"The limits to productivity growth are set only by the limits to human inventiveness" says John Kay. This understates the problem. There are other limits. I'd mention two which I think are under-rated.
One is competition. Of course, this tends to increase productivity in many ways. But it has a downside. The fear of competition from future new technologies can inhibit investment today: no firm will spend £10m on robots if they fear a rival will buy better ones for £5m soon afterwards. As someone said, it is the second mouse that gets the cheese. It might be no accident that techno-optimism exists today alongside low investment, weak stock markets and high corporate cash piles.
The second is that, as Brynjolfsson and MacAfee say, "significant organizational innovation is required to capture the full benefit of...technologies."
For example, Paul David has described (pdf) how the introduction of electricity into American factories did not immediately raise productivity much, simply because it merely replaced steam engines. It was only when bosses realized that electric motors allowed factories to be reorganized - dispensing with the need for machines to be close to a central power source - that productivity soared, as workflow improved and new cheaper buildings could be used. This took many years.
It's not just organizational change that's needed, though. So too, sometimes, is social change. For example, household appliances such as vacuum cleaners and washing machines have allowed women to join the labour market. But it is taking decades to reap this benefit, because it also requires a change in social norms to accept women as workers of equal potential.
Similarly, I suspect that if IT is to have (further?) productivity-enhancing effects, they require socio-organizational change. IT should make it easier to communicate knowledge, but this only raises productivity if it is accompanied by a breaking down of silos and methods to facilitate co-operation and the exchnage of ideas within companies. It also should facilitate working from home, which could increase aggregate productivity by reducing house prices thus shifting spending away from a sclerotic sector of the economy towards more dynamic ones.
Without these changes, the internet might be like Hero of Alexandria's aeolipile - an impressive device of little macroeconomic consequence.
However, there are always obstacles to the social and organizational change necessary for technical change to lead to productivity gains. These might be cognitive - such as the Frankenstein syndrome or "not invented here" mentality. Or they can be material. Socio-technical change is a process of creative destruction, the losers from which kick up a stink; think of taxi-drivers protesting against Uber.
Worse still, these losers aren't always politically weak Ludditites. They can be well-connected bosses of incumbent firms, or managers seeking to maintain their power base.
So great are these obstacles that Joel Mokyr has coined the phrase Cardwell's law:
Every society, when left on its own, will be technologically creative for only short periods. Sooner or later the forces of conservatism, the "if-it-ain't-broke-don't-fix-it," the "if-God-had-wanted-us-to-fly-he-would-have-given-us-wings," and the "not-invented-here-so-it-can't-possibly-work" people take over and manage through a variety of legal and institutional channels to slow down and if possible stop technological creativity altogether.
He'll not thank me for saying so, but this echoes Marx:
At a certain stage of development, the material productive forces of society come into conflict with the existing relations of production or - this merely expresses the same thing in legal terms - with the property relations within the framework of which they have operated hitherto. From forms of development of the productive forces these relations turn into their fetters.
The big question facing us is, therefore: do we have the right set of institutions to foster the socio-organizational change that beget productivity growth? These require a mix of healthy markets, to maximize ecological diversity; a financial system which backs risky new-comers; property rights which incentivise innovation; and state intervention that facilitates all these whilst not being captured by Luddites. If our politics weren't so imbecilic, this question would be getting a lot more attention than it is.