Unbundling Labor · All figures

Figure 9. Reduced dispersion of cognitive skills and within-occupation wage inequality

Panel A shows the feasible set \(\mathcal{B}\) as the dispersion of cognitive skill falls, i.e., \(\theta_X\) rises from \(2.25\) to \(3.5\). The feasible set shrinks. Asterisks mark the bundled equilibrium, which moves inward to the boundary of the smaller set (\(\boldsymbol{*}\)); the open circle (\(\circ\)) marks the unconstrained optimum on the contract curve. Panel B shows the within-occupation variance of log wages \(V_j\) for each occupation, decomposed into a price component (dashed, holding composition fixed) and a composition component (dotted, holding prices fixed). Panel C plots the change in cognitive skill price elasticity \(\Delta\beta_{jX}\) against the change in within-occupation inequality \(\Delta V_j\) for \(J=7\) occupations, with points numbered and colored from \(j=1\), the most cognitive-intensive, to \(j=7\), the most manual-intensive. Parameters: independent Fréchet marginals with \(\theta_Y = 2.25\), CES production with \(\sigma = 0.60\), symmetric economy with \(\eta_1 = \eta_2 = 0.5\) and \(\overline{X}=\overline{Y}\).

Figure 9. Reduced dispersion of cognitive skills and within-occupation wage inequality