We study a labor market characterized by search frictions in which firms choose between posting non-negotiable wage offers and bargaining wages with individual workers. We use the model to study the positive and normative implications of heterogeneous wage-setting strategies in labor markets, as well as the potential effect of policies that seek to regulate wage-setting. We analytically derive-and empirically validate-a testable prediction from the model regarding the cross-sectional prevalence of bargaining and renegotiation of wages among workers. We then estimate the model and use it to evaluate counterfactuals in which either wage-setting procedure is mandated. We find that eliminating bargaining reduces the overall gender gap in wages by 6%, the education gap by 3%, and residual wage dispersion by 12%, while leading to welfare losses for workers. Similar numbers are observed when bargaining is mandated, with ensuing welfare gains for workers. Either policy raises output by 1-3% by eliminating inefficient job mobility, but accounting for firm responses in vacancy creation can overturn these effects.