This is the question that a recent NBER working paper by Nicole Maestas, Matt Messel, and Yulya Truskinovsky (2023) aim to answer. The authors use data from the Survey of Income and Program Participation (SIPP) among individual report providing unpaid care to family and friend. The SIPP data are then linked to earnings data from Social Security Administration. Individuals who provide caregiving are matched with similar individuals based on demographics as well as earnings/employment histories. Using this approach the authors find the following results by gender:

Before women start providing care, there is no difference in their employment or earnings trajectories and those of non-caregivers or future caregivers. However, in the three years after women begin providing care, the employment of caregivers falls by 2.7 percentage points (4 percent) relative to the employment of future caregivers, or by 2.1 percentage points relative to non-caregivers. The employment gap between caregivers and comparison groups narrows three to five years after care begins. The average annual earnings of female caregivers fall by nearly $1,000 (4 percent) in the first three years after caregiving begins, relative to the earnings of future caregivers, and remains about $600 lower in years three to five, although the longer-term difference is not statistically significant.

For men, the picture is quite different. The employment and earnings of male caregivers begin to decline five or more years before men begin to provide unpaid care, relative to the trajectories of male non-caregivers and future caregivers. After they begin providing care, male caregivers experience a further employment decline of 3.7 percentage points (5 percent) relative to the control group of future caregivers. Male caregivers stay out of the labor force longer than do female caregivers, as the employment gap between male caregivers and their control groups persists in years three to five rather than narrows as seen for female caregivers.

You can read the NBER digest summary here and the full paper here.