gender wage differential: politically (in)correct paper

In a recent paper, M Daniele Paserman citing the evidence from the professional tennis, concludes that female tennis players play more conservatively and commit more unforced errors when playing critical points. Does this explain the upper-echelons wage gap?

...have seen a dramatic increase in female labour force participation rates, and a considerable narrowing of the gender gap in wages....the gender gap persists – much of it due to gender disparities at the very high end of the wage distribution where women have made only limited inroads – the famous ‘glass ceiling’ of the upper echelons of academia, management, and prestigious professions.
...under-representation is not easily explained....hypotheses, ranging from discrimination to differences in preferences, have been offered. One particularly intriguing hypothesis ...women may be less effective than men in highly competitive environments – even if they are able to perform similarly in non-competitive environments. ...study the role of gender in responses to competitive pressure, using data from the world’s most prestigious tennis tournaments. This column discusses the results and suggests some implications for future research.
Why tennis?

....well-suited for statistical analysis. The outcomes are well-defined - the last shot of a point can only be one of three things: a winner, a forced error, or an unforced error. The competitive environment is also relatively easy to judge objectively – using things such as the tournament round, the two players’ rankings, and the number of points played. Moreover, the sport’s non-linear scoring structure introduces significant variation in the importance of individual points. It is often a small number of individual points at critical junctures that determine a match’s result. A break point in the latter stages of an evenly fought early set can be more decisive than a point in the early stages of the final set. It is exactly this substantial variation in the importance of points across and within matches that allows identification of a link between performance and the degree of competitive pressure.
...Technically, it is the probability that the player wins the match conditional on him or her winning the current point minus the probability that he or she wins the match conditional on him or her losing the current point. For example, consider the 2006 Wimbledon men’s final, Federer versus Nadal. At the outset of the match, the estimated probability of Federer winning the match was about 65.1%. Winning the first point (on Federer’s serve) would have raised his probability of winning the match to 65.7%; losing the point would have lowered his probability of winning the match to 63.6%. In my measure, the importance of that first point was 2.1%. For the sixth point of the second game where Nadal (serving) faced break-point at 30-40, winning the point would have raised Federer’s probability of winning to 75.8%, losing it would have lowered the probability to 67.1%. Hence, the importance was 8.8%. ..this was the ninth most important point of the entire 2006 Wimbledon final, despite coming so early in the match.
With this measure in hand,...the influence of a point’s importance on the frequency with which players commit unforced errors and on their style of play. Using data for nearly 42,000 points in 238 matches played in four recent Grand Slam tournaments,...find important gender difference. While men’s performance does not vary much depending on the importance of the point, women’s performance deteriorates significantly as points become more important.
Multinomial logit regressions that control for the abilities of each player, the round of the tournament, the duration of the match prior to playing the point, the tournament location, and whether the match was played on the tournament’s main court show that gender matters in players’ response to competitive pressure. Women are significantly more likely to hit unforced errors at the most crucial stages of the match, while men exhibit no significant variation in performance. Specifically, about 30% of men’s points end in unforced errors, regardless of their placement in the distribution of the importance variable. For women, about 36% of points in the bottom quartile of the importance distribution end in unforced errors, but unforced errors rise to nearly 40% for points in the top quartile of the importance distribution. What is remarkable is not the difference in the levels (men are more powerful and therefore more likely to hit winners at any stage). The interest lies in the differences in the way men and women respond to increases in competitive pressure.
....contextualise the difference in the probability of making an unforced error due to greater pressure, the magnitude of the multinomial regression result is around one-fourth of the impact of changing from the fast grass courts of Wimbledon to the slow clay courts of the French Open. Given the importance that playing surface has in determining tennis outcomes, this is a fairly large effect. It is also robust to alternative measures of importance.
Is it physical?One potential explanation for the gender gap in propensity to err during crucial points is that men and women adopt different levels of aggressiveness as points become more important. For example, if players adopt a conservative playing strategy and just lob the ball from one side to the other without ever trying to hit a winner, the point will inevitably end with an unforced error. Indeed, there are substantial gender differences in the style of play as the stakes become higher.
Men hit faster first serves as importance of the point rises, while women hit significantly slower first and second serves as the stakes mount. Amongst females, serves for points in the top importance quartile are nearly three and a half miles per hour slower on average than serves in the lowest importance quartile. Adopting this less aggressive strategy increases the likelihood that the first serve will be in play, but it does not significantly improve the server’s chances of winning the point (in fact, it slightly lowers it). Moreover, women’s first serves in the fourth quartile of the importance distribution are both less powerful and less accurate than their first serves in the third quartile of importance. This result echoes previous work finding that performance anxiety elicits cautious, protective strategies that are associated with poor performance, i.e., decreases in speed without an associated improvement in accuracy.1

...the possibility that these asymmetric responses to high stakes might be due to differences in style of play resulting from physical differences between males and females, ...Though some of the results indicate that low-power players are less aggressive and make more unforced errors on important points irrespective of gender, the evidence does not contradict the basic finding that there are substantial differences in the way men and women approach important points in the match.This finding complements existing literature on performance under pressure by examining an atypical sample – extremely competitive athletes who are amongst the very best in the world in their profession. Perhaps surprisingly, even these highly competitive women exhibit a decline in performance in high-pressure situations. Moreover, this effect is present in women-only competitions, contradicting the narrower hypothesis that females perform worse under pressure only when facing male opponents.
Tennis to the labour market

Of course, it would be inappropriate to extrapolate from a single study of a very select group of individuals to the broader labour market. Professional tennis and its competitive pressures are substantially different from the activities and stresses in business and academia. First, different selection patterns may be operating between elite male and female professional tennis players. It may be that this selection pattern, rather than gender differences, accounts for my finding that top male players are better able to cope with high-pressure situations. Tennis may also involve motor skills – as opposed to cognitive skills – that may generate different responses to increases in competitive pressure. Finally, the nature of high-pressure situations in tennis – which necessitate accurate decision-making and execution in a matter of split seconds – are probably shared in only a limited number of professions.
Nevertheless, the finding of such a robust gender difference in performance under pressure, even in the extreme right tail of the talent distribution, is sufficiently interesting that it should stimulate further research into this possible explanation for the persistence of the gender gap.--------------------------------------------------------------------------------

Footnote1

Jennifer Butler, and Roy Baumeister. “The Trouble with Friendly Faces: Skilled Performance with a Supportive Audience.” Journal of Personality and Social Psychology, 1998.

I think the wage is more or less equal to the marginal revenue product, the basic microeconomic theory. In the past, fewer viewers watched womens' tennis, thus they got paid less. This is not true now, and the wage gap is shrinking or disappearing.
Also at the Grand Slam level, men get paid more because they work more (5 sets versus 3). So, in accordance with the paper in question, men provide both a better quality and larger quantity of tennis to the viewer.