverse hyperbolic sine transformation of three measures of regional patenting activity; patent count, granted patent count and citation-weighted patent count (Methods). Over the past four decades, there has been substantial variation in regional trajectories for these measures, as illustrated in Extended Data Fig. 2.

Extended Data Fig. 2. Distributional Changes in Patenting Activity in Europe.

Extended Data Figure 2 depicts how patenting activity has changed in Europe over the last four decades, from 1985 to 2020. Panel (A) illustrates patenting activity at the country level (n = 1,248), while Panel (B) illustrates patenting activity at the NUTS 1 level (n = 3,901). Based on this figure, Panel (A) demonstrates that while overall patenting activity has increased over time for some countries, there is a large degree of variation in the extent to which this is true more generally. Further, variation is much larger at the regional level than the country level, as evidenced in Panel (B). Source: PATSTAT 2024a extract.

Table 1 presents our preferred estimates, whereby the degree of intergenerational persistence, the main independent variable, is measured by the slope coefficient, and innovation is measured in terms of patent count. The relationship between persistence and innovation is consistently negative (two-sided Wald tests, P < 0.002 for all specifications), even after we control for a range of potential covariates (Supplementary Table 3; correlation coefficients for the covariates are presented in Supplementary Table 4). Equivalently, our results show that higher levels of intergenerational mobility (that is, a weaker association between parents’ and children’s education) are strongly associated with more innovation. With the inclusion of covariates, the coefficient of interest decreases in magnitude, but nevertheless remains both statistically significant and substantial in size (preferred specification coefficient in Table 1 (column 3), −1.997; two-sided Wald test, z = −5.29, P < 0.001, 95% CI = −2.737 to −1.257, n = 4,623). This relationship holds even in our more parsimonious model specifications, which incorporate region and time fixed effects or country-specific time trends (coefficient in Table 1 (column 4), −0.928; two-sided Wald test, z = −3.03, P < 0.002, 95% CI = −1.528 to −0.328, n = 4,623) that greatly contribute to explaining the variation in the number of patents (as evidenced by the notable increase in the adjusted R² values, from 0.269 without fixed effects or time trends in Table 1 (column 2) to 0.968 (column 4)).

Table 1.

Intergenerational mobility and innovation at the augmented NUTS 1 level

	1	2	3	4
Intergenerational persistence (slope coefficient)	−5.273***	−3.476***	−1.997***	−0.928***
s.e.	0.258	0.272	0.378	0.306
P	0.000	0.000	0.000	0.002
Cohort controls		X	X	X
Cohort-specific initial conditions		X	X	X
Contemporary controls		X	X	X
Year fixed effects			X
Regional fixed effects			X	X
Country-specific time trend				X
Observations	4,659	4,623	4,623	4,623
Adjusted R2	0.102	0.269	0.939	0.968
Elasticity	−2.316	−1.527	−0.877	−0.408

A subset of the complete set of specifications is shown in Supplementary Table 5. The sample consists of n = 137 regions (column 1) and n = 136 regions (columns 2–4) over time (year t = 1992 to 2020 for regions encompassed by the former Warsaw pact, and 1985 to 2020 for all other regions; Methods). The dependent variable is the inverse hyperbolic sine-transformed patent count. Persistence is measured by the slope coefficient, applying profile I cohort-participation weights (Methods). Cohort controls are the average and coefficient of variation of years of education. Cohort-specific initial conditions include a summary indicator for historical precipitation, temperature, sea level pressure, relative humidity, wind speed and global radiation associated with the respective cohorts. Both cohort controls and cohort-specific initial conditions are also transformed into annualized composite scores, weighted using profile I cohort-participation weights. Contemporary controls include variables indicative of structural transformation and local development⁴⁸. The last row shows the elasticity computed using the regression coefficient³¹. s.e. values were obtained by bootstrapping with 100 replications. P values were calculated using two-sided Wald tests; ***P < 0.01. Our calculations; data sources are described in the Methods.

To interpret the size of this association, we estimate the elasticity derived from the point estimate³¹. A decrease in the slope coefficient by 0.1, which is very close to the average change experienced by European regions from the oldest to the youngest cohort in our sample, is associated with a positive change in the number of patents of between 4% and 23% (Table 1).

Alternative specifications estimated, for example, using (1) granted patents and citation-weighted patents as the dependent variable; (2) standardized persistence as the main independent variable; (3) alternative weighting schemes when constructing the annualized measures of mobility; and (4) mobility indices computed based on alternative samples that additionally exclude or include those with a migration background (Supplementary Tables 6–10, respectively) are robust and consistent with the results in Table 1.

The results of a further series of tests, considering the three different definitions of the dependent variable (patent count, granted patent count, citation-weighted patent count), the two measures of intergenerational persistence (persistence and standardized persistence), the iterative inclusion of covariates (described in Supplementary Table 3) corresponding to seven regression specifications (Supplementary Table 5), five weighting profiles and using two different samples to construct the cohort-level measures of intergenerational persistence ((1) excluding first-generation migrants only; and (2) additionally excluding individuals with a migration background, respectively), are reported in Extended Data Fig. 3. Overall, we obtained 420 additional estimates, and corresponding elasticities, for (1) all specifications and (2) our preferred specification (Table 1 (column 3)).

Extended Data Fig. 3. Comparison of Application Regression Specifications.

Extended Data Figure 3 shows the distribution of all coefficients and elasticities obtained from additional estimations, based on a convex combination of three different definitions of the dependent variable (patent count, granted patent count, citation-weighted patent count), two metrics of intergenerational persistence (persistence and standardized persistence), the iterative inclusion of covariates (described in detail in Supplementary Information Table S3) corresponding to the seven regression specifications (see, e.g., Supplementary Information Table S5), five weighting profiles, and using two different samples to construct the cohort-level measures of intergenerational persistence (i.e., i. excluding first-generation migrants only, and ii. additionally excluding individuals with a migration background). Panel (A), which presents the results of 420 estimations, shows the results of this exercise for all seven possible regression specifications, including those without controls, such that the seven specifications correspond to the specifications reported in, e.g., (columns 1–7) of Supplementary Information Table S5 (i.e., the full set of our preferred results). Panel (B) shows only the resulting 60 estimates obtained via our preferred specification (i.e., including the same control variables as (column 3) of Table 1 in the main text). Reported shares of significant estimates are based on standard errors obtained by bootstrapping with 100 replications and refer to two-sided Wald tests for each regression coefficient with P < 0.1.

Of all estimates, approximately 89% are negative and significantly different from zero (that is, two-sided Wald tests with P < 0.1), with an average elasticity of around 14%. For our preferred specification, all estimates are negative and significant (two-sided Wald tests with all P < 0.01), with a slightly lower average elasticity of around 11%. In Extended Data Fig. 4, we demonstrate how the iterative inclusion of controls affects these estimates. In general, we provide robust evidence that the positive impact of improved intergenerational mobility on innovation is both substantial and economically significant.

Extended Data Fig. 4. Comparison of Application Regression Specifications.

Extended Data Figure 4 shows the distribution of all coefficients obtained from 420 estimations (similar to Panel (A) of Extended Data Fig. 3), using three different definitions of the dependent variable (patent count, granted patent count, citation-weighted patent count), two metrics of intergenerational persistence (persistence and standardized persistence), and using two different samples to construct the cohort-level measures of intergenerational mobility (i.e., the baseline sample, which excludes first-generation migrants, and the sample that additionally excludes those with a migration background). The legend depicts the iterative inclusion of control variables (for the covariates described in Supplementary Information Table S3), such that the seven specifications correspond to the specifications reported in, e.g., (columns 1–7) of Supplementary Information Table S5 (i.e., the full set of our preferred results). Significance levels based on two-sided Wald tests for each regression coefficient.

As an additional validation of our results, we also consider an alternative estimator designed for handling non-negative count-dependent variables, such as patents (Methods). When we replicated the series of tests with this alternative estimator (Supplementary Fig. 5), the negative relationship between persistence and innovation held for the majority of estimates, although for a smaller share (approximately 52%, two-sided Wald tests with P < 0.1) than with our main estimator. Notably, further analyses (Supplementary Fig. 6) reveal that the presence of statistically insignificant or positive estimates is primarily driven by major innovation hubs, that is, European regions within the top 10% of the patent count distribution throughout our observation period. Among this subsample of innovation hubs, and when we apply both estimation procedures, the obtained coefficients and corresponding elasticities are rather dispersed with a high s.d. In contrast to the results for the regions outside of these hubs, those associated with these historically entrenched innovation hubs point to a weak or even negative relationship between intergenerational mobility and innovation.

There are several potential explanations for this localized heterogeneity. First, major innovation hubs did not emerge during our observation period; rather, they are the outcome of decades-long historical development processes driven by factors that predate our analysis^32–34. Although intergenerational mobility might have been one of these factors, it no longer appears to be a key driver of innovation at extremely high levels of patenting activity. Second, building on this perspective, the mechanisms through which intergenerational educational mobility affects innovation may fundamentally differ between innovation hubs and non-hubs. Mechanically, a higher level of educational mobility allows more individuals to acquire the skills necessary for participating in innovation. In non-hubs, disadvantaged individuals with high latent ability, who were previously structurally excluded, are then able to engage in patenting activities. By contrast, in hubs, the local talent pool is probably already large enough such that innovation outcomes in these regions depend more strongly on agglomeration economies, dense knowledge spillovers, the concentration of highly productive inventors and the broader institutional and policy environment³⁵. This interpretation is consistent with existing evidence that shows that both growth and frontier innovation are disproportionately driven by upper-tail knowledge rather than by increases in average human capital³⁶.

Third, the strongly skewed distribution of inventor productivity may also have a role, with previous literature documenting that (1) a very small fraction of inventors and scientists accounts for a disproportionate share of patents and scientific production^37–39; and (2) highly productive inventors disproportionately come from advantaged family backgrounds, reflecting the intergenerational transmission of human capital, early exposure to innovative environments, and privileged access to elite educational and professional networks^27,40,41. In innovation hubs, rising intergenerational mobility may therefore alter the compositions of inventor cohorts and therefore lead to a temporary decline in patenting growth. Taken together, these mechanisms help to explain why, in major innovation hubs, the relationship between educational mobility and patenting activity may be statistically insignificant or even negative.

Finally, we conducted two analyses that investigate potential nonlinearities in the relationship between intergenerational educational mobility and innovation. First, we tested whether the average association between persistence and innovation is related to the initial level of intergenerational persistence. Figure 3 illustrates the shape of the response functions predicting innovation in response to changes in persistence over time at the regional level, and demonstrates that the slope is steepest for those regions that had higher levels of persistence at the beginning of the observation period (Fig. 3c,d) and in which persistence has improved substantially over time. However, the shape of this relationship differs from the average for those regions that had initially lower levels of persistence (Fig. 3b) (two-sided Wald test for seemingly unrelated regressions, χ² = 708.52, P < 0.001, n = 4,935). Second, we allow persistence to enter the analysis in a flexible, nonparametric manner by estimating variants of our preferred specification across flexible bins of the independent variable. The estimated outcomes, presented in Supplementary Figs. 7 and 8, confirm the overall pattern suggested in Fig. 3. The marginal returns to intergenerational mobility are increasing for high and medium levels of persistence (that is, when intergenerational mobility is lower), but are diminishing or even slightly revert for low levels of persistence. This evidence suggests that improvements in intergenerational mobility are particularly beneficial for economic performance in more strongly stratified societies in which mobility is low, whereas further increases when mobility is already high do not necessarily reflect additional gains in equality of opportunity or a more efficient allocation of talent.

Fig. 3. Intergenerational mobility and predicted innovation at the augmented NUTS 1 level.

a–d, Each line represents annual data for a region within a European country. Innovation is predicted on the basis of regression specification 3 in Table 1, where innovation is captured by the inverse hyperbolic sine-transformed patent count. This figure is plotted against intergenerational persistence (the slope coefficient) after application of profile I cohort-participation weights (Methods) for all regions (a) and those regions in the low (b), medium (c) and high (d) terciles of persistence in the baseline period in 1985. The share of regions in each tercile by country is shown in Supplementary Table 17. The markers indicate the most recent observation to indicate the direction of changes in mobility. Each panel also shows the linear regression line of the relationship and the respective 95% CI based on default s.e. values. Source: ESS 2002–2023; profile I weights are derived from life-cycle labour participation profiles (Methods).

This pattern may also reflect the existence of distinct phases in the development of educational mobility: (1) an initial phase in which educational attainment is generally low and highly persistent across generations, limiting innovation; (2) a transitional phase, in which younger generations begin to attain higher levels of education than their parents, leading to greater mobility and, potentially, a surge in innovation; and (3) a maturation phase, in which educational expansion means that most of the population completes a higher level of education, on average, and changes in educational persistence are stagnant or even reverse due to saturation or declining returns to education. These results suggest that the positive association between mobility and innovation is strongest during the initial and intermediate phases. One possible explanation is that of rising aspirations, whereby children increasingly envision educational and occupational trajectories beyond those of their parents, which may in turn act as a driver of innovation and productivity^42,43.

Conclusions

Theoretical models and empirical research suggest that intergenerational mobility is a driver of economic development. Here we present EUROPE-IGM-ATLAS, a longitudinal database of indices for intergenerational mobility in European regions. With this database, we analyse how intergenerational mobility has developed over time at the microregional level and identify substantial regional disparities. Moreover, in an application of our indices, studying the mobility–innovation nexus, we find suggestive evidence that intergenerational mobility fosters innovation—a main driver of economic growth in developed economies⁴⁴—particularly in regions with low to medium initial levels of intergenerational mobility and which have not (yet) evolved into major innovation hubs.

This result is highly relevant for policy stakeholders as it emphasizes the importance of better exploiting the existing talent pool to generate economic growth, underscoring the argument that improving equality of opportunity contributes to a better allocation of talent and abilities, and eventually improves the efficiency of economic systems^45–47. Our findings are derived from analyses conducted at the subnational level. Thus, although we cannot entirely dismiss the potential influence of unobserved sources of heterogeneity not accounted for in our estimations, these findings, along with the data source that we provide, substantially contribute to our understanding of the relationship between intergenerational mobility and economic performance.

The EUROPE-IGM-ATLAS database opens up various paths for future research. The indices that we developed enable researchers to measure effective intergenerational mobility of education, educational inequality and average education over time and space, thereby filling a major gap in existing databases. As a further contribution with respect to previous studies, we provide three different versions of our mobility indices, based on different samples: (1) including only individuals born in their country of residence; (2) excluding all individuals with a migration background; and (3) including all migrants. The indices have great potential in various empirical applications that aim to study the relationships between equality of opportunity, economic inequality and indicators of socioeconomic development at multiple spatial scales.

Methods

Materials

The first stage of this paper, the construction of the EUROPE-IGM-ATLAS, relies on harmonized cross-country individual-level survey data. The second stage, an application of our database in which we use the indices to investigate the relationship between intergenerational mobility and innovation, relies on aggregate datasets from several sources discussed below. These include proxies for innovation and localized controls for initial economic conditions.

To estimate intergenerational mobility of education, we use 11 waves of the ESS conducted between 2002 and 2023. The ESS is a representative cross-national survey in which 40 countries have participated in at least one round since the 2002/2003 wave. Importantly, it includes questions about the level of education and retrospective questions on parental education, therefore enabling us to measure intergenerational mobility while avoiding the bias associated with selectivity in co-residency samples⁴⁹. We pool all survey waves and apply survey design weights, normalizing the weights to make them consistent across waves³⁰. Furthermore, we restrict our sample to respondents who were at least 22 years old, and were therefore likely to have completed their education, when the survey was conducted. The analysis could be sensitive to this restriction if individuals had not yet completed their educational career. Suitable robustness checks imposing different age restrictions (for example, older than 25) yield no significant changes in the resulting estimates.

We operationalize our definition of migrants in two ways; (1) first-generation migrants, who were not born in their country of residence; and (2) second-generation migrants, those with an indirect migration background either because their parents were first-generation migrants or because they do not possess the citizenship of their country of residence. We use these definitions to construct three versions of our indices: (1) excluding first-generation migrants only; (2) excluding both first- and second-generation migrants; and (3) including migrants. As migration could be endogenously related to both human capital allocation and economic performance within regions⁵⁰, in our main application, we use the version of our indices obtained by excluding first-generation migrants, giving us a total sample size of 257,919 individuals. Estimations based on the two alternative samples (that is, the sample excluding individuals with a migration background and the one including both natives and migrants) yield consistent results (Supplementary Table 10). In general, see Supplementary Table 11 for clarification on database versioning.

To compute estimates at the subnational level, we use information about the region of residence of ESS respondents (that is, their geographical location of residence in adulthood at the time the survey was conducted). Regional information in the ESS is recorded using country-specific administrative codes that correspond to varying levels of the NUTS (Nomenclature of Territorial Units for Statistics) classification system. Participating countries provide regional identifiers at different hierarchical levels, with some countries coding at NUTS 1, some at NUTS 2, and others at NUTS 3. Moreover, there have been temporal changes in NUTS boundaries, particularly at smaller spatial scales. This creates substantial heterogeneity in regional granularity both within and across survey waves.

To achieve consistent cross-national and cross-temporal comparability, we implement a harmonization procedure. We compute estimates at both the NUTS 1 and NUTS 2 levels where possible. Thus, for countries who code at the NUTS 3 level, we aggregate upward. For regions where NUTS 2 boundaries changed substantially between survey rounds, we do not provide NUTS 2 level estimates, instead further aggregating to the more stable NUTS 1 classification to preserve temporal consistency. The version of the NUTS that serves as the basis of our harmonized definition of regional unit is the 2016 version, with the exception of Poland—which is included based on the 2008 NUTS boundaries due to regional divisions in later versions of NUTS. Our definition of regional boundaries is further augmented by the addition of non-EU countries, such as Serbia, Kosovo, Montenegro and so on. A cartographical depiction is shown in Supplementary Fig. 4.

The NUTS classification system is particularly useful for cross-national and cross-regional comparability purposes due to the statistical consistency of NUTS units. However, it is important to note that NUTS regions may not always align with regional policymaking structures.

Measuring innovation

To measure regional innovation, our main outcome variable of interest, we rely on patenting as an established indicator of innovation performance⁵¹. We retrieve patenting data from the European Patent Office’s (EPO) Worldwide Patent Statistical Database (PATSTAT, version 2024a) and construct three hierarchical measures of regional innovation: (1) patent count as a proxy for the regional quantity of innovation activities regardless of their quality; (2) granted patent count as a proxy for the regional quantity of innovation that surpasses a certain legal quality threshold; and (3) citation-weighted patent count, as a proxy for the economic value of regional innovation. In constructing these measures, we closely follow relevant guidelines and the prior literature^52,53.

Specifically, we focus on EPO and World Intellectual Property Office (WIPO) filings, prioritizing EPO filings over WIPO filings. We consolidate applications at the patent family level and select the earliest filing year as the year of invention. To assign patents to NUTS regions, we use information from PATSTAT on geocoded patent inventor locations, which reflect the location where the innovation activity took place. If a patent lists inventors from more than one region (for example, one from region A and another from region B), we apply fractional counting (that is, we assign 0.5 of the patent to region A and 0.5 to region B). We consider all patent applications from 1985 (the first year available with a one-year lag in our contemporary controls, see the ‘Covariates’ section) until 2020 (the last year that ensures a complete citation window for all patents when constructing citation-weighted patent count, given availability in the 2024a version of PATSTAT).

Our three innovation measures are formally defined as follows. First, raw patent counts are the unweighted, fractional count of patent applications⁵⁴:

$${\mathrm{PC}}_{\mathit{rt}}^{\mathrm{RAW}}=\sum _{p=1}^{N_{\mathit{rt}}}{z}_{\mathit{pr}}$$ 1

where ${\mathrm{PC}}_{\mathit{rt}}^{\mathrm{RAW}}$ denotes the unweighted, fractional count of patent applications in region r and year t; N_rt denotes the number of patent applications in region r and year t; and z_pr denotes the fraction of inventors of patent p located in region r.

Second, granted patent counts are the unweighted, fractional count of granted patents⁵⁵:

$${\mathrm{PC}}_{\mathit{rt}}^{\mathrm{GRN}}=\sum _{p=1}^{N_{\mathit{rt}}}{z}_{\mathit{pr}}\times g_p$$ 2

where ${\mathrm{PC}}_{\mathit{rt}}^{\mathrm{GRN}}$ denotes the unweighted, fractional count of granted patents in region r and year t, and g_p denotes whether a patent p was granted (g_p = 1) or not (g_p = 0).

Finally, citation-weighted patent counts are the fractional count of patent applications with citation weights residualized on application year and World Intellectual Property Organization (WIPO) technology field⁵⁶:

$${\mathrm{PC}}_{\mathit{rt}}^{\mathrm{CIT}}=\sum _{p=1}^{N_{\mathit{rt}}}{z}_{\mathit{pr}}\times {\sum }_{f=1}^{35}\frac{v_{\mathit{pf}}{C}_p}{{\left({\sum }_q^t{v}_{\mathit{qf}}\right)}^{-1}\times \left(\sum _q^{N_t}{v}_{\mathit{qf}}{C}_q\right)}$$ 3

where ${\mathrm{PC}}_{\mathit{rt}}^{\mathrm{CIT}}$ denotes the citation-weighted, fractional count of patent applications in region r and year t, and C_p denotes the number of forward citations a patent p has received within 36 months following publication. Each patent p belongs to one or more of 35 WIPO technology fields f (ref. ⁵⁷), where v_pf denotes the weight of technology field f for patent p. The numerator of the summand of the second summation in equation (3) therefore indicates the number of patent p’s citations that can be attributed to technology field f. The denominator, where N_t denotes the total number of patent applications in year t, measures the average number of forward citations that patents q applied for in year t in technology field f receive within 36 months after publication, applying the same technology-field weighting logic as the numerator. To allow for a complete citation window, in our application we consider patent applications until 2020.

Covariates

To construct control variables for contemporary regional economic conditions, we use surface groups derived from daytime satellite imagery⁴⁸, as a proxy for regional economic activity. These data are publicly available at https://www.swissubase.ch/de/catalogue/studies/20253/19048/overview. Using machine-learning techniques, the authors classify annual composites of Landsat satellite pixels from 1984 through 2020 into six different categories that describe terrestrial features of the earth with similar surface characteristics, the surface groups (built-up land, grassland, cropland, forest, land without buildings or vegetation and water). These surface groups can be aggregated at any regional level and explain a large part of the variation in regional economic activity even at low levels of aggregation⁴⁸. We aggregate the surface groups to modified nested EUROSTAT NUTS boundary shapefiles, which were modified to include non-EU countries that participate in the ESS, that is, Montenegro, Bosnia, Kosovo, Ukraine and so on (Supplementary Fig. 4). This procedure provides us with a measure of regional economic activity that covers a longer time series than other proxies, such as night light intensity.

At the same time, these measures allow us to control for regional population dynamics, such as those arising due to interregional migration, to mitigate the risk that systematic within-country migration issues may bias our estimates. As internal migration may lead to a non-random distribution of individuals across regions—as people with certain characteristics are more likely to move to specific areas—such selective mobility can generate a sorting mechanism that is similar to that observed in international migration, whereby individual self-selection affects both the composition of regional populations and their economic performance.

To demonstrate that these surface group measures are strongly associated with regional economic activity and population dynamics in our setting, we replicate the analyses⁴⁸ for the regions and years included in our preferred specification (Table 1 (column 3)), and for which gross domestic product (GDP) data were available. To do so, we use Eurostat data from June 2022, for which the NUTS territorial status version (2016) aligns with the one we apply in our construction of mobility indices and application to regional innovation. First, a regression of log-transformed annual GDP (in million euros) on the log-transformed pixel counts per surface group, including year fixed effects and country fixed effects, demonstrates that the surface groups explain 79.5% (adjusted R²) of the variation in log-transformed GDP (Supplementary Table 12 (column 1)). Similarly, using log-transformed population (inferred from dividing annual GDP in euros by annual GDP per inhabitant) as the dependent variable reveals that the surface groups explain 84.1% of the variation in log-transformed population (see Supplementary Table 12 (column 2)). Together, these results suggest that the surface groups measures capture relevant dimensions of regional economic activity and population dynamics.

We used the E-OBS database⁵⁸ to control for cohort-specific initial conditions, or the past level of economic development that could have a direct effect on both intergenerational mobility, as well as future innovation and economic performance⁵⁹. The database provides daily gridded land-only observational data for Europe, including blended time-series measures of precipitation, temperature, sea level pressure, relative humidity, wind speed and global radiation from 1950 to 2022. As historical data on economic development are not available at the regional level for all European countries in our sample, we aim to approximate the variation in economic conditions faced by cohorts using early-life weather conditions, which have been shown to have persistent effects on socioeconomic outcomes and economic growth^60,61. Simple area weighting is used to estimate attributes at the regional level, conditional on the intersection of gridded observations and NUTS boundaries based on modified nested EUROSTAT NUTS boundary shapefiles (Supplementary Fig. 4). By construction, this assumes a uniform distribution of the within-grid cell daily average. These daily averages are used to construct average conditions by region and birth cohort (for example, 1940–1959, 1960–1979 and 1980–1999).

Estimating intergenerational mobility

We estimate the degree of intergenerational mobility of education for three cohorts—1940–1959, 1960–1979 and 1980–1999—by regressing the years of education of individuals on those of their highest educated parent, controlling for sex and survey year fixed effects⁶². The subdivision of the sample into three cohorts enables us to estimate intergenerational educational mobility with a sufficiently large sample size of individuals for each country and region. In the case of missing information for one parent, we use the level of education of the available parent. As years of schooling varies between countries, we use modified ISCED measures to generate a harmonized measure of years of schooling. Using the ESS-ISCED measure, available from wave 5 onward, as the basis, we harmonize observations from earlier waves (Supplementary Tables 13 and 14), and assign an ordinal scale (Supplementary Table 15).

We refer to this indicator of intergenerational mobility as the slope coefficient. However, given potential distributional differences between the two generations, we additionally multiply the slope coefficient with the ratio of s.d. of parents’ and children’s years of education to obtain a measure of standardized persistence. These two measures are non-directional and origin-independent, capturing both upward and downward movements across the entire distribution. In both cases, the higher the indicator, the lower is intergenerational mobility. Both measures are standard in the literature on intergenerational educational mobility and constitute valuable summary indicators for equality of (educational) opportunity^63,64. Furthermore, educational mobility measures are strongly correlated with income mobility⁶³. To test the consistency of our estimates, we compared our country-level indicators with those included in the World Bank’s Global Database on Intergenerational Mobility¹⁷. Reassuringly, at the cohort-country level, the Pearson correlation coefficient is 0.86 for years of education (P < 0.001; n = 105), and 0.66 for intergenerational mobility (P < 0.001; n = 105).

In our application, a selection of our results using the slope coefficient (persistence) is shown in Table 1, and all specifications are presented in Supplementary Table 5. Those using standardized persistence (Supplementary Table 7) are consistent with the main findings.

Constructing an annualized panel

To link past intergenerational mobility with contemporary economic changes, the cohort-specific mobility indicators and cohort-specific initial conditions are transformed into annual time-series measures whereby the indicator value of a given cohort is weighted by the expected contribution of cohort members to the economy in a given year¹⁴. For example, to compute the profile I weights that can be attributed to a given cohort for each year, we use the share of each cohort’s expected effective labour supply over the total effective labour supply in a given year based on per-capita effective labour profiles over the life cycle⁶⁵. We therefore define the measures obtained using this methodology as indicators of effective mobility. To permit robustness testing of the results from our application, investigating the relationship between mobility and innovation, we also applied four alternative weighting procedures.

For profile II and III weights, we used innovation life-cycle profiles first for all patenting activity and, second, for highly cited patenting activity, respectively⁶⁶. For profile IV and V weights, we used the Luxembourg Income Study (LIS) database, accessed through LISSY, to construct cohort–year–country contribution profiles for both employment and total individual income. The results are consistent across all weighting schemes. We present results obtained using the effective labour supply weights in the main text, those derived from innovation life-cycle profiles and LIS-derived employment, and income measures are shown in Supplementary Tables 8 and 9 for persistence and standardized persistence, respectively.

The variation across years and regions is given by the interaction between intergenerational mobility and the weight, while, by construction, the methodology used to compute the effective measure of mobility P allows us to test one side of the relationship between intergenerational mobility and innovation while avoiding issues related to reverse causality. Thus, the association between intergenerational mobility and innovation in the estimations is driven by younger cohorts entering the labour market and gaining labour market experience, while older cohorts age and correspondingly reduce their labour force participation¹⁴.

The transformation of cohort-specific mobility measures into composite annual measures gives an index, which we define as our measure of effective mobility:

$$P_{\mathit{rt}}=\sum _{c=1}^C{w}_{\mathit{ct}}{p}_{\mathit{cr}}$$ 4

where the intergenerational persistence index P in region r for each year t is the weighted average mobility of people born in cohort 1940–59 (c = 1), 1960–79 (c = 2) or 1980–99 (c = 3), that is, the sum of the persistence of each cohort (p) multiplied by the respective cohort-participation weight (w). Hereby, the three weights sum up to one for each year.

Supplementary Fig. 1 depicts the age-participation profiles used to apply the aforementioned procedure for profile I–III weights. Using per-capita effective labour profiles over the life cycle as an example, w_ct is the share of the cohort’s effective labour over the total effective labour supply in a given year.

After computing the relative contribution by age as an integral fraction of the respective participation profile, absolute cohort weights at time t are computed by cohort as a sum of the contribution of the in-range ages in year t (for example, in t = 2007, the oldest members of c = 1 are no longer in range). Relative cohort weights are then computed as the share of the cohort weight in t over the sum of cohort weights in t yielding w_ct. For profile I–III weights, Supplementary Fig. 2 shows the respective weights for each cohort in every year.

For profile IV and V weights, extractions from the LIS database were used to directly compute relative cohort weights as the share of a given cohort’s contributions to the economy in country n at time t over the sum of all contributions in nt yielding w_nct, such that:

$$P_{\mathit{rt}}=\sum _{c=1}^C{w}_{\mathit{nct}}{p}_{\mathit{cr}}$$ 5

We do this for both relative employment shares (profile IV) and relative total individual income shares (profile V), as depicted in Supplementary Fig. 3. In contrast to profile I–III weights, this permits cross-country variation in the weighting procedure.

Application: empirical strategy

Using the weighted panel measures described previously, we test whether higher levels of intergenerational mobility are associated with innovation at the regional level. To do so, we estimate a linear panel regression based on the time series for each region, including confounders potentially affecting the relationship between the two variables (all covariates are described in Supplementary Table 3; the correlation matrix for the covariates used in our main specification is shown in Supplementary Table 4). For regions encompassed by the former Warsaw Pact countries with the addition of the former Yugoslavia and East Germany, we limit the time series to 1992 onward to account for potential patent data mismeasurement arising from inconsistent reporting to PATSTAT. For all other regions, the time series begins in 1985.

The fully saturated regression specification takes the form:

$$Y_{\mathit{rt}}=\alpha +\delta P_{\mathit{rt}}+{\theta \mathbf{X}}_{\mathit{rt}-1}+\Psi {\mathbf{I}}_{\mathit{rt}}+{\tau }_t+{\gamma }_r+{\epsilon }_{\mathit{rt}}$$ 6

where Y is innovation in region r and year t. P is the degree of intergenerational persistence, as a weighted average of the persistence of the three cohorts (as previously described). X is a vector of contemporary controls for region-specific characteristics in t − 1, namely proxy measures for local economic activity extracted from daytime satellite imagery collected via Landsat satellites⁴⁸. l is a vector of controls for cohort-specific characteristics: average years of education, and the coefficient of variation for years of education, and cohort-specific initial conditions, again as a weighted average across the three cohorts. To reduce dimensionality, the cohort-specific initial conditions are included as a single-index variable, summarizing precipitation, temperature, sea level pressure, relative humidity, wind speed and global radiation using factor analysis. Fixed effects are included for year (${\tau }_t$) and region (${\gamma }_r$), and in one specification, we additionally control for country-specific time trends by including country dummies interacted with a linear time trend, instead of time fixed effects. $\epsilon$ is the error term.

In this analysis, we define regions r as an augmentation of the NUTS 1 level, taking a three-step hierarchical approach to spatial scale: (1) countries in which the NUTS 0, NUTS 1 and NUTS 2 levels are identical (that is, they comprise the entire country) enter the analysis as entire countries (for example, Cyprus and Montenegro). (2) For countries where the NUTS 0 and NUTS 1 levels are identical (that is, the NUTS 1 but not the NUTS 2 level encompasses the entire country), we use the NUTS 2 definition of regions to define the subnational level (for example, the Czech Republic, Ireland and Switzerland). (3) For all other countries, we use the NUTS 1 subnational level (for example, Germany, Poland and the United Kingdom). The augmented NUTS 1 level therefore represents subnational regions whenever possible. Supplementary Fig. 4c depicts the augmented NUTS 1 level, corresponding to 148 regional units. Supplementary Fig. 9 illustrates the (unweighted) number of observations in the ESS pooled data used to construct the weighted cohort-level estimates of intergenerational educational mobility for the baseline sample at the augmented NUTS 1 level.

For our main analysis, we use the version of the EUROPE-IGM-ATLAS that excludes first-generation migrants. A subset of results obtained using profile I weights for effective labour contributions over the lifecycle are presented in Table 1, examining the relationship between the slope coefficient persistence and innovation captured by the inverse hyperbolic sine transformation of the number of patents. The results with all regression specifications are presented in Supplementary Table 5. In Supplementary Table 6, we alternatively measure innovation using granted patents and citation-weighted patents. In Supplementary Table 7, we alternatively use standardized persistence as our measure of persistence. In Supplementary Tables 8 and 9, we examine the relative robustness of our results to the weighting procedure, using the annualized indices computed based on alternative weighting profiles for persistence and standardized persistence, respectively.

Application: additional considerations

The results of a further series of tests, considering the three different definitions of the dependent variable (patent count, granted patent count, citation-weighted patent count), the two measures of intergenerational persistence (persistence and standardized persistence), the iterative inclusion of covariates (described in Supplementary Table 3) corresponding to seven regression specifications (Supplementary Table 5), the five weighting profiles and using two different samples to construct the cohort-level measures of intergenerational persistence ((1) excluding first-generation migrants only, and (2) additionally excluding individuals with a migration background, respectively), are reported in Extended Data Fig. 3. Extended Data Figure 3a presents the results of this procedure, demonstrating the distribution of 420 estimated coefficients and corresponding elasticities. In Extended Data Fig. 3b, we limit these to our preferred specification only (Table 1 (column 3) and Supplementary Table 5 (column 6), respectively). In Extended Data Fig. 4, we demonstrate how the iterative inclusion of controls affects these estimates.

Furthermore, in Supplementary Table 10, we report estimates for the two alternative versions of the database, for which our indices were computed using different sample restrictions. Supplementary Table 10a presents results for a sample that excludes both first- and second-generation migrants, while Supplementary Table 10b includes both migrants and non-migrants. However, while both are consistent with the baseline analyses, we regard Supplementary Table 10b as the least consistent owing to potential selection biases (given, on one hand, that the education outcomes of first-generation migrants are potentially unaffected by the localized opportunity structure conditional on age-at-migration and, on the other hand, that selective migration to high opportunity and highly innovative areas is probably endogenous).

Next, to investigate to what extent the labour-force contribution weights that we use to construct our annualized measures of persistence contribute to the variation of the regressor, we conduct two analyses. First, we decompose the variation in persistence (P), our main independent variable, in our regression sample according to the law of total variance. The results of this decomposition, presented in Supplementary Table 18, reveal that, across all five weighting profiles, the cohort-specific mobility measure (p) explains a much larger proportion of the total variance in our main independent variable than the contribution weights (w). That is, the variation in the regressor is not primarily driven by the contribution weights. Second, we use procedures from the literature on shift-share instrumental variables^67,68 to analyse which components of the regressor contribute to its variation. The results of this analysis, presented in Supplementary Fig. 10, reveal that all cohorts contribute fair shares to the regressor’s variation and that no single cohort or year predominantly drives this variation.

Moreover, as our dependent variables represent fractional counts, as an alternative estimator we consider Poisson pseudo maximum likelihood (PPML) with untransformed independent variables. The PPML estimator is particularly well suited to fractional count dependent variables that include zero values, and also accounts for a multiplicative and heteroskedastic data-generating process, which can occur in patent count data⁶⁹. However, PPML and other related generalized linear models with log link have been found to be more sensitive to the influence of observations with extreme values^70–72, which in our data occur due to regional differences in the level of patenting activities. Therefore, the PPML results could differ from our main results if, for example, our main regression does not adequately reflect the data-generating process underlying patent counts, or if a few extreme observations exert large influence.

Replicating our baseline analyses using the PPML estimator, the full set of PPML results in Supplementary Fig. 5 reveals a high but smaller share of statistically significant negative estimates (52%, two-sided Wald tests with P < 0.1), and a non-negligible share of statistically significant positive estimates (24%) compared with those estimated using linear regressions with inverse hyperbolic sine transformed dependent variables (89% statistically significant negative estimates, no significant positive estimates). To test whether this difference in the results originates from few influential observations, we divide our sample into two subsamples based on the distribution of patent count averaged over our observation period at the augmented NUTS 1 regional level, such that every region in our sample is unambiguously assigned to one of the two subsamples. The first subsample comprises regions in the top 10% of the distribution (that is, potentially extreme observations with high influence—or innovation hubs) and the second subsample comprises the remaining regions. Supplementary Fig. 6 shows the elasticities obtained from the subsamples and those obtained with the full sample. Supplementary Fig. 6a reports results from linear estimation using the inverse hyperbolic sine-transformed dependent variables, while Supplementary Fig. 6b presents the corresponding PPML estimates.

The results show that the distribution of PPML estimates in the non-hub sample (90% of the observations) resembles that of the baseline analysis very closely, with a substantially higher share of negative and significant estimates (66%). Notably, innovation hubs behave differently. For innovation hubs, the shares of significant positive estimates are higher than the shares of significant negative estimates (71% versus 6%) while the elasticity distributions are more widespread—a pattern that the linear estimates for this subsample also confirm (57% significant positive estimates versus 20% significant negative estimates). These differences in the results between the two subsamples support the explanation that the overall differences between our main results and the PPML results stem from few observations exerting a high degree of influence. Overall, the results support the conclusion that intergenerational educational mobility is positively associated with innovation across most regions in our sample, while major innovation hubs constitute an important exception. We discuss potential explanations for this phenomenon in the main text.

Finally, drawing on the suggestive evidence in Fig. 3 as motivation, we examine potential nonlinearities in the relationship between intergenerational mobility and innovation by allowing persistence to enter the analysis in a flexible, nonparametric way. We estimate variants of our preferred specification and compute predicted outcomes across flexible bins of the independent variable, retaining the full set of covariates as well as year and region fixed effects. Supplementary Figs. 7 and 8 present the resulting patterns separately for the three dependent variables (patent count, granted patent count and citation-weighted patent count) and for both linear and PPML estimation. The estimates confirm the qualitative patterns of the baseline analysis: marginal returns to intergenerational mobility increase at medium and high levels of persistence, but flatten or slightly decline when persistence is low (that is, when intergenerational educational mobility is already saturated).

Database structure

The EUROPE-IGM-ATLAS database that we constructed in this study encompasses 36 European countries, 108 mesoregions (NUTS 1) and 225 microregions (NUTS 2), with measures available at several spatial scales. To ensure cross-national and cross-temporal comparability, all regional units in the EUROPE-IGM-ATLAS are harmonized to consistent NUTS-based spatial definitions following the procedure described in the ‘Materials’ section. The harmonized regional classification is primarily based on the 2016 NUTS framework, with the exception of Poland, for which the 2008 NUTS boundaries are retained owing to later regional redefinitions.

Indices are available for (1) two measures of intergenerational mobility, persistence (as measured by the slope coefficient) and standardized persistence (the slope coefficient multiplied by the ratio of s.d. of the parents’ and children’s years of education); (2) educational inequality (as measured by the coefficient of variation) for both parents and children; and (3) average years of education for both parents and children. In the cohort-level version of the database, we also include information on the weighted and unweighted number of observations used in the indices’ construction for each region–cohort pair.

The database is currently available both cohort-wise and in annualized weighted form, with each of the aforementioned weighting schemes applied. Annualized weighted measures are available 1985–2025, with the exception of profile IV and V weights, which are currently available until 2023 given the availability of data extracted from the LIS used to construct the weights. Finally, both the cohort-linked measures and the annualized weighted measures are available in three versions, based on the samples used in the indices’ construction: (1) excluding first-generation migrants only; (2) excluding all individuals with a migration background; and (3) including all migrants. See Supplementary Table 11 for clarification on versioning.

Ethics statement

This study exclusively uses publicly available secondary data sources that do not contain personally identifiable information. No human participants were directly involved in the research, and no individual-level data were collected by the authors. Accordingly, the study was exempt from institutional review board and ethics committee approval.

Reporting summary

Further information on research design is available in the Nature Portfolio Reporting Summary linked to this article.

Online content

Any methods, additional references, Nature Portfolio reporting summaries, source data, extended data, supplementary information, acknowledgements, peer review information; details of author contributions and competing interests; and statements of data and code availability are available at 10.1038/s41586-026-10736-9.

Author contributions

All of the authors contributed equally to this work and the order of author names was randomly determined. S.M. and G.N. contributed to the conceptualization, and S.M., G.N. and P.L. contributed to the methodology, investigation, writing, editing and visualizations. G.N. supervised the project, provided project administration support and, along with P.L., acquired funding.

Peer review

Peer review information

Nature thanks Chiara Ravetti, Roy van der Weide and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

Funding

S.M. declares no relevant funding. G.N. discloses support from the Jacobs Foundation in the form of a Research Fellowship (grant number 2022-1484-00). P.L. discloses support from the Swiss State Secretariat for Education, Research and Innovation through its Leading House VPET-ECON (contract number 1315002234).

Data availability

All data used to construct the indices and perform the analysis are publicly accessible, and described in the ‘Materials’ section of the Methods. The raw data used in this analysis are available as follows: The European Social Survey data can be downloaded from https://ess.sikt.no/. The surface groups data derived from daytime satellite imagery⁴⁸ can be downloaded from https://www.swissubase.ch/de/catalogue/studies/20253/19048/overview. The E-OBS dataset⁵⁸ from the EU-FP6 project UERRA (https://www.uerra.eu), the Copernicus Climate Change Service and the data providers in the ECA&D project can be downloaded from https://www.ecad.eu/. For the patent data (specifically, PATSTAT v.2024a), see https://www.epo.org/en/searching-for-patents/business/patstat for access information. The Luxembourg Income Study can be accessed through LISSY at https://www.lisdatacenter.org/our-data/lis-database/. EUROSTAT data can be downloaded from https://ec.europa.eu/eurostat/databrowser/. The shapefiles used to construct our composite shapefile are available from https://ec.europa.eu/eurostat/web/gisco/geodata/statistical-units/territorial-units-statistics for the European Commission Eurostat/GISCO NUTS 0, NUTS 1 and NUTS 2 shapefile datasets, and through https://www.arcgis.com/home/item.html?id=2b93b06dc0dc4e809d3c8db5cb96ba69 for the ESRI World Countries Generalized Map shape file datasets (data providers ESRI, Garmin International, US Central Intelligence Agency (The World Factbook) and National Geographic Society). The latter of which is available through the catalogue in ArcGIS Pro with a valid ArcGIS subscription. While the EUROPE-IGM-ATLAS itself, constructed as part of this project, will continue to be updated in future, a static version has been archived along with the replication package⁷³ and intermediate datasets and can be accessed online (10.17605/OSF.IO/MQDSK).

Code availability

The code used to construct The European Atlas of Spatially Disaggregated Intergenerational Mobility or EUROPE-IGM-ATLAS, as well as our application, is available to any researcher for the purposes of reproducing or extending the analysis. It has been deposited using an Open Science Framework repository⁷³ (10.17605/OSF.IO/MQDSK). The code in this replication package uses Stata (code was last run with v.18, and tested on v.14 and v.16) to generate all tables and figures, with the exception of the two map figures (Fig. 1 and Supplementary Fig. 4), both of which were created in ArcGIS Pro (v.3.5.3).

Competing interests

The authors declare no competing interests.

Extended data

is available for this paper at 10.1038/s41586-026-10736-9.

Supplementary information

The online version contains supplementary material available at 10.1038/s41586-026-10736-9.