Those chances varied widely by the restaurant’s popularity, concludes the study, which was sponsored by Yelp. Among 3.5-star restaurants, every $1 increase in the minimum wage increases the restaurant’s chances of closing by 14 percent. But five-star restaurants don’t experience that same effect.

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“You are losing something from the market,” Michael Luca acknowledged. “But what you’re losing is the lower-quality businesses.”

The Lucas' results speak to a critical question in the debate over minimum wage: Whom will higher wages hurt in the wider economy? While this data doesn't address questions of jobs or unemployment, which many other studies have done, it does suggest that the impact on business may be less confined than some critics have expected. Rather than handicapping successful businesses, higher wages appear to shorten the time before unsuccessful businesses close. And because there's a great deal of churn in the restaurant industry, new restaurants frequently replace the old ones.

Luca has a few theories on why minimum-wage hikes might impact low-quality restaurants more than high-quality ones. For starters, five-star restaurants generally have better service. (That’s a component of the Yelp score.) It makes more economic sense for a restaurant that values and depends on good service to invest more heavily in its workforce.

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Luca’s data also suggests that five-star restaurants are generally more profitable: that makes them less susceptible to market shocks, and more likely to stay open at any wage level. A three-star restaurant would also be more vulnerable, Luca said, to something like sudden increases in rent.

“At any wage level, some businesses are doing well and some aren’t,” Luca said. “If you’re closest to the margin already, then something like a minimum-wage increase is more likely to push you over the edge.”

Importantly, Luca’s study did not look at the impact of wage increases on employment — something he emphasizes. Because food service is a high-churn industry, in which restaurants open and close and employees move around all the time, the fact that one restaurant closes does not necessarily mean more people will be unemployed.

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There is also little correlation between a restaurant’s Yelp rating and its price, Luca cautioned. While it may be tempting to come away from his results with the impression that low-end restaurants — and employees — face more risk, that is not consistent with the data, Luca said.

In his sample, the average restaurant had a tenure of almost six years, a rating of 3.6 stars, and a price indicator of 1.6 “dollar signs” — Yelp-speak for roughly $22 per head.

According to Yelp, nearly half of all the reviews on its platform give five stars. Roughly one-third award three stars or less.

“If anything, the study shows that a higher minimum wage might make the market more competitive and reduce the number of poor performers,” concluded Paul Sonn, the general counsel and program director at the National Employment Law Project. “Some firms are better at adjusting to competitive pressure than others.”

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Whether the restaurant industry needs more competitive pressure is, of course, a matter of debate. Running a restaurant is already a delicate business, with more than half of all restaurants shuttering in their first year. And lately, the industry has faced added competition from delivery services, supermarkets and convenience stores, which have all stepped up their ready-made meal games.

A February report from NPD Group, a market-research firm, found that the number of U.S. restaurants fell two percent in 2016, and that the number of restaurants per capita is at its lowest in a decade.

That backdrop has made the debate on the minimum wage even more fractious. The restaurant industry is the second-largest private-sector employer in the country, according to the National Restaurant Association, and it employs the largest share of minimum-wage workers of any business.

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Advocates for a higher wage argue that a hike would reduce poverty and inject billions of dollars into the economy, even if some businesses have to adjust. Critics, on the other hand, have cited studies like the Lucas' as evidence that a higher wage would result in even more restaurant closures and, possibly, layoffs.

In a statement, Cicely Simpson, the executive vice president of policy and government at the National Restaurant Association, described minimum-wage increases as a threat to jobs, small businesses “and the overall economy.”

“This study shows that government mandates price some businesses out of the market,” said Dan Mitchell, a senior fellow at the Cato Institute, a libertarian think tank that opposes minimum-wage increases. “Which is exactly what theory tells us.”

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Luca, for his part, warns against drawing any sweeping conclusions from his work. He doesn’t see it as a clear point for or against the minimum wage — more like a clarification of something economists already knew. A wage hike has to hurt someone, somewhere: This helps nail down who will be impacted.

“Now we know what kind of trade-offs we're dealing with,” he said.