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Linking spatial scale to changes in workplace earnings – An exploratory approach

Relation entre l’échelle spatiale et l’évolution des gains sur le lieu de travail – Une approche exploratoire
Wenjuan Li, Einar Holm et Urban Lindgren

Résumés

Le document étudie l'importance de l'échelle spatiale dans l'évolution des gains sur le lieu de travail, en utilisant la régression spatiale appliquée au niveau des micro-données sur les lieux de travail dans un but exploratoire. Une technique à grille flottante est utilisée pour définir les lieux de travail de taille égale et leurs zones d’accès quotidiens environnantes jour- divisée en trois entités spatiales: le km2 de travail, la zone locale et l'arrière-pays. Sur la base des informations géo-référencées sur les lieux de travail et les lieux de résidence ainsi que de nombreux indicateurs socio-économiques au niveau individuel, les résultats des modèles de régression révèlent que les indicateurs de la zone d’accès quotidien jouent un rôle dominant et que leur contribution varie selon les entités spatiales. Parmi les entités spatiales, le travail-carré (km carré) entourant le lieu de travail est plus important que le lieu de travail lui-même, la région et l'arrière-pays. En outre, les résultats suggèrent que des facteurs internes liés à la taille de la population, la diversité du commerce et de l'industrie et le niveau d'éducation contribuent à environ un tiers des changements dans le revenu de travail au niveau du lieu de travail. On peut en conclure que la connaissance, l'apprentissage et le capital humain sont fortement associés à l'augmentation du bénéfice.

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This study was funded by the Swedish Research Council for Health, Working Life and Welfare (Forte: 2013-1313).

Introduction

1Throughout modern times, economic growth and its driving forces have been intensively observed and analysed. Growth has been measured through indicators that more or less take spatial scale into account. By taking Sweden as an example and using population numbers as an indicator, it can be seen that growing and declining regions exist side by side. The densely populated corridor of Stockholm-Gothenburg-Malmö is often referred to as a growing region, whereas the sparsely populated Norrland (northern Sweden) is viewed as a region with severe socioeconomic and demographic problems. However, when applying a higher spatial resolution, growing as well as declining sub-regions can be found within the southwest corridor of southern Sweden and Norrland. Irrespective of spatial scale, the same questions are asked: Why do some places grow faster than others, and why do some places grow while others decline? By taking on an explorative approach, the aim of this paper is to investigate the impacts of localized conditions on workplace earnings. The relative importance of factors related to product demand, business environment, and labour resources is analysed in combination with different spatial entities. The analysis utilizes a micro database containing socioeconomic information on all Swedish citizens as well as all firms and their plants. This source of information is used to reveal the potential importance of various site and situation characteristics for income changes at the workplace level.

2Neoclassical growth models assuming decreasing marginal returns to scale predict a convergence of economies in regions and countries, which does not seem to be the case in a comparison of growth rates in developing and developed countries during the past 50 years. Another shortcoming of neoclassical models is that they do not explain why technological shifts occur. In contrast, the new growth models claim that closed economic systems (e.g. a region or a country) can become partly self-sustaining and experience dynamically increasing returns (Arrow, 1994; Arthur, 1994; Karlsson et al., 2001). These increasing returns are achieved by externalities of knowledge and learning (Arrow, 1962) and of human capital (Romer, 1986 and 1990; Lucas, 1988). The externalities are often referred to as agglomeration economies and can be further divided into MAR (Marshall-Arrow-Romer) externalities, related to specialization (localization economies), and Jacob’s externalities (Jacobs, 1969), associated with the diversity of local employment (urbanization economies).

3A great number of empirical studies focuses on these externalities because knowledge exchange and learning are found to be important for the performance of firms (e.g. Lundvall & Johnson, 1994; Maskell & Malmberg, 1999; Asheim, 2000). Boschma (2005) argues that merely geographic proximity is not sufficient for learning and knowledge transfers to take place. Other types of proximities (such as cognitive, social, institutional and organizational) are at work, and are most likely reinforced by geographical proximity. Despite the existence of widespread information technology, geographical proximity enables physical interactions between people and firms in a way which is not easily replaced by the Internet or other information technologies. The use of high-tech communications and E-business in the Nordic countries is extensive, but geographic proximity is shown to be a central aspect in the process of learning. Malmberg and Maskell (1997) analysed the sustainable patterns of regional specialization, industrial systems and agglomeration, and found that the benefits of proximity can promote spatial agglomeration in relation to firms engaged in interactive processes, some of which might involve learning.

4In spite of the valuable contribution to endogenous growth theory made by both geographers and economists, the fact that there are obvious inconsistent findings within the literature should not be ignored. For example, Glaeser et al. (1992) constructed a cross-sectional model by aggregating two-digit industry census data from 1956 and 1987 into 170 US standard metropolitan areas. The model showed that intra-industry knowledge spillover is less important than knowledge spillover across industries. Moreover, they concluded that diversity (Jacob’s externalities) contributes more to growth than other externalities. Using a similar data source from 1970 and 1987, Henderson et al. (1995) constructed a model of 224 US cities on capital goods industries. It was reported that new industries prosper in large, diverse metropolitan areas while mature industries decentralize to smaller, more specialized cities. These results could be interpreted as increasing returns created by both MAR externalities and Jacob’s externalities. Malmberg et al. (2000) studied Swedish export firms using micro statistic data, and found that internal scale economies together with urbanization economies (Jacob’s externalities) have a larger impact than localization economies (MAR externalities) on export performance. Using Swedish local labour market regions and focusing on the ICT, machinery and rubber industries, Wictorin (2007) reported that no significant connection between concentration of similar enterprises and productivity of labour was found. Using the same labour market regions and longitudinal individual data for a twelve-year period, Eriksson et al. (2008) studied effects of localization, urbanization and scale of job changes, and suggested that the concentration of similar activities may be gainful for small regions. Engelstoft et al. (2005) reported that little evidence supports the claims concerning the existence and performance of frequently identified and examined industrial clusters in Denmark. The above examples illustrate how inconsistent the various findings can be.

5These inconsistent findings do not only stress the complexity of analysing economic performance, but also hint at a possible research bias caused by the lack of spatial hierarchies or by not paying enough attention to intra- and inter-regional interaction among people, firms and institutions. Focusing on geographic scale in defining economic performance can probably contribute to the explanation of its driving forces. Schofield and Coleman (1986) noticed that there are difficulties in relating ideas at different scales in studies using geo-referenced data. Furthermore, the complexity of real life cannot easily be explained by abstract concepts or simplified models, which might however be a good point of departure. Massey (2004) emphasized the importance of relations in society: “it is not possible to have work which is predominantly ‘mental’ or ‘intellectual’ (in spite of the frequently applied epithet of ‘knowledge-based society’) without manual work. It is not possible to have supervisory work without there being activity to supervise. It is not possible to have assembly without the manufacture of components” (p. 111). These arguments point out the significance of maintaining a cohesive and holistic perspective. A confinement of the analyses to particular regions or industries might be one reason for the inconsistent findings in the literature concerning the importance of different agglomeration economies and the different views on regional growth models.

6Along this line of thought, we suggest that the analysis should incorporate a broad set of economic agents and recognize that these firms and workplaces are nested in spatial hierarchies. The study uses data from Sweden – in particular, we base the analyses on register data containing longitudinal geo-referenced demographic and socioeconomic information on individuals and firms. In the next section, a conceptual model of localized conditions for workplace earnings is presented as a device for exploring the research question of the paper.

Localized conditions for earnings at the workplace – a conceptual model

7The point of departure for constructing a model investigating the importance of internal and external factors influencing earnings is to define homogenous spatial entities enabling a comparison of different geographies. Administrative regions have been widely used as spatial entities despite their obvious heterogeneity. In Sweden, local administrative regions usually refer to the municipalities (n=290). The average municipality covers 1,552 square kilometres and is inhabited by more than 30,000 people. Striking pictures of intra- and inter-regional divergence can be observed by looking at socioeconomic indicators of each municipality. For example, in Stockholm there are nearly 4,000 people per square kilometre while the corresponding figure for Kiruna (the northernmost municipality) is one. Administrative regions have obvious disadvantages in this respect and should be used with caution when studying the space economy.

8As an alternative approach, Li et al. (2009) developed a floating grid method for the study of spatial attractiveness. Instead of administrative regions, small spatial entities (kilometre squares) were employed as spatial units of observation. Generally, the kilometre square is more homogenous than any of the smallest administrative regions. Each of the spatial units is related to a unique neighbourhood with its particular demographic and socioeconomic characteristics. In this study, the floating grid method is used once more by linking neighbourhood properties to each Swedish kilometre square in which workplaces are located.

  • 1 The reason for using the more aggregated definition of workplaces instead of the actual workplaces (...)

9Spatial squares and industrial classification codes (branch of industry) are used to define workplaces. The unit of analysis is a constructed workplace defined as the aggregate of all those employed within the same square belonging to the same branch of industry1. Squares with at least one economic activity (employment in at least one branch of industry) are regarded as working-squares. If all workers in a working-square are employed by industry j, the square can thus be referred to as a workplace of industry j. If some workers are employed by industry j and others by industry k, the square is referred to as a workplace of industry j and a workplace of industry k. In the latter case, two workplaces share the same working-square coordinates. If the number of branches in the utilized classification is n and at least one employed individual from each of these works in a single square, the square can be said to host all workplaces. The size of the working-square is 1 square kilometre.

10The Swedish standard industrial classification code SNI92 was used, and was simplified into 57 main activities, a classification denoted as SNI57 (Lindgren and Strömgren 2007) in this paper (see Appendix 1). Employing kilometre squares and SNI57, the total number of working-squares and workplaces amounts to 60,000 (13% of the Swedish territory) and 180,000, respectively. On average, this corresponds to about three workplaces per working-square and 30 employees per workplace.

11In accordance with the floating grid approach, the surroundings of a workplace can be defined by concentric zones at certain distances around workplaces. In addition to workplace and working-square, two more zones referred to as local area and hinterland were defined, as illustrated in Figure 1.

Figure 1. Workplace, working-square and its surrounding zones

Figure 1. Workplace, working-square and its surrounding zones

12The zone from the working-square up to a five-kilometre radius is referred to as the local area. The median commuting distance for Swedish daily commuters is five kilometres (Sandow 2008), which means that half of the commuters travel shorter distances to work. From a workplace perspective, the local area offers access to a large part of the labour supply on the local labour market. Moreover, the local area in urban settings also contains a good deal of local service functions.

13The functional hinterland is situated further beyond the local area. This zone extends up to 50 kilometres and is labelled hinterland. Swedish studies on commuting behaviour show that 50 kilometres can be regarded as the upper limit for the distance of people’s daily travel between home and work (Öhman and Lindgren 2003, Sandow and Westin 2006). From the workplace point of view, the hinterland comprises more or less the available labour pool, the local market, and sometimes even the most important interactions with clients and competitors.

14The spatially hierarchical structure identified in Figure 1 is termed spatial entities in the remainder of the paper. The analysis entirely disregards arbitrarily administrative regions and focuses on the specific surroundings of each workplace. Localized socioeconomic factors of the surrounding zones interact and affect the performance of workplaces which, in turn, provides a source for enhanced earnings and economic growth.

15It should be stressed that there is virtually no closed economic system in the real world. External and internal factors are intertwined and are functionally inseparable (Stough 2000). External factors create a macro milieu for a region, whereas internal factors are rooted in the specific settings of the region. These factors clearly contribute to regional growth (e.g., Li 2006). Recognizing the difficulties in separating internal and external factors, the term daily reach was introduced and is defined as the localized socioeconomic factors within the range of the hinterland of workplaces. This definition is partly justified by the empirical fact that there are socioeconomic variations between hinterlands, even for nearby ones. Adjacent working-squares do not have identical hinterlands; there are always deviations of varying magnitudes. This supports the notion that the unique content of the daily reach could work as a proxy for internal factors. Admittedly, factors within daily reach may, to a considerable extent, be an indirect result of external characteristics, institutions and processes of the nation and its global surroundings and there might be internally-related variables that are omitted in our analysis, but it seems reasonable to believe that the geographical distribution of socioeconomic factors can be helpful in distinguishing between these two sets of factors. Nevertheless, these considerations led us to incorporate national statistics on employment changes in SNI57 as a proxy for such external factors affecting the economic performance of workplaces. Therefore, it could be argued that the workplace and its surrounding zones are not treated as a closed system in the constructed model.

16In the next section, data sources, variables for daily reach and external factors used in the analysis are presented.

Data and variables

17The data sources for the study are the individual longitude database ASTRID and the 1:250,000 Swedish national general maps (Red Map). ASTRID is released by Statistics Sweden (SCB) and contains more than 130 variables depicting the annual social and economic status of each individual living in Sweden, including location information (geographic coordinates with 100-metre resolution) of each individual’s residence and workplace. The Red Map is released by the Swedish Land Survey (Lantmäteriet) and contains detailed information on landscape, land use and infrastructure. The data from the two sources can be aggregated or disaggregated based on different geographic resolutions.

18GDP is the expected and most widely used indicator of economic growth, whether it is studied at the regional, national or global level. However, it is not possible to use GDP (value added) for each workplace, simply because it is not an observable at this level; estimates of value added are only available at the firm level (often containing several differently located workplaces). The closest available surrogate is work income for everyone employed at each workplace. For private and public services as well as labour-intensive manufacture, this surrogate is fairly close to value added. For capital-intensive industries, however, the difference might be great and the share of value added used for buying labour might be small as compared to the share used for paying capital services. In the long run, a profitable capital-intensive industry also supposedly has to turn over profits to personnel and salary levels. Using change in summed salary as a growth indicator means that the performance of a capital-intensive industry is judged by its ability to pay employee salaries at its own workplaces and not at the workplaces of its suppliers of capital goods. The work income of each workplace is an indicator that is related not only to regional and national employment and GDP, but also to the daily life of every individual who is affected by regional, national and even global economic growth. So, the operational measure of workplace growth utilized in this study is change in the sum of income of all workplace employees. This change may be the result of changes in the number of employed or salary levels, or both. The change of work income at a workplace within a five-year period is used as the dependent variable Y in the regressions. The selected study period is 1998-2003, which almost constitutes a small economic cycle, including a growth peak (4.5% in 1999) and a bottom (1.1% in 2001).

19In total, 13 explanatory variables are selected to capture the internal factors for one, two or all spatial entities. They are grouped into three categories: demand, business environment and labour force factors (Figure 1). For the spatial entities, some variables are only meaningful for the workplace, some only for the surrounding zones, and the rest for both. The 13 variables were extended into 32 when counting their appearance in separate zones as different variables in constructing the spatial models as listed in Table 1.

20Demand is the basic and most important reason for why certain industries, firms or organizations exist. It can originate from global, national or local markets. In this paper, demand is divided into two parts: from outside daily reach and within daily reach. External demand factors are defined as demands from global and national levels. The underlying assumption is that stronger global or national demand contributes to local industrial growth while weaker demand creates local decline. Two variables were chosen to indicate external demand. One is the relative national growth of the industry of the workplace in question (SNIj) in terms of the number of people employed, and the other (productivity proxy) in terms of average incomes. So, industrial growth is measured as changes in employment and salary levels. The two selected indicators give a general picture of the national development of the 57 reclassified activities during the period studied. The national development also to some extent reflects the impact of global changes on conditions for different industries.

21Local demand factors are defined as demand within the daily-reach, which mainly constitutes the local market. The size of the local market is an important determinant of specialization patterns and home market effect (Helpman and Krugman 1985, Krugman 1991). Local demand is indicated by three variables: population number, income level and the deviation of the income level between workplace j and the average of the SNI57 industry. Population number and income level are direct indicators of potential local demand and size of the local market. The larger the population and the higher the income level, the stronger the local demand is expected to be. Distance plays a role in strengthening or weakening demand from the local market and, therefore, the two direct indicators were calculated separately for each of the three spatial entities: working-square, local area and hinterland. Deviation of income level is an indirect indicator and is only calculated for the workplace. Positive deviation means that workplace j has a higher income level than the national average for that industry (SNIj), indicating either that the workplace (already) performs better than average or that it is located a in high-income-level region.

22Business environment factors include three variables that are indicators of diversity, localization and private sector size. Each of the variables is measured separately for working-square, local area and hinterland. The diversity indicator is defined as the total number of economic activities (the 57 activities based on SNI57) present within each of the three spatial entities surrounding the workplace. More economic activities indicate a higher diversity level and more Jacob’s externalities. The localization indicator is defined as the total number of employees in the SNI57 activity of the workplace in each of the three surrounding spatial zones, indicating the eventual advantage of local specialization in the three spatial entities. The larger the number of people employed in the industry, the higher the localization level and the more MAR externalities are present. Private sector size is the total number of employed in private sectors in the three spatial entities. For some industries, an environment with many private sector employees might have a different impact on performance as compared to a large public sector.

  • 2 Immigrant is defined as someone originating from Eastern Europe (including Russia), East and South (...)

23Labour force factors are variables indicating the skills and characteristics of the labour force in the workplace and its surrounding zones, actually indicators of human capital. The labour force factors include education and average age of the labour force, as well as the number of women and immigrants2. Education includes two variables. One is the number of university-educated employees, which is calculated for the three spatial entities. The other is the deviation of the proportion of university-educated employees between workplace j and the average for its national SNI activity, thereby indicating the competence level of the workplace as compared to its rivals or co-operators in the same SNI57 activity. Average age, number of women and number of immigrants are indicators of the demographic situation and the labour force composition on different spatial scales.

24The data preparation differs from the traditional method of aggregating micro data into administrative regions or industries. Several steps are required to prepare the data for each workplace and its surrounding zones. First, individual information is extracted from the ASTRID database; the detailed industrial classification SNI92 is simplified into 57 economic activities, SNI57 and the 100 metres coordinates are truncated into kilometre coordinates. Second, workplaces are identified based on the SNI57 and kilometre coordinates and the variables for workplaces and working-squares are calculated. Third, the calculated variables are visualized in the 1:250,000 general maps based on their coordinates and the neighbourhood analysis tool of ArcGIS is then used to aggregate the data into local area and hinterland for each workplace.

Table 1. Explanatory variables related to spatial entities and categories (demand, business environment and labour force factors) in the models

Categories

Variables

Work-place

Work-ing-square

Local area

Hinter-land

Exter-nal factor

External factor

Demand

SNI_size_

change

FP

SNI_income_

change

FP

Internal factor within daily-reach area

—local market

Demand

Population

size

FP

FP

FP

Income

level

FP

FP

FP

Deviation_

income98

FP

Internal factor within daily-reach area

—sources of externalities

Business Environ-ment

Diversity (SNIs)

FP

FP

FP

Localization (SNIj)

FP

FP

FP

Private

sectors

FP

FP

FP

Internal factor within daily-reach area

—human capital

Labour Force

Deviation_

educ98

FP

Average age

FP

Woman

FP

FP

FP

FP

University educated

FP

FP

FP

FP

Immigrant

FP

FP

FP

FP

Note: F and P denote full and partial models, respectively, the definitions of which are presented in the Method section.

Method

25The method used for this study is to construct, in an exploratory way, full and partial spatial regression models to test how the internal factors within the daily-reach contribute to the workplace’s economic performance independently and interactively, and to identify intervals for partial explanatory effects of the variables in each category and spatial scale.

26While constructing spatial models using the dataset and the floating grid approach of this paper, estimation bias caused by spatial autocorrelation is an apparent risk to consider. Obviously, hinterland indicators are very similar for adjacent workplaces since they are based on largely the same basic observables. So, the question is not whether or not those indicators are auto-correlated at the workplace level – of course they are. The important question is instead whether this autocorrelation will bias the estimation of the partial impact of the indicator on performance. If it is actually the case that the size of the surrounding labour market affects workplace performance, it does so regardless of whether or not the measured indicator is almost the same for its neighbour workplace. Since the data is from all of Sweden, it is not the case that there is not enough observed variability in the indicator throughout the country to reveal such a relationship; the problem is narrower. Does the abundance of similar observations for nearby target workplaces bias the estimation of the size of the impact of the indicator? Or can it be treated just like another “independent” control factor with limited variation between neighbours? For instance, the attribute sex has almost only two outcomes, male and female, but is seldom regarded as problematic to use as an independent control attribute. If, for some reason, all males in Sweden were suddenly relocated to the north and all females to the south, a tremendous spatial autocorrelation would appear in the analysis (and social disorder in the country). But if nothing else is changed in the dataset, the estimated partial impact of sex on behaviour would be the same as when sex mixes spatially as observed.

  • 3 Methods and programmes have been developed to adjust the spatial autocorrelation if the data size i (...)

27The use of OLS models implies potentially unadjusted spatial autocorrelation in terms of overestimated t-values. However, in a similar analysis, estimations of OLS models were compared with spatial regression models correcting for autocorrelation. The results of the comparison showed that parameter estimates did not differ to any great extent (Li et al. 2009). Here we have also explored an alternative method, but with limited success3. For these reasons, all analyses presented in this study are based on OLS regression. All analyses presented here are based on OLS regression, which has shown to be fruitful when applying an exploratory approach.

28The basic form of the model is:

Yi = β0+ β1X1i + β2X2i …+ βkXki + εi for k independent variables. (1)

  • 4 When one more variable (one very close to the target-dependent one—the change in numbers of employe (...)

29The selected indicator of growth Y and the 32 X variables are first applied in the model referred to as the full model, and the regression result is listed in Appendix 2. The indicators for the daily-reach area and the selected external factors explained 28.58% of the variation in economic performance of workplaces4. The full model only fulfilled part of the study goal, as the contribution of each category and spatial scale to the totally explained variance has not yet been identified. Meanwhile, the interactions among the X variables need to be taken into account. In addition to the full model, more analyses are needed.

30A method aimed at decomposing the total explained variance into partial variance components and at revealing the interactions among the X variables was developed. The partial variance component is defined as the contribution by each of the categories and spatial entities. The method is to construct stepwise cumulative partial models to decompose the total explained variance, and then identify possible intervals for the partial explanatory effects. The technical details of the method are described in Appendix 3.

31In total, 36 partial models were constructed step by step in spatial entities and categories. For the variables sorted on spatial entities, partial models were constructed as outward models (from workplace to hinterland), inward models (from hinterland to workplace), first enter models (variables on each spatial scale enter first) and last enter models (variables on each spatial scale enter last). For the variables sorted on the categories, partial models were constructed as demand models (in which external demand, local demand, business environment and labour force entered step by step), resource models (in reverse order to the demand models), first enter models and last enter models. The results of all the partial models are listed in Appendix 4 and visualized in Appendix 5, clearly demonstrating the interactions among X variables. A summary of the minimum and maximum values of the partial variance components is listed in Tables 2 and 3, and visualized in Figure 2.

Results

32The regression result of the full model (Appendix 2) for all 32 X variables is statistically significant (p<0.01), and the coefficients vary over spatial entities. The variables within the daily-reach area together with the external demand factor explained 28.58% of the variation in the economic performance of workplaces as measured. Within the total explained variance, the variables within the daily-reach area explained the largest part.

33In addition to the total explained variance in the full model, the intervals of the partial variance components were identified by the partial models and were listed as minimum and maximum values in Tables 2 and 3 presented as percentages.

Table 2. Variance components over spatial entities

Spatial entities

Partial variance

Minimum

Maximum

Workplace

4.19

5.31

Working-square

11.78

16.45

5km

3.00

6.66

50km

2.54

9.78

External

0.35

0.60

Sum

21.86

38.80

Table 3.Variance components of the categories

Categories

Partial explanatory effect

Minimum

Maximum

External demand

0.35

0.60

Local demand

1.33

2.44

Business environment

1.98

7.77

Labour force

18.36

21.61

Sum

22.02

32.42

34The maximum values are R2 in percentage when the variable groups entered the full model as the first entry group. They are also the R2 of simple models in which only the X variables constitute the respective variable group. Actually, the maximum values of R2 are the partial variance of the respective variable groups, including all variable interactions. Thus, the summation is 38.80 and 32.42 for spatial entities and categories, respectively. The two summations gave different values, i.e. 38.80 and 32.42, which is caused by different interactions of variable groups. The variable interaction is counted once in every partial model; thus, in the summation, the same interaction is counted more than once and the summation is greater than the total explained variance of the full model. The over-counting is 13.22% (38.80%-28.58%) and 6.84% (32.42%-28.58%), respectively.

35The minimum values are R2-added when the variable group enters the full model as the last group, and actually constitute the minimum partial variance of the variable groups excluding any variable interaction. The summation of the minimum R2-added is 21.86 for the spatial entities and 22.02 for the categories, which indicates that the interaction among X variables contribute a 6.72% (28.58%-21.86%) and a 6.56% (28.58%-22.02%) explanatory effect in spatial entities and categories, respectively.

Figure 2. Partial explanatory effects of the internal factors in spatial entities and categories

Figure 2. Partial explanatory effects of the internal factors in spatial entities and categories

36Figure 2 illustrates how the partial variance components within the daily-reach area are distributed in the full model. It should be observed that the full model explains 28.58% (R2 = 28.58 in percentage) of the variation in Y when all the 32 X variables interact, among which the partial explanatory effect of the external demand factor is very small, only 0.35% to 0.6%. Therefore, the partial explanatory effect of the external demand factor is not displayed in Figure 2, where the left-hand bar shows the intervals of partial explanatory effects over spatial entities and the right-hand bar shows the intervals of the three categories within daily-reach area. The method of constructing full and partial models makes it possible to identify the most important variables and spatial scale that contribute to workplace earnings. Regardless of what order these variable groups enter the full model the partial variance components are within the intervals, and the total explained variance of the full model remains unchanged.

Discussion

37The models reveal that the indicators of the daily-reach area play a dominant role and the fact that their contribution varies over spatial entities. The identified intervals of the partial variance components indicate that the labour force factor is the most important condition for growth in earnings, business environment is the second most important, and local demand is more important than external demand. Among the spatial entities, the working-square (km square) surrounding the workplace is more important than the scales of the workplace itself, the local area and the hinterland.

38The regression coefficients from the full model provide more insight into how different amenities of the daily-reach area contribute to changes in workplace income (Appendix 2). The important role of the labour force factor is fully expected, although each of the variables contributes in different ways. From the parameter estimates, it can be seen that a large number of university-educated people at a workplace does not necessarily incur growth; but if the proportion of university-educated at a workplace is higher than the industry average, it does create growth. This indicates that the contribution to economic growth of possessing highly educated employees is mainly due to the comparative advantages of human capital that it gives workplaces within the same industries. If all workplaces within an industry employ an equally high proportion of university-educated employees, this does not necessarily create growth.

39The role of women and immigrants varies over spatial entities and differs from that of the university-educated. Women and immigrants generally make up two low-income groups. The effects of the number of women and immigrants go in opposite directions within workplaces in the model: Women contribute positively to the dependent variable while immigrants contribute negatively, which might indicate that women’s income level (in female industries) has improved during the study period while the same did not happen for immigrants.

40Departing from the workplace and focusing on the working-square, local area and hinterland, the full model tells us more. Unlike workplace, the number of female employees in working-square, local area and hinterland contributes negatively to the dependent variable. This means that although the income level and number of individuals employed have increased within workplaces, women still concentrate in low-income industries or belong to low-income groups. For the number of immigrant employees on the same spatial entity, at first glance the regression coefficients create some confusion. They contribute positively in the working-square and local area, but negatively in the hinterland. It is possible that this confusion-like result reflects the situation that immigrants concentrate in densely populated large cities, in contrast to the more evenly spatial distribution of women. The regression coefficients of immigrants are actually a combination of industrial agglomeration and immigrant distribution. Within five kilometres of these large cities, the positive effect of agglomeration offsets the negative impact of a large number of low-income immigrants; but the agglomeration effect weakens as distance increases from five to 50 kilometres; thus the negative impact of immigrants might offset the agglomeration effect and the coefficient once again becomes negative.

41For the business environment, the model indicates that agglomeration (both diversity and localization) significantly contributes to growth, and that spatial scale is of importance for the contribution. The model shows that diversity contributes positively to economic performance in the local area but negatively in the hinterland. Localizations both too close to and too far from competitors or co-operators in the same industries create negative impact, whereas only a medium distance seems to result in a positive contribution. The “suitable” distance is less than five kilometres for diversity and between one and five kilometres for localization. This finding gives some insight into findings based on Swedish LA regions. The size of LA regions varies significantly, and the spatial extent of most LA regions is larger than the defined daily-reach area, which might be why no significant connection between concentration of similar enterprises and productivity of labour was observed (Wictorin 2007), and why the concentration of similar activities seems gainful for small regions (Eriksson et al. 2008). Only high resolution can give a clear picture, and spatial scale is of importance.

42For the contribution of demand factors, the model shows that local demand contributes more than external demand, which supports the hypothesis of home market effects. For local demand, the income level is more important than population size, which is understandable but might also reflect hidden covariation with other positive, not measured amenities in the environment. It should be observed that external demand is only used as a controller in the full model. As such, it is positively related to economic growth, according to the model.

Conclusion

43In this paper, the exploratory approach of a floating grid and “from within”, together with a simplified industrial classification code, was applied to identify workplace and its unique set of conditions in surrounding zones. A method was developed to reveal how localized and local factors (i.e. variables of daily-reach area) affect workplace earnings. The method enables a decomposition of the total explained variance into partial variance intervals to illustrate the relative importance of different growth factors and to understand how these factors interact. By applying large-scale micro data covering all economic activities in an entire country, as is done in the paper, the method is demonstrated as suitable for the issue studied here and gives reason to believe that the result from the developed spatial models might come a step closer to the complicated web of intrinsic spatial economic activity, as compared to the general aggregate models in which the spatial dimensions are absent or, at best, just another static dimension. The findings here resolve some inconsistencies in the existing literature; a lack of spatial scale and an inadequate emphasis on interactions between different factors might be one reason for earlier shortcomings.

44The findings indicate that both external and internal factors contribute to income growth. A similar conclusion was reached using the same data source but shift-share analysis (Li 2006). The full model indicates that nearly one-third of the growth is achieved by the utilized indicators in the daily-reach area. The unexplained variance is 72%, which means that other factors contribute to growth twice as much as the observed indicators for the daily-reach area. The “other factors” could be either internal or external. Moreover, if only a small part of this remaining, unobserved causation is internal, this will substantially increase the observed one-third share. On the other hand, a part of the observed internal factors found, especially the strong impact of factors in the working-square and local area, might be partially determined by unobserved covariation with institutional factors and characteristics at national and global levels.

45In line with the discussion on endogenous growth, the findings support the claims that increasing returns can be achieved by externalities of knowledge and learning and human capital (Arrow 1962, Romer 1986, 1990, Lucas 1988). Among the 32 explanatory variables in the paper, those of labour force and business environment factors are actually indicators of human capital, externalities of knowledge and learning. The results of the models demonstrated that a substantial part of the increasing returns is due to the externalities of knowledge, learning and human capital.

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Annexe

Appendix 1: Codes and names of SNI57

SNI57

Name

SNI57

Name

0

Undefined

29

Supporting and auxiliary transport activities; travel agencies

1

Agriculture & hunting

30

Post and telecommunications

2

Forestry

31

Financial intermediation

3

Fishing

32

Real estate

4

Mining

33

Renting and business activities

5

Manufacture of food, beverage & tobacco

34

Computer and related activities

6

Manufacture of textiles & textile products

35

Research and development

7

Manufacture of wood and wood products

36

Juristic

8

Manufacture of pulp and paper

37

Stock

9

Publishing and related activities

38

Other business services

10

Manufacture of chemicals

39

Advertisement

11

Manufacture of plastic

40

Job centres

12

Manufacture of non-metallic mineral products

41

Supervision

13

Manufacture of metals

42

Cleaning

14

Manufacture of metal products

43

Administration

15

Manufacture of machines

44

Police, defence and fire department

16

Manufacture of electrical and optical equipment

45

Social work

17

Manufacture of transport equipment

46

Education (elementary school)

18

Manufacture of furniture

47

Education (high school)

19

Recycling

48

Education (college and university)

20

Electricity, gas, steam and hot water supply

49

Education others

21

Construction

50

Sick care

22

Sale, maintenance and repair of motor vehicles and motorcycles, retail sale of automotive fuel

51

Veterinarian

23

Whole sale trade and commission trade, except motor vehicles and motorcycles

52

Health care

24

Retail trade except motor vehicles and motorcycles, repair of personal and household goods

53

Waste handling

25

Hotel and restaurants

54

Organizations

26

Land transport

55

Recreation, cultural, sporting activities

27

Water transport

56

Cleaning, hairdresser, other service

28

Air transport

Appendix 2: Regression result of the full model

SNI square

km square

5km local area

50km hinterland

External

Constant

-1012606.31

(-393.06)

External demand

sni_size_change

2.11

(489.6)

SNI_income_

change

0.83

(398.22)

Local demand

Population size

-69.55

(-901-75)

-0.20

(-18.66)

-2.17

(-770.93)

Deviation_

income98

-53.34

(-127.64)

Income level

-0.06

(-572.48)

16.53

(371.73)

80.44

(395.26)

Business Environment

Diversity (SNIs)

2852.0

(120.34)

7753.93

(256.18)

-1759.30

(-61.62)

Localization (SNIj)

-238.72

(-464.83)

101.62

(1509.34)

-10.12

(-464.92)

Private sectors

-1.23

(-167.07)

-9.42

(-668.04)

-45.55

(-315.60)

Labour force

Deviation_

educ98

52466.29

(101.44)

Average age

-2330.58

(-57.54)

Woman

1400.94

(1858.70)

-573.06

(-1275.26)

-0.57

(-431.89)

0.47

(1482.64)

University educated

-536.27

(-547.87)

13.13

(25.17)

-640.94

(-551.94)

90.85

(439.62)

Immigrant

-4910.12

(-1686.43)

5199.08

(4141.61)

7202.76

(450.04)

-1374.91

(-550.70)

Note: t value is within parentheses.

Appendix 3: Constructing partial models

The model used to examine the partial variance components is an OLS model constructed step by step (Li et al., 2009). In each step, one more variable group is added into the model until all the variables enter the model. The value of R square increases with each step. The residual of R squares between two consecutive partial models is the new explained variance added by the newly entered factor group, the partial variance components. The following example demonstrates how partial models are constructed and how partial variance components are calculated. Suppose that there are three groups of X variables (β1, β2 and β3), and the basic OLS full model can be rewritten as

Yi = β0+ β1X1i + β2X2i + β3X3i. (1)

R2 or which is the total explained variance of β1, β2 and β3 to the variation of Yi. In order to know how the R2 distributes among β1, β2 and β3, stepwise accumulative partial models need to be constructed. In the first step, Model (2) with only the first group of variables β1 was constructed:

Yi = β0+ β1X1i. (2)

that is the explained variance by group β1. In a full model like (1), is defined as a the partial variance component of β1, thus component1 = . In the next step, we construct Model (3) by adding group β2 into Model (3):

Yi = β0+ β1X1i + β2X2i. (3)

that is the explained variance by both groups β1 and β2. Because we already get effect1 by Model (2), thus effect2 = - or effect2 = - effect1. Based on Models (1), (2) and (3), the effect3 of group β3 can be calculated as

effect3 = R2 - effect1 - effect2 or

R2 = effect1 + effect2 + effect3. (4)

Now the total explained variance of the full model R2 has been decomposed into effect1, component2 and component3. The relative sizes of the three partial variance components have been identified.

As previously mentioned, the independent variables are actually not completely independent of each other. In this example, if β1 and β2 are not completely independent, the interactions between β1 and β2 give the following two models

Yi = β0+ β1X1i + β2X2i (5)

Yi = β0+ β2X2i + β1X1i (6)

and although = . In other words, although the total explained variance of Models (5) and (6) is the same, the partial variance components component1 and component2 in Models (5) and (6) is different; furthermore, component1 in Model (5) is greater than component1 in Model (6) and component2 of Model (5) is smaller than component2 in Model (6). This is because the orders of variable groups entering the stepwise accumulative models affect the R-values unless β1 and β2 are absolutely independent. As a matter of fact, for variable groups it applies that the earlier they enter the model, the larger the R-squares are. Therefore, a variable group gets its maximum R-square and variance value if entering the full model first, and the minimum R-square and variance if entering the full model last. After obtaining the maximum and minimum R-squares, it is possible to identify the interval of the partial variance components for each group.

Appendix 4

Appendix 4a: Total explained variance (R2) and partial variance components over spatial entities

Outward models

(SNI sq External)

Inward models

(External

SNI sq.)

First enter models

Last enter models

R2

effect

R2

effect

effect

effect

Workplace

5.31

5.31

28.58

4.19

5.31

4.19

1km

21.41

16.10

24.39

11.78

16.45

15.97

5km

25.43

4.02

12.61

2.48

6.66

3.00

50km

28.23

2.80

10.13

9.53

9.78

2.54

External

28.58

0.35

0.60

0.60

0.60

0.35

Appendix 4b: Total explained variance (R2) and partial variance components among social economic factors

Demand models

(External demand → Labour force)

Resource models (Labour force → External demand)

First enter models

Last enter models

R2

effect

R2

effect

effect

effect

External demand

0.60

0.60

28.58

0.35

0.60

0.35

Local demand

2.83

2.23

28.23

1.45

2.44

1.23

Business environment

10.22

7.39

26.78

5.17

7.77

1.98

Labour force

28.58

18.36

21.61

21.61

21.61

18.36

Appendix 5

Appendix 5a: Variance distribution over spatial entities

Appendix 5a: Variance distribution over spatial entities

Appendix 5b: Variance distribution among social economic factors

Appendix 5b: Variance distribution among social economic factors
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Notes

1 The reason for using the more aggregated definition of workplaces instead of the actual workplaces reported in the dataset is related to problems of keeping track of workplace identities over time. The same identity number in a comparison of two different years does not necessarily refer to the very same workplace. This problem is particularly connected to the numerous small workplaces with few employees.

2 Immigrant is defined as someone originating from Eastern Europe (including Russia), East and South Asia (excluding Japan), Middle East, Africa, or South America.

3 Methods and programmes have been developed to adjust the spatial autocorrelation if the data size is within a certain scope. The statistic programme R package designed for multidimensional and spatial analysis was used in the early stage of the study, but two problems arose: the capacity of the programme and its inability to deal with the empty squares. The capacity of the current R programme is far from sufficient for the huge dataset of all workplaces and their surroundings; even a dataset for one of the 290 municipalities is beyond its capacity. In this study, the workplace and its surroundings constitute the focus, and other squares without workplaces are treated as empty squares with no data observables; however, the spatial analysis programme is not able to handle the empty squares properly.

4 When one more variable (one very close to the target-dependent one—the change in numbers of employed at workplaces) was added into the full model, the R2 increased from 0.286 to 0.932. The β coefficients of the external demands factors changed significantly because of strong correlation, while the β coefficients of the rest of the variables did not change to any considerable extent. This indicates that the variables of daily-reach area act in a stable way in the model.

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Table des illustrations

Titre Figure 1. Workplace, working-square and its surrounding zones
URL http://journals.openedition.org/cybergeo/docannexe/image/27192/img-1.png
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Titre Figure 2. Partial explanatory effects of the internal factors in spatial entities and categories
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Titre Appendix 5a: Variance distribution over spatial entities
URL http://journals.openedition.org/cybergeo/docannexe/image/27192/img-8.png
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Titre Appendix 5b: Variance distribution among social economic factors
URL http://journals.openedition.org/cybergeo/docannexe/image/27192/img-9.png
Fichier image/png, 129k
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Pour citer cet article

Référence électronique

Wenjuan Li, Einar Holm et Urban Lindgren, « Linking spatial scale to changes in workplace earnings – An exploratory approach », Cybergeo: European Journal of Geography [En ligne], Aménagement, Urbanisme, document 740, mis en ligne le 19 septembre 2015, consulté le 06 décembre 2021. URL : http://journals.openedition.org/cybergeo/27192 ; DOI : https://doi.org/10.4000/cybergeo.27192

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Auteurs

Wenjuan Li

Institute of Agricultural Resources and Regional Planning of CAAS, No. 12 Zhongguancun Southern Street, Haidian District, Beijing P.R. China
Contact information (corresponding author): Email liwenjuan@caas.com

Einar Holm

Department of Geography and Economic History, Umeå University, 901 87 Umeå, Sweden, Email Einar.Holm@geography.umu.se

Urban Lindgren

Department of Geography and Economic History, Umeå University, 901 87 Umeå, Sweden, Email Urban.Lindgren@geography.umu.se

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