The aggregation of sectoral or regional Phillips curves yields an
inflation–unemployment trade-off that is not vertical in the long
run if there are mismatches between supply and demand in the regional
or sectoral labor markets. This remains true even when the
individual Phillips curves are all vertical. This result stems from
variations in the slope of the individual short-run Phillips curves,
rather than from changes to the equilibrium level of unemployment.
It implies a role for the management of the distribution of demand
over different sectors or regions, in order to minimize the natural
rate of unemployment.