Are functional regions more homogeneous than administrative regions? A test using hierarchical linear models

We investigate whether economic functional regions capture spatial clustering of core economic indicators better than administrative regions. For this purpose, we use hierarchical linear models to measure the degree of homogenization of different regional delineations. Our results for Germany show that economic functional regions tend to capture spatial clustering better than administrative ones. However, a considerable amount of clustering at a lower aggregation level cannot be accounted for by economic functional regions, especially around metropolitan centres. Furthermore, economic functional regions, which depict commuting interrelations well, are less able to capture spatial homogenization than other economic functional delineations. El artículo investiga si las regiones económicas funcionales capturan la agrupación espacial de los indicadores económicos básicos mejor que las regiones administrativas. Para ello utiliza modelos lineales jerárquicos, con el fin de medir el grado de homogeneización de las diferentes delimitaciones regionales. Los resultados para Alemania muestran que las regiones económicas funcionales tienden a capturar mejor la agrupación espacial que las administrativas. Sin embargo, las regiones económicas funcionales, especialmente aquellas alrededor de los centros metropolitanos, no pueden explicar una cantidad considerable de agrupaciones a un nivel de agregación inferior. Además, las regiones económicas funcionales, que representan bien las interrelaciones de desplazamiento al trabajo, capturan peor la homogeneización espacial que otras delimitaciones económicas funcionales. 本稿では、経済的機能区域が、行政区域よりもコア経済指標の空間的クラスタリングをよく捉えるかどうか検討する。そこで、階層的線形モデルを使用し、異なる区域の均質化の程度を測定する。ドイツの結果は、経済的機能区域は、行政区域よりもコア経済指標の空間的クラスタリングをよく捉えることを示す。しかし、低い集積レベルでは多数のクラスタリングがあるが、経済的機能区域、特に大都市中心部の周辺には重要ではない。さらに、経済的機能区域は、通勤の相関性を描出するが、他の経済的機能区域よりも空間的均質化を捉える性能が低い。 Functional regions are essential for analysing labour market and economic policy (Van der Laan & Schalke, 2001). These regions are defined as areas with strong commuting and economic activity within and few connections to outside regions (Hensen & Cörvers, 2003). In contrast, administrative units are typically designed for administrative purposes and have historical roots. They therefore neglect spatial interrelations due to commuting and economic patterns. This can lead to distorted statistics when indicators are reported either at the place of residence, such as unemployment, or at the place of work, such as income or gross domestic product (GDP). In Germany, this applies particularly in the case of city-states such as Berlin or Hamburg, which are characterized by high inward commuting flows (Wixforth & Soyka, 2005). Moreover, multivariate analyses based on such interrelated regional data violate an important assumption that underlies any regression analysis, namely, the assumption that all units of the analysis are independent (Anselin, 2003; Arbia, 2001). In this regard, functional regions—according to the narrow definition by Van der Laan and Schalke (2001)—are assumed to capture in particular the spatial clustering of economic indicators resulting from commuting interrelations. As a result, such economic functional regions can be assumed to be more homogeneous in terms of their economic indicators than administrative regions, because they take into account economic interactions which lead to harmonization processes (see Cörvers, Hensen, & Bongaerts, 2009) for a formalization of the association between harmonization and economic interactions). Although this would be an important issue for regional labour market research and economic policies, it is an assumption that has seldom been tested to date. The study by Cörvers et al. (2009) for the Netherlands is a first attempt to investigate whether functional regions are characterized by more homogeneity within their boundaries and more heterogeneity between regions. They consider regional disparities in income, employment, unemployment and housing prices and find that functional delineations do not outperform administrative ones. In Germany, there are different economic functional delineations for regional policy and research purposes (cf. section 3). The explanatory power of these regions has not yet been evaluated systematically in the research conducted so far. However, first descriptive statistical results indicate that such regions seem to be more homogeneous in terms of GDP per capita or unemployment rates than administrative regions (Kropp & Schwengler, 2016). More precisely, Kropp and Schwengler (2016) show that the standard deviations of these indicators are smaller between the districts within economic functional regions than across all districts. This paper aims to explore whether economic functional regions are more homogeneous than administrative regions and how well different regionalizations capture the spatial clustering of economic indicators. We draw on intraclass correlation coefficients (ICC) to measure the degree of homogenization or spatial clustering within regions resulting from different delimitations. This is a new methodological approach to our research problem. Measures of ICC are based on hierarchical linear models, which make it possible to evaluate the within-cluster and between-cluster variance even when there is a large number of clusters, as is the case in many functional and administrative regions. Additionally, in contrast to spatial statistical models, these kinds of models can easily be extended to take clustering at multiple regional levels into account. We draw on core economic and labour market indicators at the level of associations of local authorities (LAU 1 – local administrative units in the EU statistics) and compare: (1) two-level models with different regionalizations at a higher level of aggregation; and (2) three-level models that additionally take into account spatial clustering at a lower aggregation level. Furthermore, multivariate analyses allow the use of control variables, which are very important when comparing functional and administrative regions and which in turn vary considerably, for instance in terms of size. The paper starts by theorizing spatial clustering resulting from spatial interrelations and by discussing the problem of regionalization. Next, we provide an overview of administrative and economic functional regions in Germany. In the subsequent section, we present our data and the statistical methods deployed before reporting the results of our modelling steps. The paper concludes with a discussion of our findings. Spatial clustering of socio-economic phenomena, such as unemployment, is the result of spatial interrelations between observational units in space, such as points, regions or nations. In other words, one particular observation somewhere on the landscape is dependent on or influenced by one or several other observations on the landscape (Combes, Mayer, & Thisse, 2008; Fujita & Mori, 2005; Krugman, 1991). From this perspective, regional labour market conditions may be mitigated or reinforced by surrounding areas. Such spillover effects (Anselin, 2003) mainly arise due to social interactions (Akerlof, 1997), with the exchange of resources (labour or goods) being the most relevant kind of interaction in this context. Previous research on mobility at the level of German administrative districts has indeed shown both mitigation and reinforcement processes. On the one hand, labour mobility reduces regional disparities in unemployment (Niebuhr, Granato, Haas, & Hamann, 2012). Similar results have been found for the United Kingdom (Patacchini & Zenou, 2007). On the other hand, there is also strong evidence that selective migration of labour leads to a divergence of regional outcomes: while the migration of low and medium-skilled labour levels out regional disparities in unemployment rates, the migration of highly skilled labour does the opposite (Granato, Haas, Hamann, & Niebuhr, 2015). There are some other studies (Berry & 2005; & 2005; 2005; which also contrast to the of migration may regional disparities in and Although the the can be with to commuting (see for a discussion on both migration and From a perspective, all kinds of spatial mobility are by both conditions socio-economic and conditions unemployment, & & They their spatial in terms of both the of interrelations between units as a result, the spatial clustering or of socio-economic such spatial interrelations in regions not be as as of a socio-economic This is has in when social with From a methodological of spatial are in or spatial statistical for any regression analysis (Anselin, More spatial are also of for the of regional disparities & & economic functional regions homogeneity better than administrative Furthermore, we can different delineations by of The degree of in terms of strong commuting interrelations within functional regions and commuting interrelations between is such an and is well in regional & Cörvers et Van der Laan & Schalke, 2001). However, on is not an measure for functional as with the number of regions, with a of one all regions are Kropp and Schwengler the as a for the The measure to clustering in & and the of within a with the of that would be a the commuting between districts or clustering the number of in a is than the number of in the This approach a with the number of in which degree the of and the are In this the important of the as a The approach can be with the with and the between and as a of all interaction of with that the of all units than the number of units is the for the the to the of The outside the the of units that are not within between labour market The of the of the the of important of the is that the can be by the of and by the of and In the this product is to the The the with the the number of in a or labour market is than the number of in the The typically between and in the of areas in which are For commuting in which high levels of clustering in higher can be with the degree of homogenization of economic indicators within economic functional in the problem which that the results of regional data analyses are highly to the of units delineations of units in and of functional regions in particular be evaluated with to spatial and spatial the problem to the or of the defined the problem to the particular of boundaries on any are important & & 2003; & and be when comparing administrative and functional regions. This is a research we do not whether functional regions the by the better than administrative regions, or in more regional delineations with the For the Cörvers et al. (2009) to investigate the issue of spatial in their analyses of the of functional and administrative regions several economic and labour market indicators. They use commuting data at the level of and a in which the number of functional regions the number of administrative regions. The analyses that they present to 1 regions regions in the they use regression analyses to the explanatory power of these functional regions with of their administrative They do not find in income levels between administrative and functional regions, housing prices do in their study for all of regions. In their results show for and unemployment rates for of the regions However, there are with their they do not with spatial as a a issue for regional they functional regions by an for the number of regions, which is not for the of the This they do not find in the explanatory power of functional regions to administrative ones. economic functional regions at a lower aggregation level more homogeneous than economic functional regions at a higher aggregation In Germany, different regional delineations are in use for different delineations are the which regions administrative regions or administrative districts 1 and and These units are the for a of Furthermore, there are districts of the that as units for labour market for for reporting unemployment the there are several economic functional delineations that are for different for instance for regional policy or regional Spatial the spatial regions defined by the for on and Spatial within the for and for their In economic and regional policy has defined labour market regions for regions that are or less well in and economic terms and are for regional for from the of the regional labour defined by and of these delineations in are to and these functional Kropp and Schwengler (2016) a new of labour market regions that are very in size. more local labour market regions is additionally 1 German administrative delineations. The first in 1 the of Germany into large regions, and and the hierarchical of the different German administrative regions. the different functional regions that are units of analysis this regional disparities in labour market their analyses on both and unemployment and rates, income levels and housing prices et 2016). In our analyses for Germany, we this approach on indicators. We are to present results based on housing as no data are at the level of and associations of local the data we use are from the The data on unemployment and rates are by the for on and Spatial which a regional based on several data is as the number of per of namely, the The the of the to are in to social at their place of the does not in employment, or the unemployment and the are not the of For this their correlation is of the regional income we on data from the statistics of the German 2016). the of all in Germany have to the to The per is by the gross per by the number of in the for In to investigate the of economic functional regions than administrative regions, we use data at the regional level of associations of local which are within different regional delineations. We use these more homogeneous regions as units level 1 of the because German vary in size. We our analyses with the of hierarchical linear models & 2012). spatial statistical models & are for analysing as they make it to the standard of regression by statistical between observations within regional units at a higher aggregation and to evaluate the within-cluster and between-cluster Furthermore, can easily be extended to take more than levels into account. We draw on core economic and labour market indicators and income per at the level and compare: two-level models with different regionalizations at a higher aggregation and three-level models, which additionally consider spatial clustering at a lower aggregation level. In the first we two-level models with units of local within different administrative and functional regions. In these models, the of regional units at a higher aggregation level are to from one The variance of the models can to the degree to which the different regions level 1 units and homogeneous For this purpose, we the intraclass correlation (ICC) based on the variance The ICC the degree of between level 1 units to the at a higher aggregation level. The is defined as the of the variance between the units at a higher aggregation level and the the variance which is to the regions at a higher aggregation level and which can be by regional In other words, the ICC is a of the of the of with high ICC regional clustering of the of level 1 units and a high of the regional In to allow for more local labour market in a we three-level models with level 1 units within administrative districts which are in turn within different administrative and functional regions. We administrative districts as the level because their boundaries with the boundaries of all other regional delineations. we the models based on This approach to the of spillover effects at a lower aggregation level between units within and additionally the of administrative or functional regions at a higher aggregation which may capture spatial interrelations between districts. In all analyses we use a of control to the of different units in terms of the to which they can capture spatial is essential as administrative and functional regions in et control for the different we as we take the number of units within regional into account. This number can easily be from the we consider the that the der We these indicators at the level of aggregation labour market Furthermore, we control for large German and & which are shown in the first of this would lead to an of the for all regional as the areas capture a large degree of In a first we explore the of the different delineations in terms of their to capture commuting as the of economic For this we the of between regions, and the in The and of these in the to the research the of the the labour market regions In the local labour and the regions high These delineations low commuting as well as high of The for the with a lower for indicate that a is not functional with to commuting In this and at some regions that have strong commuting with regions. In economic functional regions in Germany do not capture economic interaction between regions in commuting better than administrative regions. This be into when our research In a we explore the degree of homogeneity of the economic indicators within different functional and administrative regions by the (Anselin, as a measure of spatial that the correlation between the of and their We the spatial interrelations of the units on the of whether they the functional or administrative The results in show the of the spatial for the spatial to be higher for functional regions than for administrative regions. However, spatial also to with the number of regions seem to be less able to capture homogeneous which is in with research on effects & et 2003). These results the or effects of the et Although several studies have the between spatial and the there is the effects of the & & & et the in the standard of the economic indicators for the different For the standard of the unemployment rates at the level of within administrative districts on with all other delineations. However, there at one with a very strong in unemployment rates, The results show that the for the between spatial and the number of as reported in is that the variance of the economic indicators within regions by the number of the units & et Furthermore, regional delineations that capture commuting well, most and by the indicators in do not units with very high in 3). In other words, within these regional strong commuting interrelations seem to be with a high level of On and the regions seem to more homogeneous units in 3). We find between the number of regions and the standard deviations of our for unemployment, for rates, and for a analysis of homogeneity within regions consider this In to take a at the spatial of homogeneous areas Germany, we additionally which the correlation between and spatial that the spatial of (Anselin, The are based on to take into account the that regions to other are more than regions that are we consider regions which are to As an we the results for unemployment in The a high degree of spatial especially in the and in the of Germany However, there also is a high degree of spatial clustering in the results our approach to take the between the large German areas into account (see section on Furthermore, the results a degree of spatial as This is of the areas around the in the and regions of Germany or within large especially in the of Germany high unemployment in a is by low in the surrounding areas. The in how a can capture homogeneity with to unemployment these by comparing an administrative on the with a functional on the We and because these delineations an number of regional This to on the problem while the problem (see 3). first the The is that Hamburg, or less in the In both areas low unemployment rates, and areas high The more the of within one the more the In other words, the of units with of a homogeneous regionalization. the of in the it that some regions units with low unemployment rates as well as units with high This is especially of the of Germany and the in the For both the administrative and the functional the in unemployment rates by within a is in the In both with low unemployment is with less regions the case of Berlin The of the unemployment in a low in the surrounding is of all functional regions. that the most administrative delineations and especially therefore this of this lead to commuting being These descriptive provide first into spatial clustering by different regionalizations and the of the The results that spatial clustering does not to strong that capture commuting well, or functional delineations in therefore do not more homogeneous regions. However, for analyses of how different regionalizations we within and between and take into account of regional as important We our analyses with two-level models for the economic indicators and income per with administrative and functional regions level the models take into account the of the to the different the models consider regional in labour market conditions in Germany in the large areas and (see section on data and to the between the indicators and the 1 we 1 from the the for the different delineations. The the degree of of units within the different regions. in the present the results of the the economic all the delineations show the of explanatory the the regional for unemployment and the for per capita The of between the different regional delineations. the functional the and the administrative the functional delineations do not better results than administrative delineations. The results are for functional regions, and even the results for regions and do not first the results the functional and the administrative seem it be by spatial and spatial of the On the one hand, regions at a lower aggregation level may capture local spatial processes that are based on spatial On the other hand, the regions may units that are interrelated due to spatial and therefore homogeneous the spatial interrelations more we three-level models with different regional at level and the lower aggregation regions, at level also in the These models the degree of homogeneity by the local level and the more level of other administrative or functional delineations. to the on the of show that the variance at regional level when for level regional clustering unemployment, for the ICC from in to and lower in the the variance at level for the different regional of for by The of the variance at level and level for the regionalizations regions that capture commuting interrelations well by and and administrative high and low at the In with the in these regions more units in In contrast, more functional delineations and which are to local can capture more level variance at the of level The of level level is for all delineations. economic functional regions do not homogeneity better than administrative regions the functional delineations and in spatial Moreover, when comparing the functional and administrative regionalizations and the functional a higher degree of In to research delineations that capture commuting flows and are regions. Moreover, in both the level and level models, with ICC even these are not Furthermore, research our analyses that local spatial processes seem to lead to a homogenization of economic which especially units at a lower aggregation such as or are able to However, when at the results of the three-level local spatial there is a large degree of spatial that cannot be by any administrative The correlation between the number of regions and the is in the level models for the unemployment and and the level models for This paper to evaluate whether economic functional regions are more homogeneous than administrative regions better able to capture spatial clustering of economic at the level of resulting from spatial interrelations. This would indeed be a in of functional regions because it to a of within functional regions. In to on the of functional regions, we draw on level as well as on level hierarchical linear models and intraclass correlation coefficients which to the degree of homogenization at different levels of This is a new approach to evaluate different to how the of different delineations are to processes of The as to economic functional regions be more homogeneous than administrative regions is that they capture economic interactions mobility which are to be for homogenization processes. However, our descriptive analyses that German functional delineations do not capture mobility flows of the labour better than administrative ones. functional delineations are based on commuting flows and and their As the and the are very unemployment, and income functional regions are characterized by a degree of these in the results of our analyses are not we find that economic functional regions do not homogeneity better than administrative regions. This especially for functional regions that capture mobility very They lower than administrative regions such as administrative districts or districts. our research we find that delineations with high do not more homogeneous regional units than other delineations. In the opposite is this is not our research it that more delineations are better at homogeneous regions. In our analyses a between delineations and the to homogeneous regions. For Germany, the spatial of and income is not by commuting patterns. In some strong commuting flows very regions, which and their This is in with some that show how mobility processes can even regional et & 2005; methods that capture commuting well are not for homogeneous regions, at for Germany. There are at that the on the effects of For that high regional unemployment resulting in an Furthermore, even spatial may lead to there be other processes at as well, such as which lead to for due to different levels of regional and commuting or the migration of for homogenization may indicators neglect research on spatial mobility be with to both conditions socio-economic and conditions unemployment, is to these findings. we the of homogenization commuting and and economic to be of the spatial in other lead to a different of homogenization and processes. This is an for to the we are to the as to whether economic functional regions with it better than administrative regions, or to it kind of regional delineations with the However, our analyses that both of the and spatial be into spatial we found strong evidence of the of functional regions administrative all the regional labour by and As spatial we found relevant spatial clustering of economic indicators by the less level in our case is the to take this kind of clustering into because the boundaries of regions with all other regional at a higher aggregation our results for Germany that economic functional delineations are not able to capture both commuting interrelations and spatial clustering or homogeneity very This is an in of not on to such as or of interaction & may be for well functional which are especially of spatial clustering at a lower aggregation level

Cluster analysis · Econometrics · Economic geography · Economics · Geography · Hierarchical clustering · Homogeneous · Homogenization (climate · Metropolitan area · Statistics · Mathematics · Regional Economics and Spatial Analysis · Spatial and Panel Data Analysis · Urban Transport and Accessibility

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