Online prices of personal computers fell by 12.3 percent, for example, but the C.P.I. showed just a 6.9 percent drop. Toy prices online slumped 12 percent, while the C.P.I. put the drop at just 7.8 percent. Online prices for photographic equipment and supplies fell 9.2 percent compared with the 0.6 percent decline registered by the official measure.

The government said on Tuesday that the C.P.I. increased 2.8 percent in May from 12 months earlier, with much of that jump coming from higher prices for gasoline and other energy items. Not including food, energy and housing, which tend to change a lot from month to month, the index was up a much more modest 1.3 percent. The monthly figures are based on a sampling of 140,000 products sold both in stores and online. Adobe’s digital index solely includes internet sales, but the range of products covered is much bigger: 2.1 million transactions every month.

“A lot of what’s in the C.P.I. is not bought on the internet, like health care and housing,” said Mr. Goolsbee, who was also an adviser to former President Barack Obama. But if you compare the same set of goods, he said, “there is massively more deflation” online — by as much as 2.5 percentage points. A deflationary cycle, where prices keep dropping, as has happened in Japan, can mire an economy in decline.

“Prices are going down a whole lot faster than the C.P.I. shows for the same things,” he said.

After all, as bargain hunters know, comparison shopping is a cinch online. The result is that merchants are leery of raising prices. The ease of entering the marketplace, regardless of location, further ratchets up the competition. At the same time, internet retailers can often operate at a lower cost than their brick-and-mortar competitors.

Jerome H. Powell, the Federal Reserve chairman, has called it “the Amazon effect story.”

Research into online commerce in Europe also suggests that comparison shopping — even across national borders — keeps prices low. This work helps explain “why firms might be less able to change prices,” said Brent Neiman of the University of Chicago, one of the authors of the research.

New online research offers more evidence that “the more efficient method of selling through e-commerce is holding inflation down compared to what it would have been otherwise,” said Robert Gordon, an economist at Northwestern University.