There is greater cause for optimism, however, when we study changes over time. We find the more positive evidence in another new book, “The Silent Sex: Gender, Deliberation and Institutions” (Princeton University Press, 2014) by Christopher F. Karpowitz, professor of political science at Brigham Young University, and Tali Mendelberg, professor of politics at Princeton.

Drawing upon data from politics, business meetings and behavior in the corporate boardroom, they portray a society where women participate less in many public settings, especially those in which real power is exercised. This links up with the experimental results described in Mr. Eswaran’s book, because an underparticipating group that doesn’t resist discrimination is more likely to suffer.

This sounds gloomy so far. But the authors show that once women achieve a critical mass in a particular area, their participation grows rapidly, at least after basic norms of inclusion have been established.

In fact, the general method of economics provides foundations for some feminist views. First, economics emphasizes that incentives matter and that incentives can be changed. These are common themes underlying feminist thought, which stresses how a fairer social environment can give people greater reason to choose better behavior.

Second, the long-term response to a change in incentives is often much greater and more important than the short-term response. For instance, Mr. Karpowitz and Ms. Mendelberg show that, over time, men behave in a less stereotypically male way when more women are participating in an organization or an activity.

As a former chess player, I am struck by the growing achievements of women in this great game — one in which men were once said to have an overwhelming intrinsic advantage. (Among the unproven contentions was that men were better at pattern recognition.) Although women were never barred from touching the chess pieces, strong female players were few in number.

These days, many more women play very well, and the gap between the top men and women in the game is narrowing. The main driver of the change appears to be that more and more women are playing chess, creating a cycle of positive reinforcement that encourages ever more women to excel. We’ve seen a similar dynamic in the workplace, as more women have made great strides in the areas of law, medicine and academia. And this process may spread to other sectors of the economy as well, such as technology industries.

This longer-term, optimistic perspective has deep roots in economics, and was articulated eloquently in “The Subjection of Women,” John Stuart Mill’s 19th-century essay. Mill said men and women were indeed different, but he saw the achievements of women as dependent on incentives and the work environment, which he thought could be improved beyond what most people in his day — and perhaps ours, too — could easily imagine. For all the sexist behavior we economists measure in the lab, the research around the bigger picture is supporting Mill’s optimism about a better world to come.