What explains the persistent under-representation of women at the top organizations within high status occupations? The phenomenon has been documented across countries and neither the closing and reversal of education gaps nor family policies appear effective in closing the gaps. We offer an explanation for the persistence of under-representation based on the mutually reinforcing dynamics resulting from returns to organizational prestige at top organizations (The Matthew Effect) and gender stereotypes in hiring arising from the imperfectly observable ability of workers (The Larry Effect). Our model predicts that when organizational prestige is important and complementary to ability in production, fewer women will be found and hired at higher status organizations, there will be a wage premium for both women and men when they move to them but a greater proportion of men will succeed in doing so, regardless of ability. An aggregate level gender wage gap is thus generated from between-organization wage differences and segregation of women and men to lower- and higher-status organizations respectively. We test the predictions of the model in academia where recognized measures of prestige exist and Matthew effects are well documented. We make use of an employer-employee administrative panel comprising the universe of UK academics and find evidence consistent with the model's predictions: persistence of women's under-representation in higher status organizations and a wage premium for moving of about 3 percent for both women and men.