It is something every restaurateur and hotel owner knows: good reviews boost takings while terrible ones can close you down. And, in an age when everyone can be an online critic, ratings have never been more important. But until now no one could be sure just how important the online star ratings system employed by sites such as Toptable and Tripadvisor could be for a business's fortunes.

Work by two economists at the University of California, Berkeley, Professors Michael Anderson and Jeremy Magruder, published in this month's edition of the Economic Journal, represents the first attempt to gauge the relationship between online star ratings and customers' purchasing decisions. The pair focused on the effects of positive online ratings on 300 San Francisco restaurants that were then collated to form a star system on Yelp.com, a popular US ratings site.

They found that a restaurant with a rating improved by just half a star – on a scale of 1 to 5 – was much more likely to be full at peak dining times.

Indeed, an extra half-star rating caused a restaurant's 7pm bookings to sell out on from 30% to 49% of the evenings it was open for business.

Significantly, the two economists found that the increase in trade happened without any change in prices or the quality of food and service, confirming that it was the reviews that brought in the new customers.

The economists write: "The findings of this study demonstrate that – although social media sites and forums may not generate the financial returns for which investors yearn – they play an increasingly important role in how consumers judge the quality of goods and services."

The economists conceded that, while restaurants with strong reviews on the site did better business than poorly reviewed restaurants, establishing cause and effect was difficult.

"After all, restaurants that get good reviews are those that appeal to consumers and they would probably do well even in the absence of any reviews," the pair write. However, they are confident the research is robust. They note that, when Yelp.com computes a business's average rating (which ranges from 1 to 5 stars), it rounds off to the nearest half-star.

So, two restaurants that have similar average ratings can actually appear to be of very different quality to online viewers. For example, a restaurant with an average rating of 3.74 displays a 3.5-star average rating, while a restaurant with an average rating of 3.76 displays a 4-star average rating.

This, the economists claim, allows them to make important comparisons between restaurants that have different ratings – for example, 4 stars versus 3.5 stars – but are of nearly identical quality (for example, a 3.76 average versus a 3.74 average). Their conclusion? That half a star makes all the difference.

The economists write: "Differences in customer flows between such restaurants can therefore be attributed to the ratings themselves rather than differences in the quality of food or service."

The study collected reviews and daily reservation availability for 328 restaurants in San Francisco. It found that moving from 3 stars to 3.5 stars increased a restaurant's chance of selling out during prime dining times from 13% to 34%. Moving from 3.5 stars to 4 stars increased the chance of selling out during prime dining times by 19 percentage points.

The pair conclude that changes in consumer preferences "occur even though restaurant quality is held constant. This study demonstrates that these reviews have become a salient factor in consumer decisions."

Significantly, they found that the effect was even more profound when alternative information was hard to come by, opening up the possibility that invented reviews could boost fortunes.

The pair write: "These returns suggest that restaurateurs face incentives to leave fake reviews, but a rich set of robustness checks confirm that restaurants do not manipulate ratings in a confounding, discontinuous manner."

Concerns that retailers and restaurant owners are seeking to manipulate the online ratings system are becoming a key issue for the internet.

"Everyone's trying to do something to make themselves look better," Linchi Kwok, an assistant professor at Syracuse University in New York who is researching social media and the hospitality industry, told the New York Times last month. "Some of them, if they cannot generate authentic reviews, may hire somebody to do it."

Tripadvisor places a "red flag" against the names of hotels that it suspects have planted enthusiastic reviews on its website.