No. Not since the 63.
Title VII of the Civil Rights Act of 1964, the Equal Pay Act of 1963, the Equal Employment Opportunity Acts of 1964 and 1972, and the Lilly Ledbetter Fair Pay Act of 2009 makes it illegal to pay women less for the same work in America. Women are not, in fact, paid 77 cents on the dollar for doing the same work as men.
I just recently noticed the second part of the question...
"If not, how do you explain the gender pay gap?"
This supposed wage gap is a matter of choice. Women, on average, choose careers that offer lesser or flexible hours, choose careers that offer more vacation or time off, choose careers that are not labor-intensive or dangerous and therefore lower-paying. It isn't a social problem that can be fixed and feminism has no real solution to this non-issue anyway.
If there really is a real gendered wage gap, how can it be resolved? What is your solution to this non-issue? I'll give you an answer: Communism. Socialist communism like that in Cuba where everyone is paid the same... no matter what the vocation or tenure or amount of hours worked in a week. With the left's disdain for Capitalism and meritocracy, it really seems that Communism is what feminism wants.
We could fix this imaginary gendered wage gap if we had a communist state. I think feminism really wants communism without knowing it. With a quota, we could force men (against their will) into female-dominated industries: Fashion, Interior Design, Social Work, Nursing, Teaching, Occupational Therapy & Flagging; and with a quota, we could force women (against their will) into male-dominated careers: Mechanical, Electrical, Aerospace and Civil Engineering, Politics, Computer Science, Physics, and Construction (but not flagging).
Feminism is no longer a movement that desires 'equality of opportunity'... it desires 'equality of outcome'. The supposed equality desired by modern third-wave feminism can ONLY be achieved by a socialist authoritarian communist dictatorship. We, the people would all be equals! Equal rights, equal pay,… This is why I am anti-feminist, the supposed equality desired by modern third-wave feminism can ONLY be achieved with communism. Feminism wants and needs communism to fix their imaginary gendered wage gap and all their other fantastical issues.
We can either have equality of outcome and force parity among all people (communist Marxism) or we can have equal opportunity and freedom of choice. We can't have both.