Women who go to medical school just for the financial rewards of being a doctor could be making a mistake, according to a study published in the Journal of Human Capital.

The research found that after factoring in the high upfront costs of becoming a doctor, most women primary-care doctors would have made more money over their careers becoming physician assistants instead. For the median man on the other hand, becoming a doctor pays a substantial premium over becoming a PA.

Two factors drive the results, say the study's authors, M. Keith Chen and Judith Chevalier of the Yale School of Management. First, there's a wage gap; women doctors earn a lower hourly wage than male doctors. But the most important factor is that most women doctors do not work enough hours to make their expensive training pay off compared to PAs.

"One of the takeaways here is it's not all wage gap," Chevalier said. "It's mostly an hours gap. Many women who become doctors simply don't work enough hours to amortize the upfront costs. It's also true for some men, but a much smaller fraction."

Chen and Chevalier used data on thousands of doctors and PAs from the Robert Wood Johnson Community Tracking Physician Survey and the American Academy of Physician Assistants. The data included wages and hours worked for males and females in both professions. The researchers used those data to calculate the net present value of each occupation, taking into consideration the training costs in time and money for both professions. Net present value (NPV) is a calculation economists use to determine whether the gains from a long-term venture are worth the costs.

For men, becoming a doctor is a far better deal than becoming a PA. The NPV of becoming a doctor for the median male was around $2.3 million, while the value of becoming PA was around $1.9 million. But for the median woman, becoming a doctor offers no such advantage. The NPV for women of becoming a doctor was about $1.67 million, while the NPV of becoming PA was $1.68 million.

Most of the male/female NPV disparity is driven by the fact that women doctors tend to work fewer hours than male doctors in the prime of their careers. Early in their careers male and female doctors work similar hours, the researchers found. But between the ages of 31-35, the median male doctor works 50 hours per week while the median female works 40. And a gap in hours worked remains through age 55.

The results add to a growing literature suggesting that women may be overinvesting in professional degrees, the researchers say. The question is why women invest in these degrees when higher returns can be found elsewhere.

It could be, Chevalier says, that women simply perceive that being a doctor will be more satisfying work. But it's also possible that women "don't foresee the extent to which they're going to cut back working when they have kids."

"There are lots of reasons the decision to be a doctor could be rational," she adds. "But for the median woman, it doesn't make financial sense."