Figure 5

Estimates for the critical density of immigrants obtained by fitting data on number of exporting firms: their distribution and their average values suggest robust behaviours among provinces.

Note: We select the four largest provinces (Madrid, Barcelona, Valencia and Sevilla) out of the available N_p and for each of them we consider the data for trades Y_p,f performed between the province p and the foreign country f. The data for trade relationships Y_p,f are then analysed versus the fraction of migrants Γ_p,f residing in p and hailing from f and we perform the best fits according to the theoretical law in equation (17). In this way we obtain estimates for the critical density of immigrants Γ_c and the related R², which are plotted in the upper panel. Different symbols and colours refer to different provinces as explained by the legend. Each data point represents a different pair (p,f). The most reliable fits (that is, R² close to 1) suggest that Γ_c is distributed around 10⁻⁵, and this holds for all the four provinces analysed. Focusing on estimates corresponding to R²>0.85, we build the histogram of Γ_c (shown in the middle panel) and calculate its arithmetic average to get ${\overline{\Gamma }}_c$, which is plotted in the lower panel as a function of the population of the related province.