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Figure 6 | EPJ Data Science

Figure 6

From: A network theory of inter-firm labor flows

Figure 6

Behavior of \(\log _{10} [\operatorname{Pr}(L_{i}|k_{i}/\lambda _{i})/\operatorname{Pr}(L^{*}_{i}|k_{i}/ \lambda _{i}) ]\) (surface \(\mathcal{S}\)) with respect to \(\log _{10} L_{i}\) and \(\log _{10} k_{i}/\lambda _{i}\) for Finland. The data is logarithmically binned as follows: \(L_{i}\) belongs to bin b (a non-negative integer) if \(L_{\mathrm{min}}\zeta ^{b}< L_{i}\leq L_{\mathrm{min}}\zeta ^{b+1}\) with \(\zeta >1\) (for this plot \(\zeta =2\)) and \(L_{\mathrm{min}}=\min [\{L_{i}\}]\) (smallest firm size in the data); \(k_{i}/\lambda _{i}\) is binned in the same way with ζ and \((k/\lambda )_{\mathrm{min}}=\min [\{(k_{i}/\lambda _{i})\}]\). Blue points represent the local maximum of \(\mathcal{S}\) at each bin. The vertical plane \(\mathcal{P}\) is parametrized as \((k_{i}/\lambda _{i}, C_{L} k_{i}/\lambda _{i},z)\) where z is a free parameter. \(C_{L}\) is chosen to minimize \(\sum_{b} (L^{*}_{b}-C_{L}(k/\lambda )_{b} )^{2}\) with the first three bins excluded because the smallest firm size is 1. The large range within which the intersection of \(\mathcal{P}\) and \(\mathcal{S}\) runs parallel to the maxima of \(\mathcal{S}\) strongly supports Eq. (17)

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