Three-Step Method for Delineating Functional Labour Market Regions

Abstract

Kropp P. and Schwengler B. Three-step method for delineating functional labour market regions, Regional Studies. This paper proposes a new three-step method to find delineations that adequately define functional regions with strong interactions within the region and few connections with outside areas based on commuting flows. A graph-theoretical approach is used to create many meaningful delineations for labour market regions in Germany and the modularity concept from network analysis is employed to select the delineation that captures the commuting flows best. As a result, a delineation of 50 German labour market regions that are quite heterogeneous in terms of size is obtained. Using the modularity measure, the current delineation is compared with previous functional delineations.

Kropp P. and Schwengler B. 描绘功能性劳动市场区域的三步骤方法，区域研究。本文提出一种崭新的三步骤方法，根据通勤流动，寻找适切定义在内部具有强烈互动、对外部区域少有连结的功能区域之描绘。本文将运用图论方法，为德国的劳动市场区域创造诸多具有意义的描绘，并应用网络分析中的模块概念，选择能够最佳捕捉通勤流动的描绘。研究结果获得了五十个规模相当歧异的德国劳动市场区域的描绘。本文将运用模块方法，比较目前与过往的功能性描绘。

Kropp P. et Schwengler B. Une méthodologie en trois étapes pour délimiter des bassins d'emploi régionaux fonctionnels, Regional Studies. Cet article présente une nouvelle méthodologie en trois étapes pour délimiter avec précision des régions fonctionnelles dont les interactions au sein de la région s'avèrent fortes et dont la connexion avec des zones à l'extérieur est faible en termes des migrations quotidiennes. On emploie une approche théorique graphique afin de créer de nombreuses délimitations significatives pour ce qui est des bassins d'emploi en Allemagne et pour appliquer la notion de modularité qui provient de l'analyse des réseaux afin de sélectionner la délimitation qui capte le mieux les migrations quotidiennes. Il s'ensuit une délimitation de 50 bassins d'emploi assez hétérogènes en Allemagne en termes de leur taille. À partir de la mesure de la modularité, on peut comparer la délimitation en vigueur aux délimitations fonctionnelles antérieures.

Kropp P. und Schwengler B. Ein dreistufiges Verfahren zur Abgrenzung von funktionalen Arbeitsmarktregionen, Regional Studies. In diesem Papier wird ein dreistufiges Verfahren vorgeschlagen, mit dem funktionale Regionen auf Basis von Pendlerverflechtungen abgegrenzt werden können, so dass starke Pendlerverflechtungen innerhalb dieser Regionen und geringe zwischen ihnen bestehen. Wir verwenden einen graphentheoretischen Ansatz, um viele mögliche Abgrenzungen von Arbeitsmarktregionen in Deutschland zu produzieren. Unter diesen wählen wir mit Hilfe des Modularitätsansatzes aus der Netzwerkforschung die Abgrenzung aus, die die Pendlerströme am besten einfängt. Als Ergebnis erhalten wir eine Abgrenzung von 50 deutschen Arbeitsmarktregionen, die sehr größenheterogen sind. Mit dem Modularitätsmaß vergleichen wir die aktuell gefundene Abgrenzung mit früheren funktionalen Abgrenzungen.

Kropp P. y Schwengler B. Método de tres pasos para delimitar las regiones funcionales de empleo, Regional Studies. En este artículo proponemos un nuevo método de tres pasos para hallar las delimitaciones que definen adecuadamente las regiones funcionales con fuertes interacciones dentro de la misma región y pocas conexiones con zonas externas en base a los flujos de desplazamientos. Mediante un planteamiento teórico con gráficos, creamos numerosas delimitaciones significativas para las regiones funcionales de empleo en Alemania y aplicamos el concepto de modularidad desde el análisis de redes para seleccionar la delimitación que capte mejor los flujos de desplazamientos. Como resultado, obtenemos una delimitación de 50 regiones de empleo alemanas que son bastante heterogéneas en cuanto a su tamaño. Mediante la medición de modularidad, comparamos la actual delimitación con delimitaciones funcionales previas.

• Functional regions
• Regional labour markets
• Modularity
• Germany

• 功能区域
• 区域劳动市场
• 模块
• 德国

• Régions fonctionnelles
• Bassins d'emploi régionaux
• Modularité
• Allemagne

• Funktionale Regionen
• Arbeitsmarktregionen
• Modularität
• Deutschland

• Regiones funcionales
• Mercados laborales regionales
• Modularidad
• Alemania

JEL classifications:

• C49
• D85
• J61
• R23

Acknowledgements

The authors are grateful for the very valuable comments made by two anonymous referees on earlier versions of this paper. The responsibility for errors remains with the authors alone.

Notes

1. This comparison had all methods applied without restrictions, such as maximum commuting times or minimum sizes.

2. For early examples, see Smart (1974, pp. 252ff.).

3. Finding groups – nodes or units that are strongly related to each other – in networks has become an important subject in the study of complex networks (cf. Girvan and Newman, 2002; Palla et al., 2005).

4. Nevertheless, analyses based on all 12 000 municipalities to control the used method have confirmed the robustness of the results (see the fifth section).

5. In this way, the current procedure is similar to that used by Rabino and Occelli (1997). These researchers combined the graph theory approach with the threshold value procedure using threshold values for the minimum magnitude of the dominant commuting flows and the minimum size of the catchment areas (measured in terms of inhabitants and the number of municipalities). Tree graphs are formed only by commuting flows that exceed a certain threshold. Haag and Binder (2001) also used this extended concept for spatial analyses in the Stuttgart and Turin areas.

6. Fig. 3 demonstrates the iteration process with a threshold of 7.

7. A symmetric interaction matrix, as described in the original paper by Newman and Girvan (2004, p. 7), was implemented in standard software packages for network analysis as Pajek, ucinet or R. However, it would be possible to employ Newman’s (2003, p. 2) work on assortative mixing, in which an asymmetric case was discussed, and specify:

with

The authors thank Michał Bojanowski for recommending this solution. As inflow and outflow of the labour market regions appear to be very balanced, this paper relies on the established formula.

8. Methods other than the current graph-theoretical approach can be used as a cluster generator rather than, or in addition to, this approach.

9. As a rule, the labour market regions were named after the municipality or municipal region which was the terminal point of the subgraph. Only in cases in which this name did not typify the labour market region was a more appropriate label chosen.

10. The island of Borkum was merged with the labour market region of Oldenburg because it would otherwise form an exceptionally small labour market. Two municipalities with insufficient data and three misplaced municipalities with fewer than 500 employees in total were assigned to a surrounding labour market region. Misplacements may result from data problems; however, in some cases, municipalities were most strongly connected to another (nearby) labour market region than all their neighbours.

11. Here the share of commuters (employees who live and work in different labour market regions) of all employees was computed.

12. The commuting ratio between labour market regions should generally decrease, and the level of self-containment should generally increase with fewer labour market regions. The measure Q, however, does not have such a bias. It could be argued that these results are due to the small number of labour market regions rather than the method. However, the current cluster generator produced delineations with comparable numbers of labour markets but with higher modularity values and lower commuting ratios (e.g., a 99-region delineation with Q = 0.8304 and 13.6% commuters, a 153-region delineation with Q = 0.8133 and 15.8% commuters, and a 274-region delineation with Q = 0.7640 and 22.0% commuters) (see also Fig. 2).

13. The values for a district-level delineation were also close to 100, but had a much higher standard deviation.