Demographic Polarization and Regional Innovativeness: An Explanatory Spatial Data Analysis for German Labour Markets

Transcription

1 Demographic Polarization and Regional Innovativeness: An Explanatory Spatial Data Analysis for German Labour Markets Terry Gregory ZEW Centre for European Economic Research, Mannheim, Germany Roberto Patuelli University of Bologna, Italy The Rimini Centre for Economic Analysis (RCEA), Italy Preliminary Version: February 1, 2012] Abstract Demographic change has raised concerns that an aging population weakens the competitiveness of knowledge-based economies by diminishing the economy s ability to generate technological advances. The objective of this paper is to explore the spatial and temporal patterns of the population age structure and innovation for German labour market regions in order to derive hypotheses to be tested by regression models within any firm- or regional-level analysis. For this aim, we conduct an Exploratory Spatial Data Analysis (ESDA) using spatial and temporal spatial statistics tools to inspect the characteristics of innovation and the demographic age structure. Besides the commonly used tools, we apply newly developed (visualisation) techniques which allow investigating the space-time dynamics of the spatial distributions. Overall, we find strong clustering tendencies of the demographic variables and very specific outliers with regard to innovation. The results suggest that spatial econometric techniques should be applied, when investigating the effects of the demographic age structure on regional innovativeness, in order to generate data that are free from any spatial dependencies. Keywords: regional innovativeness, population age structure, explanatory spatial data analysis JEL: C23, R12, R23 The authors would like to thank the Fritz Thyssen Foundation for financial support. Terry Gregory is Research Fellow at the ZEW Centre for European Economic Research, L7, 1 D Mannheim, Germany, gregory@zew.de, phone: , fax: Roberto Patuelli is Assistant Professor at the University of Bologna, Via Angherà, 22, Rimini (RN), Italy, roberto.patuelli@unibo.it, phone: fax:

2 1 Introduction Demographic ageing in Europe has raised concerns on whether an ageing population may affect productivity, innovative capability and thus, ultimately, competitiveness in the global, knowledgebased economy (Poot 2007). Contributing to this debate, a sizeable body of literature has used firm-level data to examine the effects of an ageing workforce, mainly suggesting that individual productivity decreases with age due to declining cognitive abilities (Verhaegen and Salthouse 1997) and a higher resistance to technological developments (Canton et al. 2002, Fent et al. 2008). While these studies suggest that population ageing may weaken the competitiveness of knowledgebased economies, they are unlikely to reveal the whole story because macro-level effects may not simply be the aggregation of firm-level phenomena. For instance, a related strand of the literature has pointed at collective learning processes resulting from social interactions and networking that take place both at the firm and at the regional level (Capello 1999, Storper 1997). In particular, older and younger workers may interact by sharing (tacit) knowledge within and across firms, thereby creating network externalities (Kuhn and Hetze 2007). These interactions thereby do not come to a halt at the regional boundary, causing spatial autocorrelation in regional (areal) data that, if not accounted for, may lead to biased estimates in any firm- or regional level analysis. Therefore, we propose a more integrated approach that considers both the firm and regional level and that takes into account spatial associations and spatial heterogeneity of the data. Up to the authors knowledge, no such comprehensive study exists sofar. The objective of this paper is to (1) describe the spatial and temporal pattern of regional innovation output, population age structure and average education; (2) detect spatial regimes or other forms of spatial heterogeneity; and (3) ultimately derive testable hypotheses for the implementation of future regression models. For this aim we conduct an Exploratory Spatial Data Analysis (ESDA) for 150 labour market regions in Germany during the time period Throughout our analysis, we focus not only on average age, as most existing studies do, but also investigate the age diversity of regions to account for social interaction and collective learning processes. By incorporating education into our analysis, we account for a possible channel through which regional innovativeness is affected by the population age structure. Following these objectives, we proceed as follows. First, using patent data from the European Patent Office (EPO) and German administrative data, we investigate and visualize global and 1

3 local patterns of spatial autocorrelation for the investigated variables. spatial regimes and other forms of spatial heterogeneity in the data. This allows us to detect By using the number of published patents as a direct measure of the innovation process at the regional level, we better able to capture innovativeness than more general indicators of economic performance as has been done for instance by (Beaudry and Collard 2003, Feyrer 2008, Lindh and Malmberg 1999). Second, instead of only using static (spatial) methods, we apply newly developed visualisation tools such as directional Moran scatter plots (Rey et al 2012) and spatial grid maps (Laurent et al. 2012), which allow investigating the space-time dynamics of the spatial distributions. These methods help detecting clustering and polarization tendencies and their evolution over time. In addition, spatial Markov-chain based transition probability matrices (Rey 2001) are applied to study the temporal (in)stability of the investigated variables. Finally, we move towards a multivariate analysis order to detect preliminary evidence for spatial correlation between the demographic age structure of a region and its innovative performance. We find clusters of low innovative regions in East Germany while the main drivers of innovation are located in the southern part of Germany. Moreover, we show that old and homogenous workforces are largely concentrated in East Germany, while young and heterogenous workforces cluster in the southern part of Germany. However, while innovation does not show any specific dynamics over time, the opposite is true for the demographic age structure. Here we observe strong positive clustering tendencies with respect to the average age among West German regions. Interestingly, the results further indicate that East German regions are becoming increasingly less homogenous. The paper is structured as follows. Section 2 introduces the data base while Section 3 presents the results of the ESDA. In particular, Section 3 provides tests on global spatial autocorrelation (Section 3.1), presents local indicators of spatial autocorrelation (Section 3.2) and shows the results for the space-time dynamics (Section 3.3). In Section 4 we move towards a multivariate analysis before Section 5 concludes. 2 Data For our analysis, we use 150 functional regions proposed by Eckey et al. (2006). The regional definition is based on an aggregation of administrative regions by means of their interconnectivity in commuter or migration flows. The regions therefore constitute relatively self-contained labour 2

4 market regions. As a measure for regional productivity, we use patent data which are provided by the European Patent Office (EPO). The use of such a direct outcome measure is still rare in the literature, especially in regional level studies, but should be better able to capture innovativeness than more general indicators of economic performance. Our data set contains patent data both at the level of the applicant and the inventor. While the applicant is the holder of the patent right, the inventor(s) are the actual inventors in the document. We focus on patent inventors since we are interested in the spatial distribution of the actual innovators rather than the location of the formal holder of the patent right, which is often the firms headquarter. Since patents may have been developed by serval inventors located in different regions, we apply a fractional counting approach to assign every region the respective share of the patent. For each of the 150 labour market regions, we then calculate the number of weighted patent applications for the years For the same time period we further exploit regional workforce data from the regional file of the Institute of Employment Research (IAB) employment subsample provided by the German Federal Employment Agency. The administrative data set contains information on the working population jobs that are subject to social insurance payments, thus excluding civil servants and self-employed individuals. The data allows for reconstructing individual employment histories on a daily basis and contains information on the age and education of workers. We use yearly cross sections to the cut-off date June 30th and calculate regional indicators of the workforce structure such as the average age, age dispersion and skill composition for each of the 150 labour market regions. Table 1 shows descriptive statistics for the number of patents, average age, age dispersion as well as for average education for the 150 regions during the the 10 year period. We thus observe = 1500 observations for each variable. The table includes the interquartile range (Iqr), that is the difference between the 25th and 75th percentile of the distributions as well as the coefficient of variation (CoV). As Table 1 shows, a region exhibits on average 125 patents per year, although the regional and time variation is large. In fact, the coefficient of variation for patenting activity is 1.93, that is the standard deviation is almost twice as high as the mean. In contrast, the variation of the remaining variables is much lower. Figure 1 shows maps for the number of patents, mean age, age dispersion as well as average education 1 Since the number of patent applications might be driven by the size of the workforce, we also look at the number of patents per worker. Since the results didn t change, we do not consider this any further. 3

5 Table 1: Descriptive Statistics for 150 Labour Market Regions in Germany ( ) Variable Mean Sd Min Max CoV Iqr Obs Number of patents overall between within Average age overall between within Age dispersion overall between within Average education overall between within for the 150 labor market regions. The map for patenting activity shows that the number of patents varies largely across regions. In particular, the most innovative regions are located in West Germany along the main North-South arteries between Hamburg, Cologne, Frankfurt, Stuttgart and Munich. In East Germany, Berlin and Dresden are an exception of high innovative regions and are surrounded by mostly low innovation regions. We have stressed that an aging society might diminish a region s potential in generating innovative products. Looking at the corresponding maps in Figure 1, we observe that East German regions are aging faster than the remaining parts of Germany. In contrast, the youngest regions are located in the South-East and North-West of Germany. According to the literature, a further driver of innovation might be age diversity. The corresponding map in Figure 1 shows that East German regions are not only old, but also very homogenous agewise. Its seems that the amount of young people complementing the old workforce is low. The same is true for some regions in central Germany. The opposite holds for the South and to some extend for North German regions, as for the instance Munich, Stuttgart, Regensburg, Allgäu regions as well as the region of Hamburg and Flensburg. All these regions show a high degree a heterogeneity with respect to workforce age. 4

6 Figure 1: Regional Maps of Patenting Activity, Demographic Age Structure and Education ( ) Since a possible channel of the influence of demographic change on innovativeness is education, we further investigate the spatial distribution of the average education years per worker. We find that 5

7 East German regions have higher education years as compared to most West and South German regions. The result reflects an old workforce that has accumulated human capital over the working life. However, young people at the beginning of their education are rare in East Germany and rather situated in South-East and North-West of Germany. Overall, the maps in Figure 1 give first indications of spatial associations that will be analysed explicitly in Section 3 3 Explanatory Spatial Data Analysis In the present section we conduct an ESDA in order to describe and visualize the spatial distribution of the data. In particular, we aim at identifying patterns of spatial clusters, spatial outliers and discover space-time dynamics. For this aim, we first provide standards tests on the existence of global spatial autocorrelation using the MI coefficients (Section 3.1). We thereby define Spatial autocorrelation as the correlation amongst the values of a georeferenced variable that is attributable to the proximity of the objects to which the values are attached (Cliff and Ord 1981). Spatial autocorrelation may be due, among other reasons, to selfcorrelation, omitted variables, redundant information, or spatial spillover effects. It is most evident, in the case of Germany, in the stillexisting East-West economic divide. Secondly, using LISA indicators we investigate and visualize local patterns of spatial associations (Section 3.2). Thirdly, we analyse time trends in the data by calculating Markov-Chain based probability transition matrices that give insights into the dynamics of the different types of clusters and visualize the space-time dynamics using recently developed grid maps and directional scatter plots that reveal the movements of clusters over time (Section 3.3). Finally we move towards a preliminary multivariate analysis in order to detect evidence for spatial correlation between the demographic age structure of a region and its innovative performance (Section 4). 3.1 Global Spatial Autocorrelation Since the distribution of workers can not be expected to be purely random in space, we first conduct a test for spatial autocorrelation using the Moran s I (MI) statistic. The measure allows us to investigate whether on average regions with a high (low) value are often surrounded by regions that 6

8 also have a high (low) value. For this analysis, we first define a rook-based contiguity spatial weights matrix W. We standardize the weights matrix so that the elements of each row sum to one. The elements of the standardized matrix are defined as follows: W ij = W ij nj=1 W ij where i and j are defined as neighbours. The diagonal values of the weights matrix are set to zero. We then calculate the global MI as follows (Aldstadt 2010): I = N S o ni=1 nj=1 W ij (y i ȳ)(y j ȳ) ni=1 (y i ȳ) 2, i j where S o = n n W ij i=1 j=1 The term N represents for the number of observations (regions) and y i represents the values of the observations as, for instance, the number of patent applications of region i. S o is a scaling factor equal to the sum of all elements of W. The MI is similar to covariance and correlation statistics, and can be seen as a regression coefficient resulting from the regression of Wy on y (Anselin 1996). In particular, MI measures the similarity between two locations i and j by multiplying the deviations of the value at each location and the global mean ȳ. The product is then weighted by the spatial proximity of the two locations and the sum of the resulting values for all pairs of locations in the spatial autocovariance. The expected value for a spatially random distribution is E(I) = 1/(n 1) which equals in our case of 150 regions. Values of I greater than E(I) indicate positive, while values smaller than E(I) indicate negative spatial autocorrelation. The MI computed from our data are reported in Table 2. 2 For mean age, age dispersion and average education, Table 2 indicates a high degree of spatial autocorrelation. The results suggest that the distribution in space is far from random, that is the MI clearly indicates that there are significant clustering tendencies for demographic age structure and the skill composition of regions in Germany. Regions with a high (low) value of the respective variable are often surrounded by regions that also exhibit a high (low) value. For patenting activity, we find less evidence of clustering. 2 The global MI coefficients are calculated in STATA using the spatgsa command. 7

9 Table 2: Moran s I Coefficients for Average Patenting Activity, Demographic Age Structure and Education ( ) I sd(i) z p-value Number of patents Mean age Age dispersion Average education years Figure 2: Morans s I for Patenting Activity, Demographic Age Structure and Education, by Year ( ) Global Moran's I Year invshare sdage mage meduc Figure 2 shows the Morans s I for patenting activity, demographic age Structure and education, by year for the time period The developments show that mean age, age dispersion and average education are clustered over the whole period, although the extent of clustering is quite volatile. The extent of clustering is particularly pronounced with respect to average age. In contrast, we again observe less evidence of clustering for patenting activity over time. So far we have detected general tendencies towards clustering with respect to the variables of interest. However, the questions of where these clusters are located in space and what their spatial extent is, remains open. For instance, is there an East-West or a North-South divide? Since these questions cannot be answered by means of global measures of spatial autocorrelation, we use LISA indicators proposed by Anselin (1995), and which are presented in the following section. 8

10 3.2 Local Spatial Autocorrelation We investigate local patterns of spatial association using Local Indicators of Spatial Association (LISA) proposed by Anselin (1995). For this we first construct a Moran scatter plot (Anselin 1996), a bivariate scatter plot with values y i on the horizontal axis and the spatial lag Wy i for the same variable on the vertical axis. A spatial lag is the spatially weighted average value of a variable evaluated at neighbouring units, and is calculated as follows: Wy i = W ij y ij W ij Figure 3 shows the Moran scatter plot for patent applications as an example. 3 The vertical and horizontal lines that cross at the average values of x i and Wy i divide the scatter plot into 4 quadrants that correspond to the following 4 different types of spatial associations (clockwise from top right): high-high (HH), low-high (LH), low-low (LL) and high-low (HL). For instance, HH is a region with a high number of patent applications surrounded by regions that also exhibit high numbers of patents and so forth. Both HH (hotpots) and LL (coldspots) represent regimes of positive spatial association, while LH and HL indicate negative ones. The calculated MI for global autocorrelation in Section 3.1 exhibits the slope of the line interpolating all points in the scatter plot, since it is based on standardized values. Figure 3 confirms weak evidence of spatial autocorrelation for patenting activity. Since the MI scatter plot does not give any implication on the significance of the spatial clustering, we defin we calculate the local MI for each region, I i, as follows: I i = nj=1 W ij (y i ȳ)(y j ȳ) 1 n nj=1 (y i ȳ) where I i represents a decomposition of the global MI. Similar to the global MI statistic, the significance can be determined through the expected value and variance. A positive I i again indicates clustering of HH or LL values, while a negative I i indicates a spatial outlier. For a geographical visualization, Figure 4 shows the LISA cluster maps that depict the spatial distribution of the 4 categories for patenting activity, average age, age dispersion and average education. 4 The maps show only those locations with a significant Local Moran statistic. The LISA 3 The MI scatter plot is done in STATA using the splagvar command. 4 The local MI coefficients and its significance for the LISA cluster maps are calculated in GeoDa. 9

11 Figure 3: Morans s Scatter Plot for Average Patenting Activity ( ) (Moran's I= and P-value=0.0200) Spatially lagged invshare invshare Winvshare Fitted values cluster map for patenting activity shows islands of clusters with limited extend. In particular, we observe small HH clusters in parts of West Germany around Mannheim and Aachen and in South Germany around Regensburg and Ulm. Several outliers of LH regions are attached to these clusters, especially East and West Munich. Bigger clusters of LL regions are located in East Germany in the area around Leibzig and Erfurt as well as in the northern Stralsund. Furthermore, Berlin and Dresden constitute two spatial outliers with high innovative regions with weak innovative neighbours (HL). Turning to the LISA cluster maps for average age and age dispersion, we can observe that East Germany is almost entirely identifiable as a large cluster of homogenously old workforces. The only regions in East Germany where an old workforce is compensated by a high share of young workers are the regions Potsdam, Lündeburg and Dresden. Despite their high average age, these regions constitute outliers with a very heterogenous workforce in East Germany. Large clusters of very young and heterogenous workforces are found in South Germany around the Munich region. Few LH outliers are found in the eastern part of South Germany around the black forest region. A cluster of heterogenous regions is also found in the northern area around Kiel. The results reflect large flows of particularly young migrants moving from East to West Germany during the observed time period (Burda and Hunt 2001, Hunt 2004). For average education we observe large clusters of HH regions in East Germany. One explanation might be the high share of old workers in East Germany that have accumulated a large stock of 10

12 Figure 4: LISA Cluster Maps for Patenting Activity, Demographic Age Structure and Education human capital during their working life. Clusters of lowly educated regions surrounded by lowly educated regions (LL) are found in South-East Germany near the border to Austria and Czech 11

13 Republic. These regions are the attractive regions for young migrants from eastern Europe. 3.3 Space-Time Dynamics So far we have gained insights into the spatial dimension of the regional distributions of the variables analysed, measured by its average value across the time period We are now interested in how the distributions evolved over time? Are there any observable time trends? How stable are the spatial patterns observed? Most studies so far, that have analyzed the evolution of a variable s spatial distribution over time, have compared values for two points in time. While these approaches may be insightful for the overall development, they say less about the underlying spatial dimensions of a variable s change. For this reason we apply several newer (visualization based) methods that are designed to address this limitation Directional Moran Scatter Plots In the following section we investigate the region dynamics using Directional Moran Scatter Plots. For this, we calculate LISA scatter plots for the years 1995 and 2004 separately as described in Section 3.2, using values relative to the national value. We then visualize a regions value in the scatter plot for the year 1995 and 2004 in one scatter plot and connect the points by drawing movement vectors. We normalize all vectors by the value in 1995 to receive the Standardized Directional Moran Scatter Plot (SDMS) (Rey et al. 2011) shown in Figure 5. While the arrowheads point to the regions value in 2006, the vectors starting point represents the regions value in Therefore, the directional Moran scatter plot helps to analyse the direction of movement, independent of the location in the original scatter plot in Movements towards the first quadrant (HH) reflect the strengthening of positive spatial clustering (hotspots), while movements towards the third quadrant (LL) reflect the enlargement of negative spatial clustering (coldspots). The analysis so far have shown that large differences between East and West Germany exit. For this reason we show the SDMS by East and West Germany. 5 Looking first at the SDMS for East Germany, we can only observe relatively small movements (mainly to the North), confirming that East German regions seem to be overall rather static regions with respect to patenting activity. For West Germany the picture looks different. The SDMS for patenting activity shows big vertical 5 Since we look at labour market regions, we are not able to separate East and West Germany my means of political borders. For this reason we define a new border as shown in Figure?? in the appendix. 12

14 Figure 5: Standardized Directional Moran Scatter Plots for Patenting Activity, Demographic Age Structure and Education Relative to the National Value ( ) Spatial lag of invs West East invs Spatial lag of mage West East mage West East West East Spatial lag of sdage Spatial lag of meduc sdage meduc movements to the North and South, indicating positive and negative movements of neighbours without changes of the region itself. Thus, we do not find any significant spatial associations for East and West German with respect to innovation production. The SDMS for mean age shows no clear picture for East Germany, while for West Germany movements to the first (HH) and third (LL) quadrant are dominant. The finding indicates tendencies towards positive and negative clustering within West-Germany. Additional insights on the dynamics of the demographic age structure can be found by looking at the results for the age dispersion. Here we find dominant movements to the first quadrant (HH) in Eastern Germany, while for West Germany only slightly dominant movements towards the South-West (LL) can be observed. Thus, we find strong evidence in favour of positive clustering tendencies with respect to the age diversity in East Germany. The findings can be interpreted as further evidence for a demographic polarization trend in Germany. East German regions are old and homogenous in their age structure on average, as shown in the static analysis (Section 3.2), but are also increasingly becoming more heterogeneous over time. 13

15 Even within West Germany a polarization trend with respect to the dynamics of the average age is observable in the data. Obviously the north and south parts of West Germany are developing in a very different ways. The evidence so far however does not really tell us how the polarization trend is effecting the distribution from a geographical point of view. We therefore apply spatial drift maps that give us more information of a possible movement in space. For instance, are there trends between East and West or between North and South Germany? These question are addressed in the following section Spatial Drift Maps In order to examine geographical trends Figures 6 and 7 show construct spatial drift maps (SDM) described by Laurent et. al (2012). 6 For this we proceed as follows. First, we interpose a grid on our map and impute the mean of each point falling into the cells. Second, we plot the mean and median of each row to the right of the grid map as well as the corresponding values for the columns to the bottom. Differences between the mean and median indicate the presence of outliers in a given row or column. Figures 6 and 7 show SDMs for each variable for both years 1995 (left) and 2004 (right) separately. The SDM for patenting activity in Figure 6 show a decrease in 1995 when moving North. The same is true when moving East. The mean and median are close to each other, indicating that outliers don t seem to be important. Thus, we find evidence of a East-West and a North-South divide, that is regions in the South-East are the most innovative regions, while regions in the North-East perform only poorly in terms of innovation. Comparing the years 1995 and 2004 shows no significant change, again confirming the stability of patenting activity over time. Considering the SDM for the average age, in 1995 we can again see an increase when moving North and when moving East. Interestingly, the heterogeneity increases when moving East which is due to a particularly old workforce in East and a young workforce in South Germany. The development between 1995 and 2004 shows that the average age has increased by almost 3 years from 37.5 to 40.5, although East and West Germany differ by almost 1.5 years. The maps suggest, that East Germany seems to be suffering most from an ageing workforce, while young workers prefer South German regions. 6 The drift maps are calculated in R using the GeoXp package (see Laurent et. al 2012). 14

16 Figure 6: Spatial Drift Maps for Patenting Activity, Demographic Age Structure and Education ( ) Mean Median Mean Median N N E W E W Mean Median N 41 E W W E S S Variable : Mean age (1995) Variable : Mean age (2004) N 38 Mean Median S Variable : Number of patent applications (2004, in logs) S Variable : Number of patent applications (1995, in logs) The vertical line for age diversity in 1995 shows a crescent-shaped pattern, together with an increasing heterogeneity between regions when moving North. The map reflects East German regions with a very old and homogenous workforce, while the southern and northfern parts of Germany include quite diverse workforces. Comparing the maps for 1995, and 2004, we can observe that diversity has increased overall and the curvature of the means interpolation has decreased. Clearly, East-German regions have become more diverse during the ten year time period. The development of for education years is similar as for the average age. It again might reflect the already observed possible correlation between age and education, that is the accumulation of human capital during their working life. 15

17 Figure 7: Drift Maps for Patenting Activity, Demographic Age Structure and Education ( ) (con t) N Mean Median N E W E W Mean Median S 10.5 S N Mean Median N W E 13.0 S E 13.1 W Mean Median Variable : Age sd (2004) Variable : Age sd (1995) Variable : Average education years (1995) S Variable : Average education years (2004) Spatial Markov Transitions In the following section we apply the Spatial Markov Approach approach put forward by Rey (2001). The Spatial Markov approach allows to track the evolution of the investigated variables over time by calculating transition probability matrices. While in the Classical Markov Approach transition dynamics are assumed to to hold for all regions and all time periods and interactions between transitions of regions are ignored, the Spatial Markov Approach extends the Classical Markov Framework to the regional context by conditioning a region s transition probability on the initial state of its spatial lag. The Spatial Markov approach allows us to derive probabilistic measures for the movements of single regions from a group (or quantile) to another. For the calculation, we proceed as follows. 16

18 Table 3: Types of Transitions in a LISA Markov HH t+1 LH t+1 LL t+1 HL t+1 HH t 0 I III II LH t I 0 II III LL t III II 0 I HL t II III I 0 First, instead of looking at the quantiles of the distribution, we classify the values of the variables into the four different states according to the quadrants of the Moran scatter plot (HH, LL, LH, HL) as described in Section 2. This version of the Spatial Markov is also known as the LISA Markov. Second, we specify a state probability vector P t = [P 1t, P 2t, P 3t, P 4t ] that represents the probability of a region to be in one of the four states in period t where t = 1, 2,..., 10. Third, we define a 4 4 dimensional transition probability matrix, M = [m ijt ], showing the likelihood of a region to remain in it s initial state i or to move from state i in period t to state j in period t + 1 during the 10 year time period. Given these assumptions, the state probability vector in period t + b can be written as follows: P t+b = P t M b Overall there are 12 different transitions a region may experience over time. These 12 transitions can be classified into three different types of transitions, shown in Table 3. Type I is a relative move of only the region. Type II is a transition involving only the neighbours. Type III is a transition of both a region and its neighbour. The results are shown in Table 4. 7 For patenting activity the transition probabilities on the main diagonal are relatively high, especially for HH and LL. For instance, the probability of a high innovating region surrounded by high innovating regions (HH) to remain in his state is 93 per cent, while the probability of staying a LL region accounts to 94 per cent. Looking at the off-diagonal probabilities reveals some further insights into the dynamics of the innovation process. For instance the 9.5 per cent probability of moving from HL to LL shows that low innovative neighbouring regions seem to have a negative influence on outlier regions with high patenting activity. The result could 7 The calculations of the LISA Markov Transition Matrices were done in PYTHON using the PYSAL library. The source code is available from the authors upon request. 17

19 Table 4: LISA Transition Probabilities (in Per Cent) for Patenting Activity and Demographic Age Structure ( ) Variable HH t+1 LH t+1 LL t+1 HL t+1 Initial Steady value state Number of patents HH t LH t LL t HL t Mean age HH t LH t LL t HL t Age dispersion HH t LH t LL t HL t reflect that outperforming firms in low-innovative regions tend to move towards agglomerated areas. Table 5 shows the sum of the transition probabilities by transition type. For patenting activity, Type I and Type II transition probabilities add up to 23 and 10 per cent. Type III transitions do not play a role in any of the 4 discussed variables, probably because of the limited time interval studied. Overall, innovation activity is quite stable over time, which might be explained by the fact that the process of innovation implies a high degree of infrastructure that a region cannot change overnight. Looking at the transition probabilities for the average age and age diversity, we find much more instability, especially for age diversity. The probabilities on the main diagonal are lower than for patenting activity, especially for outliers. For instance, the probability of staying a LH region is 78 per cent for the average age and only 59 per cent for age dispersion. Considering the off-diagonal probabilities, we particularly find higher probabilities of moving from LH to HH and from HL to LL. The figures show significant evidence for clustering. Overall, Table 5 shows that Type I and Type II probabilities are 36 and 20 per cent for mean age and 59 and 40 per cent for age dispersion, that is much higher than for patenting activity. 18

20 Table 5: Sum of Transition Probabilities, Type of Transition by Number of Average Age Average patents age dispersion education Type I Type II Type III Total Multivariate Analysis To be added. 5 Conclusion This paper contributes to the debate on demographic change in Europe and its effects on productivity and innovative capability in a globalized, knowledge-based economy. In particular, it describes the spatial and temporal patterns of regional innovation output and population age structure for German Labour markets in order to detect spatial regimes or other forms of spatial heterogeneity that might lead to biased estimates in any firm- or regional level analysis. Using global and local indicators of spatial associations, we find clusters of low innovative regions in East Germany while the main drivers of innovation are located in the southern part of Germany. Moreover, we show that old and homogenous workforces are largely concentrated in East Germany, while young and heterogenous workforces cluster again in the southern part of Germany. Applying newly developed visualisation tools that allow investigating the space-time dynamics of spatial distributions, we also find that while innovation does not show any specific dynamics over time, the opposite is true for the demographic age structure. Here we observe strong positive clustering tendencies towards old regions surrounded by old regions (HH) and young regions surrounded by young regions (LL) for West German regions. Interestingly, the results further indicate that East German regions are becoming increasingly less homogenous. Our results reveal a demographic polarization trend in Germany, showing that demographic aging has been evolving very differently on a regional scale. One explanation for this development are 19

21 age-selective migration flows within Germany that have aggravated the shrinking process of certain regions, as for instance in eastern Germany. At the same time, the observed increase in age diversity among East German regions might reflect future potential for such regions in generating technological advances by attracting young workers that might complement the existing older workforce. Our findings are relevant for any analysis trying to measure the impact of demographic aging on firm or regional performance measures. The presence of strong clustering of the demographic variables, and of very specific outliers with regard to innovation, suggest that spatial econometric techniques should be applied, when investigating such research question as shown, for example, by Patuelli et al. (2010) and Patuelli et al. (2010), in order to generate data that are free from any spatial dependencies. From an econometric viewpoint, it may be interesting, in particular, to investigate whether demographic variables interact in pushing technological development. Additionally, the presence of clusters might be explicitly modelled in a regression framework. From a policy perspective, these results indicate that East German regions must keep developing policy instruments that stop out-migration of young individuals from eastern regions. In addition, regions with a high share of old workers might exploit chances that are given by their experience and knowledge that can be shared with younger workers through social interaction and networking. 20

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