This paper considers a simple model of self-fulfilling expectations that leads to a multiple equilibrium of gender gaps in wages and participation rates. Rather than resorting to moral hazard problems related to unobservable effort, like in most of the related literature, our model fully relies on statistical discrimination. If firms believe that women will quit their jobs more often than equally productive men when shocks affecting household chores take place, our model predicts that this belief will increase the wage gap in favour of men which, in turn, will exacerbate lower female participation in the labour market. Hence, both effects lead to a gendered equilibrium with large gaps, even though an ungendered equilibrium with no gaps is feasible. We examine the effects of gender-based and gender-neutral subsidies and find that the latter are more effective in removing the gendered equilibrium. Empirical analysis based on a time use survey for Spain is provided to test some implications of the model.