Before revision:  Theoretically, pay transparency represents an information shock that alters the bargaining power of male and female employees vis-\`a-vis the firm in an asymmetric way. As women are currently underpaid , this shock may improve women's relative  outcomes.
After revision:  Theoretically, pay transparency represents an information shock that alters the bargaining power of male and female employees vis-\`a-vis the firm in opposite ways. Coupled with the potential negative effects of unequal pay on firms' reputation , this shock may improve women's relative outcomes.