An analysis of a large dataset on immigrant integration in Spain. The Statistical Mechanics perspective on Social Action

TL;DR

This paper introduces a statistical mechanics-based model to analyze how immigrant integration in Spain varies with density, revealing linear and non-linear growth patterns influenced by social action, and providing insights for policy optimization.

Contribution

It presents a novel mathematical framework using statistical mechanics to distinguish and model different integration growth behaviors driven by social action.

Findings

Non-linear growth in integration quantifiers explained by social action effects.

Linear model underestimates or overestimates integration measures depending on density.

Unified model accurately captures both linear and non-linear integration behaviors.

Abstract

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 quantifi?ers 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.