Why do many occupations show a gender bias?

I'm hesitant whether to write this as an answer or as a comment for why this question should be closed as off-topic, since the reasons likely have little to do with economics. Since you did specifically ask about economic reasons, though, I'll attempt an answer.

The economic part of your question is:

What are the economic reasons why, when encountering low pay (or anticipating it at the start of their careers), women should not simply respond to economic incentives, and choose to transfer to higher-paid occupations to increase their earnings?

Yet, the assumption that women don't take compensation into account when choosing a field is almost certainly false. It's just that neither men nor women solely consider compensation when choosing a field and the other reasons are mostly psychological and/or sociological in nature, not economic. In particular, people tend to go into fields that they enjoy, that bring them satisfaction, at which they are adept, and/or that are more likely to have work/life balances matching their needs regardless of their gender or the relative compensation levels of those fields.

While there are obviously both men and women who enjoy almost every field, it shouldn't come as an especially large surprise that those don't occur at equal rates in every field or even in most fields. Far more women than men prefer being school teachers or nurses or doing clerical work, while far more men than women prefer being engineers, airline pilots, or construction workers, for example. A quick look at gender enrollment rates by major at any university which teaches those subjects will confirm this, in addition to data on people actually in the workforce.

For the United States, the U.S. Department of Labor produces detailed statistics on gender breakdown by occupation.

According to this dataset, women constitute 46.8% of the U.S. workforce in 2020. Of the detailed occupations listed for which % female data is available for 2020, only 106 of the 358 had female percentages that were even within 15% on either side of the 46.8% average. 131 of the fields had less than 31.8% females, while 121 of them had more than 61.8% females. Looking at fields within 5% on either side of the average, less than 10% - only 34 - of those 358 detailed fields were between 41.8% and 51.8% female, compared to 159 below 41.8% and 165 above 51.8%

In general, female percentages are incredibly low (mostly under 10%) for occupations that involve large amounts of manual labor and especially heavy lifting. Given the risk involved in these fields, their pay levels tend to be higher than other fields that require equivalent amounts of experience or education. For example, among all occupations in the "Installation, Maintenance, and Repair Occupations" category, only 4.1% of workers are female. In the "Construction and Extraction" (i.e. mining) category, only 4.0% of workers are female. Only 4.4% of firefighters and 17.1% of police officers were female.

On the flip side, for the "Office and Administrative Support" category, 72.7% of workers are female, while "Personal Care and Service Occupations" have 77% females. For "Healthcare Support Occupations" (think home health aids, nursing assistants, and other medical aids, but not doctors or nurses,) 85.3% are female. These fields largely require similar amounts of experience and education as those in the previous paragraph (generally ranging from no experience to trade school, but almost all less than Bachelor's degree requirements,) yet most have much lower personal risk and more personal interaction and/or direct caretaking.

For fields requiring a college degree (Bachelor's, but not Doctorate,) STEM fields tend to attract relatively few females, but have the highest starting salaries of all such fields. Only 16.5% of Architecture and Engineering occupation workers were female and only 25.2% of those in the Computer and Mathematical occupations category. Of the latter category, only statisticians were majority female at 50.3% and the only other groups near the overall workforce average were web and digital interface designers (44.8%) and operations research analysts (42.9%.)

On the other hand, Community and Social Service occupations had 68.8% female workers. In the Education, Training, and Library occupations, 73.5% of workers are female, but the numbers vary dramatically in regards to the age of the people being taught. Post-secondary education is actually pretty equitable at 51.1% female (though this almost certainly varies dramatically based on field being taught, which is not listed in the data.) On the opposite extreme, 98.8% of preschool and kindergarten teachers were female. 79.6% of elementary and middle school teachers and 58.8% of secondary school teachers were female.

Going too far into why women and men, on average, prefer different fields at different rates is not really on-topic here, as it's more a question of psychology or sociology than economics. Those reasons could include innate differences, differences in gender roles taught by society, or, seemingly much more likely, some combination of both. But what is very clear from the data is that men and women have very different average preferences on occupation, regardless of compensation.

There have been several good answers that tackle the economic reasons already; but let me take a different approach. More or less the same approach of INNONOTING, but he got downvoted probably because he didn't really back up his claims.

It is often said that occupations have a gender bias because men and women are raised to fit a certain role-pattern and that it's hard to escape.

However, studies have shown that these role patterns aren't necessarily taught but are born. They are part of our biology. When giving children a certain set of toys the girls will usually pick toys that simulate something (dolls, play-kitchen, ...), while the boys will pick something that has some kind of "mechanic" attached to it, like spinning wheels (toy cars, lego/duplo, ...)

There have been numerous experiments performed on this, and the outcome was always the same. Even more so... the experiment has even been performed on Rhesus monkeys, and even there the results were clear. The male and female monkeys had different preferences for the toys that were left in their habitat.

Here is a video demonstrating the experiment.

Slate Star Codex has a long, well researched article. TL DR: It is very likely that women as a group have more members who care about persons / living things and men as a group have more members who prefer things / concepts. There is a strong correlation between prenatal testosterone and interested in things. Women with a high prenatal testosterone production due to a genetic mutation (CAH), are more likely to be interested in things.

In their own study, they compare 125 such women and find a Things-People effect size of -0.75 – that is, the difference between CAH women and unaffected women is more than half the difference between men and unaffected women. They write:

The results support the hypothesis that sex differences in occupational interests are due, in part, to prenatal androgen influences on differential orientation to objects versus people. Compared to unaffected females, females with CAH reported more interest in occupations related to Things versus People, and relative positioning on this interest dimension was substantially related to amount of prenatal androgen exposure.

Jobs which are prefered by more women than men are btw. not always paid worse.

Whenever I ask this question, I get something like “engineering and computer science are two of the highest-paying, highest-status jobs, so of course men would try to keep women out of them, in order to maintain their supremacy”. But I notice that doctors and lawyers are also pretty high-paying, high-status jobs, and that nothing of the sort happened there. And that when people aren’t using engineering/programming’s high status to justify their beliefs about gender stereotypes in it, they’re ruthlessly making fun of engineers and programmers, whether it’s watching Big Bang Theory or reading Dilbert or just going on about “pocket protectors”.

Meanwhile, men make up only 10% of nurses, only 20% of new veterinarians, only 25% of new psychologists, about 25% of new paediatricians, about 26% of forensic scientists, about 28% of medical managers, and 42% of new biologists.

Note that many of these imbalances are even more lopsided than the imbalance favoring men in technology, and that many of these jobs earn much more than the average programmer. For example, the average computer programmer only makes about $80,000; the average veterinarian makes about $88,000, and the average pediatrician makes a whopping $170,000.

https://slatestarcodex.com/2017/08/07/contra-grant-on-exaggerated-differences/

James Damor (Phd. Candidate in Havard with evolution as research field) has written a nice memo about it. And was fired from google for it.

Differences in distributions of traits between men and women (and not “socially constructed oppression”) may in part explain why we don’t have 50% representation of women in tech and leadership.

https://firedfortruth.com/

I don't consider myself an expert and will not attempt a full answer.. Just wanted to add an interesting and in my view empirically quite convincing paper I recently saw (Brenøe and Zölitz, 2020) which points to non-trivial differences in peer effects among male and female youth as one channel impacting occupation differences. Here is the abstract:

"We investigate how high school gender composition affects students’ participation in STEM at college. Using Danish administrative data, we exploit idiosyncratic within-school variation in gender composition. We find that having a larger proportion of female peers reduces women’s probability of enrolling in and graduating from STEM programs. Men’s STEM participation increases with more female peers present. In the long run, women exposed to more female peers are less likely to work in STEM occupations, earn less, and have more children. Our findings show that the school peer environment has lasting effects on occupational sorting, the gender wage gap, and fertility."