Figure 3

Fit of experimental data on the total number of exporting firms with our theoretical law and analysis of the fitting coefficients.

Left panel: Extent of trade relationships Y versus fraction of immigrants Γ for three different provinces as explained by the legend; we choose the three largest provinces for the sake of readability and for consistency with the analysis of the following sections. However, we checked that analogous plots hold also for the other provinces. In this plot empirical data (symbols) are compared with the theoretical prediction (solid line). More precisely, each data point corresponds to a different year and the solid lines represent the best fit according to equation (17) and the goodness of the fit is R²=0.94 (Madrid), R²=0.97 (Barcelona), and R²=0.95 (Valencia). By repeating the same procedure for all the N_p provinces, we derive for each province p the best-fit coefficients Γ_c, a, and b. The histograms for these coefficients are shown in the right panels. In particular, Γ_c, is Poissonian distributed with peak around 0.003 (upper panel), a spans over several orders of magnitude (due to the broad range along which Y_p spans)—and this is why we actually represent the histogram of log(a) (middle panel), the coefficient b is peaked in agreement with the fact that $\overline{J}$ is a property of the country as a whole and it is quite homogeneous from province to province.