It's become an article of faith among politicians, investors and entrepreneurs that the Internet — and access to it — is an economic engine. It helps connect Americans to education and government services. It serves as a platform for new ideas and companies that wind up changing the world. And it reduces costs for consumers and businesses everywhere.

With that in mind, a new study finds that access to next-generation Internet speeds may be connected to better economic growth. According to a report by the Boston-based Analysis Group, cities that offer broadband at 1 gigabit per second — roughly 100 times the national average of 10 megabits per second — report higher per-capita GDP compared to cities that lack those Internet speeds. Of course, all the normal caveats apply: It's hard to draw a causal inference from the study, and it's possible there's something else about the 14 gigabit cities that made them better off to begin with. Still, the paper's methodology seems relatively straightforward.

Drawing from federal statistics, the Analysis Group identified 14 metropolitan areas, such as Chattanooga, Tenn., Sioux Falls, S.D., and Salem, Ore., where over half of the population had access to gigabit speeds in 2011 and 2012. Then the researchers compared those areas against 41 neighboring cities where gigabit Internet wasn't widely available.

Cities with gigabit connections reported 1.1 percent higher per-capita GDP than their slower counterparts, the study found. That might not sound like much, but consider that per-capita GDP in the entire United States has been growing at a pace of one to two percent a year since the recession, according to the World Bank.

If you add it all up, that amounts to $1.4 billion in extra growth, the study says. The findings are consistent with predictions from economists that Internet access will enhance U.S. productivity. More than a decade ago, Alice Rivlin and Robert Litan observed in a Brookings Institution report that investments in information technology helped drive annual productivity growth in the 1990s past three percent.

"Isolating the potential impact of the Internet on productivity is important," they wrote, "because even a few tenths of a percent impact on the growth rate could represent a significant portion of any permanent surge in productivity that is maintained in the future."