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