Perhaps the most fundamental task facing economists is to measure the change in human welfare over time.

To get to a measure of spending power you need to measure incomes and prices over time. Incomes are relatively straightforward, prices less so. To gauge the changing standard of living you need to measure thousands of prices in constantly changing representative basket of goods and services.

The story of Western progress over the last two centuries has been one in which incomes rise faster than prices lifting living standards.

The economic historian Brad DeLong from the University of California at Berkeley has graphically illustrated this by comparing the price of goods in 1895 and 2000 against average wages. He tracked down a catalogue of goods sold in 1895 by Montgomery Ward, the largest mail order retailer in the US at that time. It was modern industry's conduit to the 40% of Americans living in small towns or farms. DeLong compared the catalogue prices of 1895 with prices in 2000 map the changing affordability of products over time.

His analysis shows huge gains in spending power through the twentieth century. In 1895, for instance, the average American had to work for 44 hours to finance the purchase of a 100-piece dinner set. In 2000 it took just 3.6 hours to earn the money to make the purchase, a 12-fold rise in spending power. High-end products saw a less pronounced fall in prices but a fall nonetheless. In 1895, a Steinway piano cost 2400 hours of work. By 2000, that had more than halved to 1108 hours.

DeLong's analysis underscores how a gauge of the standard of living needs reliable estimates of income and prices.

But how accurate are the conventional, official measures of prices – the national consumer price or inflation indices?

Research conducted by Yale University economist William Nordhaus in the nineties suggests that we systematically overestimate inflation, especially when comparing prices of goods that have seen transformative changes in quality, due to technological innovation.

To illustrate his point, Nordhaus studied how the cost of artificial lighting has changed over the years. He first investigated how prices of the inputs to sources of illumination, such as firewood, whale oil, kerosene, gas or electricity, evolved over time. According to his calculations, the price of lighting increased by a multiple of three to five over the nineteenth and twentieth centuries.

But this calculation took no account of the improvements in the quality and efficiency of lighting. For example, given the same amount of energy as input, a compact fluorescent bulb from the 1990s produces 507 times the amount of light produced by a whale oil lamp from the early nineteenth century. Nordhaus set about measuring the changing cost of a lumen hour, an hour's worth of one unit of illumination, from each of these sources. Instead of an increase in prices, his study revealed that the cost of a lumen hour had fallen by a factor of 325 in the two centuries from 1800.

This overestimation of inflation means that traditional measures of wage growth, deflated by inflation, are likely to be significantly underestimated. Nordhaus estimates that correcting for the improved quality of lighting alone would add 7% to US real wage growth over the past two centuries.

Over the years many economists have tried to gauge the scale of such mismeasurement. In 1996, a commission chaired by Stanford University economist Michael Boskin found that accounting for quality improvements in goods could shave up to 0.6 percentage points off US annual inflation estimates.

In most developed economies, adjustments are now made to inflation calculations to better capture quality improvements. In the UK, the Office for National Statistics provides examples of products where quality adjustments are particularly important. High-tech and electronic goods such as laptops, telecommunication equipment, cars and software have seen major innovations over the years.

Computer processing capacity is a well-measured feature and quality adjustments on this basis are easily made. Similarly, improvements in the safety, comfort and reliability of a car, though more complex, can be captured. The changing characteristics of goods generally manifest in physical differences which can be measured – as Nordhaus did with lighting.     

It is harder to account for changes in the non-physical characteristics of services. Just consider trying to measure the effects on the consumer experience brought about by the introduction of internet banking services or self-service checkouts in shops. This is particularly tricky given that different consumers have different views on such innovations.

The existence of an agreed measure of light output, the lumen, facilitates direct comparisons of light quality over time. Doing the same for the internet and communications technology is anything but straightforward.

For all the sophistication of modern society we still struggle to capture quality changes, both good and bad, in services. But it seems likely that those quality changes are on balance, positive, and welfare-enhancing. The good news is that we are probably better off than the official numbers tell us.

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