Why do firms report that they cannot find workers instead of preemptively raising wages? Using German administrative data, we show labor-constrained firms pay lower wages and quasi-exogenous wage increases alleviate constraints, consistent with monopsony. Yet constrained firms' delayed wage increases point beyond this mechanism. We develop a dynamic matching model combining wage-setting power with incomplete information and downward wage rigidity. Consistent with the model, firms raise wages when initial wage plans prove too low, especially for peripheral occupations, and face constraints after wage shocks to adjacent sectors, suggesting that firms' inaccurate beliefs and learning about market wages shape labor constraints.