J-PAL just sent in their newsletter this study report from April, that seems to address this exactly, judging by its abstract:
In cities with conservative norms or high crime, female workers may face greater restrictions on their
physical mobility. This limits women’s labor market opportunities and the pool of workers that firms
can attract. In this study, we experimentally vary access to a transport service in Lahore, Pakistan, to
quantify the overall impact of transport to work on men, women, and the differential impact of
transport exclusively for women. We show that reducing physical mobility constraints has a large
impact on job searching for women, including women who are not searching at baseline. Women’s
response is driven by a women-only transport treatment arm, suggesting that safety and social
acceptability, rather than simply cost, are key constraints.
J-PAL just sent in their newsletter this study report from April, that seems to address this exactly, judging by its abstract: