The Fight for $15 movement has notched a string of victories over the past couple of years, getting higher minimum wage legislation passed in the states of California and New York as well as several cities. And earlier this month, McDonald’s announced that it was going to begin installing touchscreen ordering kiosks in its restaurants, which should allow restaurants to serve more customers with fewer workers.

And in a post for Forbes, former McDonald’s CEO Ed Rensi argues these two trends are connected.

“I told you so,” he writes. “In 2013, when the Fight for $15 was still in its growth stage, I and others warned that union demands for a much higher minimum wage would force businesses with small profit margins to replace full-service employees with costly investments in self-service alternatives.”

Now, Rensi says, his prediction is coming true. McDonald’s is just one of several restaurants around the country that are experimenting with automated restaurant technologies. If jurisdictions continue to push up the minimum wage, more and more businesses will look for ways to automate their operations in order to avoid having to pay higher wages.

The economic logic of Rensi’s argument is impeccable. If you make the minimum wage high enough, businesses will look for more opportunities for automation and hire fewer workers. The question is whether a $15 minimum wage is high enough to induce a lot of employers to switch to more automated systems.

No one knows the answer to this question. Indeed, when I asked two economists on opposite sides of the debate to predict the effects of California’s minimum wage hike earlier this year, they actually had the same response: The increase was so large that we don’t know what’s going to happen. “This will be a big experiment,” economist Arindrajit Dube told me. “It's far outside of our evidence base."“

The McDonald’s experiment with touchscreen ordering systems illustrates the potential problem with making high minimum wages effective across big states like California and New York — both of which passed minimum wage increases this year. If McDonald’s automates its locations in Manhattan, San Francisco, and Silicon Valley, displaced workers shouldn’t have too much trouble finding alternative work in the booming economies of these cities as barbers, servers at full-service restaurants, nannies, and so forth. With lots of wealthy customers around, there’s a robust demand for unskilled service workers there.

But the outlook might not be so rosy in cities like Fresno, California, or Rochester, New York, where the economy is not booming and average wages are much lower. If a $15 minimum wage causes fast-food jobs to be automated in these cities, workers may not be able to find alternate work. A law designed to put more money in workers’ pockets could wind up putting a lot less money in their pockets instead.

It’s easy to get people fired up about an alliterative slogan like “Fight for $15.” But alliteration isn’t necessarily a good way to choose a policy goal. The implicit idea here — that people everywhere should get the same minimum wage whether they live in a booming, expensive metropolis or a struggling town with a low cost of living — doesn’t make a lot of sense.