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The Master Equation in Migration Theory

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Modelling with the Master Equation

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Abstract

This chapter investigates the dynamic development of spatial patterns based on human activities. The topic is a fundamental issue of regional sciences and spatial economics. Migration processes in all their theoretical and empirical aspects are of overwhelming importance to all spheres of society. Since migration and especially the demographic composition of the stream of migrants and their social affiliation are among others factors of population growth they influence directly fundamental economic and social indicators of our society. After a reconsideration of the famous Gravity model, the Weidlich-Haag migration model is derived. It is shown how the rank-size distribution of settlements can be understood as a dynamic self-organization process.

As an important application of the WH-model the interregional migration in Germany on the level of 402 districts is investigated. The algorithm for the estimation of all model parameters is explained in detail. A multiple regression was also performed for the spatial preferences on the district level. The regression results well confirm that variables related to the housing market, the labour market, the innovation power of the region under consideration as well as accessibility measures are important explanatory variables for the regional preferences in Germany.

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Notes

  1. 1.

    Details of the estimation: Number of observations: 6162, degrees of freedom: 6150, R 2 = 0.43

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  1. Institute of Theoretical Physics II, University of Stuttgart, Stuttgart, Germany

    Günter Haag

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Haag, G. (2017). The Master Equation in Migration Theory. In: Modelling with the Master Equation. Springer, Cham. https://doi.org/10.1007/978-3-319-60300-1_8

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