A stochastic approach for quantifying immigrant integration: the Spanish test case

Abstract

We apply stochastic process theory to the analysis of immigrant integration. Using a unique and detailed data set from Spain, we study the relationship between local immigrant density and two social and two economic immigration quantifiers for the period 1999-2010. As opposed to the classic time-series approach, by letting immigrant density play the role of 'time' and the quantifier the role of 'space,' it becomes possible to analyse the behavior of the quantifiers by means of continuous time random walks. Two classes of results are then obtained. First, we show that social integration quantifiers evolve following diffusion law, while the evolution of economic quantifiers exhibits ballistic dynamics. Second, we make predictions of best-and worst-case scenarios taking into account large local fluctuations. Our stochastic process approach to integration lends itself to interesting forecasting scenarios which, in the hands of policy makers, have the potential to improve political responses to integration problems. For instance, estimating the standard first-passage time and maximum-span walk reveals local differences in integration performance for different immigration scenarios. Thus, by recognizing the importance of local fluctuations around national means, this research constitutes an important tool to assess the impact of immigration phenomena on municipal budgets and to set up solid multi-ethnic plans at the municipal level as immigration pressures build.

How integrated are immigrants?

“…Our systemic approach has the ability to guide us in this work. Our quantitative analysis describes the average behaviour of the integration process across numerous localities in the system under study, and the standard deviations (Agliari et al 2014;Barra et al 2014). Therefore, once having established the characteristics and performance of a particular integration process, we can easily extract information about fluctuations around the mean values with a view to identify localities in the system that over and under-perform.…”

Social interaction effects on immigrant integration

“…The fraction of mixed marriages m mix , collected each year and for each municipality, is studied vs. the fraction γ of immigrants on the total population. While previous studies of analogous databases from Spain Agliari et al, 2014;Barra et al, 2016), France, Germany and Switzerland (Agliari et al, 2015), all reported an average smooth law for the evolution of mixed marriages vs. the migrant's percentage (alternating a square-root behaviour vs. a linear growth), the Italian database does not show the existence of an underlying average law if analyzed as a whole: in other terms, it is not possible to map the statistical sample into a well defined function m mix (γ). Since this feature is generally the signature of a mixture of two, or more, different phenomena that need to be disentangled we split the database into large and small municipalities with respect to a proper tuning of a threshold θ over the population size.…”

“…In this paper, we investigate a data set collected by the Italian National Institute of Statistics (ISTAT) for the years 2002 to 2010 on the social choice (Weber, 1978) (for a native) of marrying a person from the host country (i.e., Italy) or from a different one. This quantifier is used, among other classical ones (Portes and Sensenbrenner, 1993;Rannala and Mountain, 1997;Agliari et al, 2014;Barra et al, 2014), to study the level of integration of migrants. The fraction of mixed marriages m mix , collected each year and for each municipality, is studied vs. the fraction γ of immigrants on the total population.…”

The continuous sample of working lives: improving its representativeness

“…The CSWL is a dataset that has been used in a considerable number of studies, especially on labour economics (Treviño et al 2008;Benavides et al 2010;Vall Castello 2012;Hospido 2013, 2016;Solé et al 2013;Agliari et al 2014;Arranz and García-Serrano 2014;Barra et al 2014 and Nagore García and van Soest 2016) and the Spanish public pension system (Antón Pérez et al 2007;Argimón et al 2007;Boado-Penas et al 2008;Moral Arce et al 2008;Vidal Meliá et al 2009;Cairó Blanco 2010;Peinado Martínez 2011;Devesa et al 2012;Domínguez Fabián et al 2012;Meneu Gaya and Encinas Goenechea 2012;Vicente Merino et al 2012;Conde Ruiz andVegas Sánchez et al 2013). Other studies give detailed descriptions of its characteristics, advantages and limitations.…”