The stagnation effect is not the effect of stagnation, just that the technology advances along axis that we didn't foresee, or because we don't really understant the exponential curves. Back in the 70s it was obvious that digital technology would become something awesome, but most of it was still at the start of the exponential curve, meaning that it took many more years before it got to critical mass (ca 1990s).
And when technology "stagnates" yet again, it is because quick growth in one area typically requires similar growth in a different, neglected area (some tangential, needed technology, or policy, or other - flying cars are nice, but where the heck are we supposed to fly them?).
Kodak died because they weren't able to properly understand the curve, even when they had engineers that had quite properly predicted when the digital camera technology would be ready for prime time.
And even understanding how the technology itself grows, one still needs to understand the effects. As performance soars exponentially, costs follows the other way. My smartphone, advanced as it is, costs a 5th of the suitcase mobile my father bought 25 years ago.
From there it should be obvious that the GDP can't grow with the technology itself, but rather with the effects of it, including all those things that have become so much cheaper to do. And I'm sure productivity has been part of it, but also better quality of life (at least in countries not destroying themselves with inequality) such as shorter work days, longer vacations, healther lives and so on. And a lot of businesses are struggling with these things, because they have business models that are inherently premium, but where technology makes it possible to be a whole lot of cheaper (banking is one example).
Other services aren't really premium as such, they just happen to benefit from technology to make things simpler for the user (taxis where the costs still are cars and drivers (technology may of course eventually eradicate the drivers ...)).
Wish I'd remembered this at the Apple Watch intro <g>
Krugman cleverly reprises Hitchhiker to question tech: "Remember Douglas Adams’s 1979 novel “The Hitchhiker’s Guide to the Galaxy”? It began with some technology snark, dismissing Earth as a planet whose life-forms “are so amazingly primitive that they still think digital watches are a pretty neat idea.”"
The Point: "...at this point, the whole digital era, spanning more than four decades, is looking like a disappointment. New technologies have yielded great headlines, but modest economic results. Why?
...Another possibility is that new technologies are more fun than fundamental. Peter Thiel, one of the founders of PayPal, famously remarked that we wanted flying cars but got 140 characters instead. And he’s not alone in suggesting that information technology that excites the Twittering classes may not be a big deal for the economy as a whole."