Figure 8

Behavior of \(\log _{10} [\operatorname{Pr}(U_{i}|k_{i}/\xi _{i})/\operatorname{Pr}(U^{*}_{i}|k_{i}/ \xi _{i}) ]\) (surface \(\mathcal{S}\)) with respect to \(\log _{10} U_{i}\) and \(\log _{10} k_{i}/\xi _{i}\) for Mexico. The data is logarithmically binned as in the same way as in Fig. 6 (\(\zeta =2\)) with \(U_{\mathrm{min}}=\min [\{U_{i}\}_{\{i\}}]\) (smallest firm-specific unemployment size in the data) and \((k/\xi )_{\mathrm{min}}=\min [\{(k_{i}/\xi _{i})\}_{\{i\}}]\). Blue points represent the local maximum of \(\mathcal{S}\) at each bin. The vertical plane \(\mathcal{P}\) is parametrized as \((k_{i}/\xi _{i}, C_{U} k_{i}/\xi _{i},z)\) where z is a free parameter. \(C_{U}\) is chosen to minimize \(\sum_{b} (U^{*}_{b}-C_{U}(k/\xi )_{b} )^{2}\) with the last five bins excluded at the point where the linear relationship breaks down. The large range within which the intersection of \(\mathcal{P}\) and \(\mathcal{S}\) runs parallel to the maxima of \(\mathcal{S}\) strongly supports Eq. (21)