Women don't speak up!

Katie Coffman has a new paper forthcoming in the QJE on Evidence on Self-Stereotyping and the Contribution of Ideas

The abstract reads:
"We use a lab experiment to explore the factors that predict an individual's decision to contribute her idea to a group. We find that contribution decisions depend upon the interaction
of gender and the gender stereotype associated with the decision-making domain: conditional
on measured ability, individuals are less willing to contribute ideas in areas that are stereotypically outside of their gender's domain. Importantly, these decisions are largely driven by
self-assessments, rather than fear of discrimination. Individuals are less confident in gender
incongruent areas and are thus less willing to contribute their ideas. Because even very knowledgeable group members under-contribute in gender incongruent categories, group performance suffers and, ex post, groups have difficulty recognizing who their most talented members are. Our results show that even in an environment where other group members show no bias, women in male-typed areas and men in female-typed areas may be less influential. An intervention that provides feedback about a woman's (man's) strength in a male-typed (female-typed) area does not significantly increase the probability that she contributes her ideas to the group. A back-of-the-envelope calculation reveals that a lean in style policy that increases contribution by
women would significantly improve group performance in male-typed domains."

Here's the killer figure: The Probability of a Missed Opportunity: that is, someone knew the right answer, but their answer wasn't chosen and intead the group got the answer wrong (because the person knowing the answer didn't speak up enough or the other too much).

For each score (i.e. how many answers they got correct in a test in that category), the chance a man (black) or a woman (light grey) with that score had a missed opportunity.

The figure below is for Male Typed Categories (Environmental science, Sports, History, Geography)

So, women with a perfect score (5) in a male typed category, have a higher chance to have a missed opportunity than men with a score of 1 out of 5. 

The best women just have a barely lower chance to not miss an opportunity compared to men who got everything wrong.