The conventional hypothesis of why women earn less on average than men is that women leave the workplace for child care, therefore the employer does not long-term invest, e.g., on-the-job training, in female employees as much, leading to less promotion and raises.
Not all women leave the workplace for child care, so this is an imperfect information signaling game. Are the signaling mechanisms working, or is there market failure? What signaling mechanisms are happening?
Radical hypotheses: Lesbian, F2M transgender, might be groups less likely to have children. It would be surprising if these are deliberate signaling, as they seem to be identity unrelated to employment signaling.
Also: A credible attitude of "I hate children" is pretty obvious as a signaling mechanism.
A hysterectomy or other irreversible procedure would be a very radical signaling mechanism, though unclear its cost outweighs the income benefits. Are elective surgeries like this happening? (Incidentally, if an employer wants to decrease the incidence of women leaving for child care so maximize their return on investment in the employee, they should definitely offer health insurance that covers abortions and birth control. I'm surprised that prior to Obamacare, there weren't employers offering insurance that only covers abortions and birth control.)
Less radical (famous) hypothesis: education and training paid for by the employee.
We suspect the wage gap cannot be reduced to zero through signaling: signaling cannot be perfect, unless there is some risk other risk of leaving that men are more likely to have then women. Maybe life expectancy?
A more sophisticated model does not assume that the decision to leave the workplace is deterministic: A women will compute expected future earnings and compare it with the utility of leaving the workplace for child care. This can lead to a feedback effect: an employer promises low pay, the woman chooses to leave based on that (and prior to that, chooses not to invest in education), leading to the expectation among employers that women will leave, so employers give low pay. Is this feedback effect causing market failure?
We suspect not: for any particular female employee, an employer can study the signals about the employee's relative utilities of money versus leaving for child care, and decide or decide not to pay an amount sufficient to keep the employee. This is the same process as everyone else (i.e., men) in the labor market. Once again, we need signaling to be accurate and precise.
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