Heterogeneous Downward Nominal Wage Rigidity: Foundations of a Nonlinear Phillips Curve

We propose a model with heterogeneous downward nominal wage rigidity for individual labor varieties. The model delivers a nonlinear wage Phillips curve linking current wage inflation with current unemployment that is relatively steep at high levels of inflation and flat at low levels of inflation. The predicted nonlinear Phillips curve matches well the pattern of wage inflation and unemployment observed in the United States over the past 40 years. In particular, it accounts for the resilience of the labor market in the tightening cycle following the Covid-19 inflation spike and for the missing inflation in the recovery from the 2008 great contraction. Finally, although the model features occasionally binding constraints for individual labor types, there are no such constraints in the aggregate, making the model amenable to perturbation analysis.