Forecasting the integration of immigrants

ABSTRACT

In this research, we develop and introduce a theoretical and mathematical forecasting framework of immigrant integration using immigrant density as a single driver. First, we introduce the integration concepts we aim at forecasting. Thereafter, we introduce a theoretical and mathematical model of the relationship between integration and immigrant density. Based on this model, we develop a methodological forecasting framework. We test the framework using immigrant integration data from Spain. We produce the forecasts, and conduct the proper evaluation of them. Finally, we conclude with a brief discussion of the wider implications of our results.

KEYWORDS:

• Forecasting
• immigrant density
• immigration
• social and labor-market integration

Notes

¹ It should be noted that the causal relationship between immigrant group size and integration has received ample attention in Blau et al. (1982) and Blau et al. (1984). These findings are not contradictory to Barra et al.’s. (2014) work, but complementary. However, in difference with Blau et al. (1982) and Blau et al. (1984), Barra et al. (2014) model the interaction component explicitly.

² Note that the absence of interaction in labor market participation couplings does not mean that social networks are irrelevant in the job market. What the data analysis suggests is simply that the propensity of hiring immigrants over natives is unaffected by whether other employers have or have not hired immigrants over natives before. Social networks are still likely to be determinant for the individuals’ chances of landing a job (see Granovetter, 1974, on the latter).

³ The proposed solution is a generalization of the so-called monomer–dimer model (Heilmann & Lieb, 1970) with the addition of an imitative interacting social network component with random topology in agreement with the small world–scenario (Watts & Strogatz, 1998). See Barra et al. (2014) for a full account of the model, proofs, and empirical tests.

⁴ This period corresponds to the period in which Spain received most of its current immigrant population. For those unfamiliar with the Spanish immigration context, the following brief information may be useful. In 1999, Spain received fewer than 50,000 new documented and undocumented immigrants. Since then, annual immigration levels have increased dramatically, reaching a peak in 2006 and 2007, with inflows exceeding 800,000. Spain’s documented and undocumented foreign born population has risen from little more than 1 million to over 6.5 million in the analyzed period. Its share of the total population has risen from less than 3% to over 13% in the same period. Currently, there are immigrants from almost all nations in Spain. However, some 20 immigrant origins account for approximately 80% of Spain’s total immigrant population. Immigrants from Romania form the largest minority in Spain (767,000 at the end of 2008), followed by immigrants from Morocco (737,000 at the end of 2008) and Ecuador (479,000 at the end of 2008). Europe and South America together account for over 70% of Spain’s total immigrant population.

⁵ The control parameter tunes the total number of possible cross-link couplings between immigrant and native populations (see Barra et al., 2014).

⁶ For the binning criteria, we used and tested the constant information approach. In this approach, the width of the bin will vary over and there is a constant robustness quality across all bins (Barra et al., 2014).

⁷ Since our quantifier values are in the shape of fraction, we compute the averages by using the method of global mediant. In the method, the averages are obtained by computing the ratio between the statistical average of nominators and the statistical average of denominators (see Barra et al., 2014).

⁸ We used the Adjusted Mean Absolute Percentage Error which is a valid quantity to show the accuracy of the predictions: where and are observed and forecasting values respectively (Armstrong, 1985).

⁹ R² indicates how well the observed outcomes are replicated by the statistical model. The measure ranges from 0 to 1 such that the larger numbers representing better fits and also 1 indicates a perfect fit: where y₁,…,y_n are the observed values, f_1…, f are the forecasts, and is the average of the data (Draper & Smith, 1998).