Privately Efficient Wage Rigidity Under Diminishing Returns

Matching frictions have been shown to reconcile wage rigidity and private efficiency in settings with constant marginal returns to labor. A recent line of research has studied the implications of wage rigidity in models with matching frictions and diminishing returns. I show that the allocation of labor is privately inefficient off the equilibrium path in the models used in this line of research, and thus inconsistent with any theory of wage determination that yields private efficiency. The culprit is rigidity of the wage with respect to firm-level employment. I examine how wage rigidity can be reconciled with private efficiency, focusing on two polar specifications. In the first, wages are rigid with respect to aggregate shocks and flexible with respect to firm-level employment. The labor market responds strongly to aggregate shocks. Yet novel policy implications obtained by this line of research are lost, and thereby shown to be driven by rigidity with respect to firm-level employment. In the second, the wage only adjust when called for by private efficiency, and workers fully appropriate rents in the event of adjustment. Novel policy implications obtained in this line of research are restored, including the existence of unemployment in the limit as matching frictions vanish. But fighting this type of rationing unemployment is much easier than in existing models.