In some cases, online companies like Amazon and eBay are fighting among themselves for customers. But in others — here is where the cannibals enter — the companies are eating up traditional advertising, media, music and retailing businesses, said Joel Waldfogel, an economist at the University of Minnesota who has studied the phenomenon.

“One falls, one rises — it’s pretty clear the digital kind is a substitute to the physical kind,” he said. “So it would be crazy to count the whole rise in digital as a net addition to the economy.”

There is no disputing that a wide spectrum of businesses, from e-marketers to pharmaceutical companies, are now using huge amounts of data as part of their everyday business.

For now, though, he acknowledges that most of the raw data flowing across the Web has limited economic value: far more useful is specialized data in the hands of analysts with a deep understanding of specific industries. “The promises that are made around the ability to manipulate these very large data sets in real time are overselling what they can do today,” Mr. Marks said.

Some economists argue that it is often difficult to estimate the true value of new technologies, and that Big Data may already be delivering benefits that are uncounted in official economic statistics. Cat videos and television programs on Hulu, for example, produce pleasure for Web surfers — so shouldn’t economists find a way to value such intangible activity, whether or not it moves the needle of the gross domestic product?