An analysis of a large dataset on immigrant integration in Spain. The statistical mechanics perspective on socialaAction

How does immigrant integration in a country change with immigration density? Guided by a statistical mechanics perspective we propose a novel approach to this problem. The analysis focuses on classical integration quantifiers such as the percentage of jobs (temporary and permanent) given to immigrants, mixed marriages, and newborns with parents of mixed origin. We find that the average values of different quantifiers may exhibit either linear or non-linear growth on immigrant density and we suggest that social action, a concept identified by Max Weber, causes the observed non-linearity. Using the statistical mechanics notion of interaction to quantitatively emulate social action, a unified mathematical model for integration is proposed and it is shown to explain both growth behaviors observed. The linear theory instead, ignoring the possibility of interaction effects would underestimate the quantifiers up to 30% when immigrant densities are low, and overestimate them as much when densities are high. The capacity to quantitatively isolate different types of integration mechanisms makes our framework a suitable tool in the quest for more efficient integration policies.This work is supported by the FIRB grants RBFR08EKEV and RBFR10N90W. A.B. is grateful to Sapienza Universita` di Roma; P.C. is grateful to Universita` di Bologna for partial financial support. RS is grateful to the project ‘‘Competition, Adaptation and Labour-Market Attainment of International Migrants in Europe (CALMA)’’ granted by the VI National Plan for Scientific Research, Spanish Ministry of Economy and Competitiveness (CSO2012-38521), for partial financial support