“This experiment is probably telling us much the same thing,” Mr. Dube added in an email. “But if we want to know what would happen if N.Y. or C.A. raised its minimum wage to 15/hr, I doubt that this online experiment — neat as it is — will shed much light.”

When the minimum wage goes up for everyone, it is not so easy for employers to substitute better-skilled workers because the new minimum would not offer a more attractive wage. In many cases, more highly skilled workers see their wages rise after minimum-wage increases to keep them above the new minimum, making it all the more difficult to lure them away.

Zane Tankel, chief executive and equity partner in a group that owns and operates several dozen Applebee’s restaurants in the New York City area, said replacing low-skilled workers with higher-skilled ones after the state’s recent minimum-wage increases is “not something that we try to do.”

Mr. Tankel argued that differences in the productivity of low-level workers in his industry are not very big. “It’s just a lot more money for the exact same job description,” he said. He is accelerating automation in his restaurants, including tablet devices for ordering certain items and payment, to offset the costs of the higher minimum.

Mr. Horton is quick to acknowledge that there are many reasons his experiment might not capture employer behavior in the wider economy. But he says a higher minimum wage could attract more highly skilled workers who were not previously in the labor market — say, college students. At the same time, less-skilled workers might lose their jobs and drop out of the labor force.

More broadly, he said, the contribution of his paper is to show that one impulse of many employers in the face of a minimum-wage increase will be to find more productive workers, even if there are limits on how much they can follow through on this desire.

“There are lots of reasons to think this is probably happening and we haven’t detected it because we don’t have the data,” he said. “I know in my career, people have fine-grained opinions about who’s better than who, and we talk about them endlessly. We’re constantly ranking. But when we talk about other labor markets, we pretend the same distinctions don’t exist.”