San Francisco's higher minimum wage is causing an increasing number of restaurants to go out of business even before it is fully phased in, a new study by the Harvard Business School found.

The closings were concentrated among struggling, lower-rated restaurants. The higher minimum also caused fewer new restaurants to open, it found.

"We provide suggestive evidence that higher minimum wage increases overall exit rates among restaurants, where a $1 increase in the minimum wage leads to approximately a 4 to 10 percent increase in the likelihood of exit," report Dara Lee and Michael Luca, authors of " Survival of the Fittest: The Impact of the Minimum Wage on Firm Exit." The study used as a case study San Francisco, which has an estimated 6,000 restaurants in the Bay Area and is ratcheting up its minimum wage. Restaurants are one of the largest employers of minimum wage workers.

The city's minimum wage is currently $13 an hour, compared with California's rate of $10.50 and the federal rate of $7.25. The city's rate is set to increase to $14 in July and again to $15 next year. That rate, unlike federal law, does not include an exception for tipped employees. The rest of the Golden State will see the minimum rate rise to $15 in 2022. States are free to set rates higher than the federal level, and cities can do the same regarding state minimums.

The Harvard study used reviews on the social media site Yelp as a gauge of relative quality. It found that lower-rated eateries in particular were more likely to go under as the minimum wage was raised. Five-star restaurants were largely unaffected, while ones with a 3.5 star rating were 14 percent more likely to fail when the city's minimum pay rate rose 10 percent above the state's minimum. The failure rate increased steadily as the restaurant's ratings declined.

"The impact on exit is concentrated among lower quality restaurants, which are already closer to the margin of exit. This suggests that the ability of firms to adjust to minimum wage changes could differ depending on firm quality," the study found. The higher-rated restaurants can adjust, primarily through working their employees harder.

Higher minimum wages also reduce the rate at which new restaurants open by 4-6 percent per $1 increase in the minimum, the study found.