The Economist explains why it’s hard to calculate:
Measuring the economic impact of all the ways the internet has changed people’s lives is devilishly difficult because so much of it has no price. It is easier to quantify the losses Wikipedia has inflicted on encyclopedia publishers than the benefits it has generated for users … This problem is an old one in economics. GDP measures monetary transactions, not welfare. Consider someone who would pay $50 for the latest Harry Potter novel but only has to pay $20. The $30 difference represents a non-monetary benefit called “consumer surplus”. The amount of internet activity that actually shows up in GDP—Google’s ad sales, for example—significantly understates its contribution to welfare by excluding the consumer surplus that accrues to Google’s users.
Some researchers tried to measure it using leisure time as an indicator:
Erik Brynjolfsson and Joo Hee Oh of the Massachusetts Institute of Technology note that between 2002 and 2011, the amount of leisure time Americans spent on the internet rose from 3 to 5.8 hours per week. The authors conclude that in so far as consumers must have valued their time on the internet more than the alternatives, this increase must reflect a growing consumer surplus from the internet, which they value at $564 billion in 2011, or $2,600 per user. Had this growth in surplus been included in GDP, it would have raised economic growth since 2002 by 0.39 percentage points on average.