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Or, if cloning weren’t an option, you could take a bunch of women, randomly select half of them, and magically switch their gender to male, leaving everything else about them the same, and do the opposite with a bunch of men.

Unfortunately, economists aren’t allowed to conduct such experiments. (Yet.) But individuals can if they want to. It’s called a sex-change operation.

So what happens when a man decides to employ surgery and hormone therapy to live as a woman (a so-called MTF, or male-to-female transgender) or when a woman decides to live as a man (an FTM, or female-to-male)?

Ben Barres, a Stanford neurobiologist, was born Barbara Barres and became a man in 1997, at the age of forty-two. Neurobiology, like most math and science disciplines, is heavily populated by men. His decision “came as a surprise to my colleagues and students,” he notes, but they “have all been terrific about it.” Indeed, his intellectual stature seems to have increased. Once, after Barres gave a seminar, a fellow scientist turned to a friend of Barres’s in the audience and issued this left-handed compliment: “Ben Barres’s work is much better than his sister’s.” But Barres doesn’t have a sister; the commenter was slighting Barres’s former, female self.

“It is much harder for men to transition to women than for women to transition to men,” Barres admits. The problem, he says, is that males are presumed to be competent in certain fields—especially areas like science and finance—while females are not.

On the other hand, consider Deirdre McCloskey, a prominent economist at the University of Illinois at Chicago. She was born a male, Donald, and decided to become a woman in 1995, at the age of fifty-three. Economics, like neuroscience, is a heavily male field. “I was prepared to move to Spokane and become a secretary in a grain elevator,” she says. That proved unnecessary, but McCloskey did “detect a queerness penalty toward me in some of the economics profession. I reckon I’d make a little more money now if I were still Donald.”

McCloskey and Barres are just two data points. A pair of researchers named Kristen Schilt and Matthew Wiswall wanted to systematically examine what happens to the salaries of people who switched gender as adults. It is not quite the experiment we proposed above—after all, the set of folks who switch gender aren’t exactly a random sample, nor are they the typical woman or man before or after—but still, the results are intriguing. Schilt and Wiswall found that women who become men earn slightly more money after their gender transitions, while men who become women make, on average, nearly one-third less than their previous wage.

Their conclusion comes with a number of caveats. For starters, the sample set was very small: just fourteen MTFs and twenty-four FTMs. Furthermore, the people they studied were mainly recruited at transgender conferences. That puts them in the category of what Deirdre McCloskey calls “professional gender crossers,” who aren’t necessarily representative.

“One could easily believe,” she says, “that people who do not just become women and then get on with their lives, but keep looking back, are not going to be the most successful people in the workplace.” (She may have changed gender, but once an economist, always an economist.)

Back in Chicago, in a chic neighborhood just a few miles from where the street prostitutes work, lives someone who was born female, stayed that way, and makes more money than she ever thought possible.

She grew up in a large and largely dysfunctional family in Texas and left home to join the military. She trained in electronics and worked in research and development on navigation systems. When she rejoined the civilian world seven years later, she took a job in computer programming with one of the world’s largest corporations. She made a solid five-figure salary and married a man who earned well into six figures as a mortgage broker. Her life was a success, but it