Gender-wage gaps are an important phenomenon on labor markets. They can possibly be caused by the institutional framework. This question is addressed in this paper. When only joint output can be observed in team production, individuals may submit self-reports of their contribution to a principal. In a multi-employee gift exchange experiment, we study how men and women behave differently with and without such self-reports. We cannot reject that self-reports left the overall efficiency of the gift exchange interaction unchanged, but detect notable gender differences. Women reported similar effort levels as men, but contributed significantly less. The difference in contributions led to a significant gender gap in wages, depending on gender group composition. These effects were only present when participants did not know each other's gender, however. When instead gender was observable, the behavior of men and women converged. The results suggest that parts of wage gaps may be related to different behavior within incomplete contract and imperfect information environments, depending on details of the informational context.