If you want to know how much Google and Facebook are worth to you, try thinking about how much money it would take for you to stop using them

On my morning commute last week I decided to dip into a bit of eighteenth century philosophy: Hume’s fork, Kant’s Critique of Pure Reason. Then I veered off into some physics: Newton’s law of universal gravitation, Einstein’s theory of general relativity.

But what’s even more remarkable than my geekiness is the fact that I did all this on my smartphone. The articles were on Wikipedia. And I started out not with a planned reading list but with Google.

In those ancient days before smartphones, WiFi on public transport, and, of course, the internet, I would have needed to go to a library to read up on such an eclectic range of topics.

Or I would have needed to carry a number of books around with me, carefully selected before leaving the house. We all know that digital technologies have changed our lives over the past decade. But what is harder to pin down is how much this benefit is worth to us economically.

Leaving aside for a moment the issue of advertising and our personal data, there is no upfront charge to use a search engine like Google. Wikipedia is, of course, a public resource. But this means there is no price tag for economists to use in order to impute the value we all derive from such new services.

But that doesn’t mean economists have given up on estimating it. In 2010 Yan Chen from the University of Michigan conducted an experiment to see how much time people save through searching for information online relative to the older methods.

She found that the average online search time for a given task is seven minutes, versus 22 minutes for the offline search. We should perhaps take the research with a pinch of salt given that it was partly funded by a Google research grant. Yet there seems little reason to doubt the basic result that online search is around three times quicker than the older methods. When was the last time you went to the library, or opened an old fashioned dictionary to look up a word’s spelling?

So how does that help us to value such services? Time is money. To get a very rough estimate of the value of your time consider how much you get paid per hour. Now consider how much time a day you spend searching online for information. Multiply the time spent searching by your hourly pay rate. Now double it. That’s a rough estimate of how much online search engines benefit you financially. Or, if you’re searching of information as part of your job, that’s how much the technology benefits your employer by making you more productive.

But let’s think about it from another perspective. Google saves us time. But is there not value from spending longer on the internet sometimes too? Think of time on social media catching up with friends and family.

Erik Brynjolfsson of MIT conducted a survey in which Americans were asked how much they would have to be paid not to use the internet for a month. From these results he and colleagues were able to derive a rough estimate of how much value individuals derive from various online services.

The value of social media – the likes of Facebook, Instagram and Snapchat – for Americans in 2017 was put at $322 a year. The value of search engines was put at a whopping $17,500.

Brynjolfsson presented his results at an Office for National Statistics conference about measuring the economy last week, hosted by the Bank of England. He argued that such benefits for consumers from the new digital economy are being missed in the national accounts of countries like the US and the UK – and that statisticians should consider using work like his to incorporate them. It wouldn’t be a trivial adjustment. Brynjolfsson’s figures suggest free sites added around $100bn a year to the US economy between 2007 and 2011, around 0.75 per cent of GDP.

Speaking at the same conference was Hal Varian, Google’s in-house economic guru. Varian made a point about free cloud storage for digital photos, offered by firms like his employer. How much is this service worth? Well, he noted that Kodak used to say that people would rush into a burning home for three reasons – to retrieve family members, pets and, finally, photo albums. Again, the fact this claim came from a photography company might detract a bit from its credibility. But it rings true.

The implication of the fact that many people would be willing to risk their very lives for their photos implies the digital photo revolution has an implicit financial value to people – and a significant one.

So should statisticians be making substantial adjustments to their national accounts as Brynjolfsson, Varian and many others suggest, in order to capture the undeniable value to consumers of new free online services? Aren’t we underestimating an important area of economic growth by our failure to do this?

There are reasons to be a bit cautious. First, as mentioned earlier, there is a question mark over whether we actually should regard all these services as free given some of these firms run a business model in which they sell our personal data to advertisers. Wikipedia might be a non-profit, but Google and Facebook most certainly are not.

Second, there are many other goods beyond the digital realm that people value – and which one could attempt to measure through surveys – which do not enter the national accounts. Consider clean air, or friendship, or political freedom. How much would we pay not to choke on smog? How much would we pay to be free of the fear of being locked up by a repressive regime?

Perhaps the problem is less that official measures such as GDP are not fit for purpose in the digital age but that, in the digital age, we place too much weight on GDP as an indicator of our changing quality of life.