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It is commonplace to say that the pace of technological change is speeding up. From Twitter to online shopping our everyday lives are, apparently, being transformed.

One of the central puzzles of modern economics is that this change is not being seen in the hard economic data. Throughout the West rates of GDP and productivity growth have slowed in the last 20 years. If the official data are right, the great digital revolution is having surprisingly little effect on prosperity.

The great inventions of the past, such as the steam engine and electricity, changed lives and raised growth. Their modern counterparts seem to be changing lives – the media and most of us can hardly stop talking about them – but not GDP.

One explanation is that the GDP data are right and our impressions are wrong. The US economist Robert Gordon believes that the impact of today’s innovations on human welfare are trivial compared to the great innovations, such as indoor plumbing and antibiotics, of the past.

A more optimistic explanation is that technology is raising welfare, but in ways that are not captured by conventional measures of economic activity. On this argument GDP underestimates the full benefit to consumers of today's technology.

GDP relies on the prices of goods and services to measure value. But many of today's technologies are, in part or in full, free, paid for by advertising, monetising consumer data, patient investors or created by fellow users. The benefits we receive from, for instance, Google Maps or TripAdvisor, are not fully captured by today’s measure of GDP.

The unmeasured gain to welfare is known as the consumer surplus. It represents the difference between what a consumer pays and what they would have been prepared to pay for the goods or services they use. Because consumers obviously only buy goods and services that deliver net benefits – where the value to the consumer exceeds the cost – the consumer surplus is always positive.

Thus GDP has always understated the gains consumers receive from new products and services. But as more digital services become free the gap between measured GDP and the benefits consumers receive has risen.

The consumer sector is awash with technology for which we pay little or nothing directly. Products such as Wikipedia, TripAdvisor, Google and Twitter create value for users far in excess of the advertising sales or donations that fund them. There are also existing services, such as shopping, banking or travel, where the consumer experience has been improved at little cost by the internet.

Economists are creating new ways to measure the consumer surplus generated by modern technology.

One approach is to measure the time saved by internet-based services. Researchers at the University of Michigan found they saved an average of 15 minutes answering each of a series of questions using the internet rather than the university library. Assigning a monetary value to time, Google's chief economist, Hal Varian, estimated that internet searches create $65-$130 billion in consumer surplus in the US each year. This is likely to be an underestimate as the experiment compared the internet with a university library – an asset to which few people have access.

An alternative approach, used by Erik Brynjolfsson and fellow MIT researchers, utilises surveys to estimate the amount of money people would need to forgo access to internet services. These surveys find that the median American Facebook user would require $576 to give up their service for a year.

Internet search is the most highly valued service, with an estimated annual value of $17,530 for the average American. Email is in second place, with a value of $8,414. Email is followed by mapping, video and e-commerce services which respondents valued well above social media and messaging.

The surveys also asked respondents to rank, in terms of willingness to forgo them, existing basic goods and services such as the toilet and public transport against giving up computers and digital services. People chose having a toilet at home as the most crucial service. But, perhaps surprisingly, respondents rated access to the internet and personal computers above meeting friends in person. Having a TV at home was rated above having access to a smartphone. For anyone living in a big city it is striking that respondents rated access to online maps, video streaming and Facebook as being of greater value than public transport.

These new measures of consumer surplus offer an insight into how consumers value new technologies. But this is not the whole story. In measuring the overall welfare effects of the technology we need to consider the negative as well as the positive effects. The huge amount of time we spend online makes us sedentary, more distracted and, for some, more anxious and envious. Few innovations come without any problems. The motor car, for instance, brought mass mobility and also pollution and accidents.

Technology is improving our lives in ways which are not fully captured in today’s measure of GDP. And, as in the past, nor are we capturing the adverse effects of innovation.

The fact that after ten years of sluggish growth measured happiness in the UK is at record levels testifies to the limited value of GDP in gauging human welfare. To understand that, we need far wider measures of progress.

PS: Facebook’s announcement of plans to launch a new digital currency called Libra next year was one of the biggest stories last week. We have written about digital currencies in the past and how central banks would very carefully consider such initiatives because the effectiveness of monetary policy depends on their ability to control the supply and flow of money. This was reflected in the immediate response to Facebook’s announcement from the G7, which is setting up a high-level forum of regulators to examine the risk posed by such currencies to the financial system. The Bank of England’s governor Mark Carney said that if Facebook was successful in attracting users it would “instantly become systemic and will have to be subject to the highest standards of regulation”. This is by no means a sign that central banks are averse to financial innovation. In last week’s news, the Bank of England also announced that it will allow tech companies running payment systems to store funds in its interest-bearing accounts, a privilege so far enjoyed only by commercial banks and one that should help level the playing field for fintechs.