This paper investigates how labour supply trends might have affected the OECD labour markets in the last decades. It is argued that changes in supply cannot be considered as homogenous: they involve more young and more adult female workers, who are complements with skilled men and substitutes with low-wage groups (young, unskilled). Such labour supply trends since the ''50s may have increased competition between women, young workers and low skilled workers in some segments of the labour force. These mechanisms are described by a model and an empirical strategy is undertaken to test its predictions. Disaggregation by gender is necessary. Endogeneity of participation levels with respect to unemployment is treated in two ways, by instrumental variables estimators, and with time series techniques. Significant causal relations between participation and unemployment cannot be rejected.