Trait variability as a partial explanation of gender gaps

When an outcome is caused by a trait or covariate, gender gaps in average outcomes can arise solely from differences in trait variance. Thus, average gender disparities in outcomes such as wages, patent registrations, STEM degrees, and imprisonment rates may emerge if one group is more variable in traits such as cognitive ability, personality traits, aggression, or risk preferences, even in the absence of discrimination and mean trait differences. As the variability of traits can differ between males and females, with males most often exhibiting greater variability, this channel of gender gaps warrants thorough exploration. This study develops a formal framework, using analysis and examples, to demonstrate how the convexity or concavity of the function mapping traits to outcomes plays a critical role in determining average gender gaps in outcomes. These results hold when the trait distribution is symmetric and unimodal, such as the normal distribution. A simulation exercise demonstrates how popular statistical decomposition methods, such as regression analysis, may produce misleading conclusions about gender disparities and their sources. Overall, gender gaps in social outcomes are complex and context-dependent, and greater male variability in traits may be a significant contributing factor.