Wage posting models of job search typically assume that firms can commit to paying workers the posted wage. This paper investigates the consequences of relaxing this assumption. Under ``downward'' commitment, firms can commit only to paying at least their advertised wage. We show that wage posting is always an equilibrium, although in special cases other equilibria can exist. Surprisingly, the wage posting equilibrium in our economy is identical to the equilibrium when firms can commit to paying exactly their posted wage. When firms cannot even commit to paying at least their advertised wage, equilibrium exhibits job auctions with wage dispersion which generally is not constrained efficient.
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