This study re-examines the relationship between women on corporate boards (WOCB) and corporate social performance (CSP) for a sample of companies from the Fortune 1000 ranking over the period 2004 to 2018 (ranked from 501 to 1000). To take into account the complex and non-linear relationship as well as endogeneity issues, we use a two-stage generalised additive model. This contribution is significant, as many authors have demonstrated the non-linearity of factors influencing performance, whether of a financial or social nature. Consistent with token and critical mass theories, our results shows that the effects of WOCB on CSP vary significantly depending on their numerical representation and that there are departures from linearity. Our findings provide explanations for the existing mixed empirical results, which all rely on parametric methods. As such, we suggest the use of semiparametric methods takin into account endogeneity issues to assess WOCB–CSP relationship. This study sheds some new light on that relationship, which remains a controversial issue.