Consumer price index construction

How can a single number stand for the price of everything a household buys?

Inflation is announced as a single figure. Rents, haircuts, aubergines, insurance premiums, second-hand cars, streaming subscriptions — millions of prices, moving in different directions at different speeds, compressed into one decimal.

Before asking whether that number is accurate, ask something prior: what would it even mean for it to be accurate? There is no object in the world called "the price level" sitting somewhere waiting to be measured. So what is the index a measurement of?

The honest answer is that it is not a measurement in the way a thermometer reading is. It is a representative — a stand-in built to speak for a population far too varied to speak for itself. Once you see it that way, the question stops being "is it right?" and becomes "what choices went into choosing the representative, and whose experience do they favour?"

There are four such choices, and each one is a place where a defensible decision quietly changes the answer.

The first is whose spending it represents. The weights — how much beef matters relative to rent — come from a household expenditure survey, and the standard construction weights each household by how much it spends. So a household spending twice as much counts twice as heavily. That is a reasonable choice if you want a figure for total consumption in the economy, and a strange one if you want to know what happened to a typical family. Build the index the other way, averaging each household's own price experience equally, and you get a different number. Statisticians call the two the plutocratic and democratic weightings, and neither is wrong — they answer different questions.

The second is which goods. The index compares this year's cost with last year's, and for that comparison to mean anything the basket has to be held fixed: otherwise you are comparing two different things and learning nothing about prices. But households do not hold their baskets fixed. When beef rises and chicken does not, people buy chicken. A fixed basket keeps buying beef, so it overstates what it now costs to be as well off as before — substitution bias. This is not a flaw that can be removed, because the fixing is exactly what makes the comparison valid. It can only be traded off, which is why the United States also publishes a chained index that allows substitution and typically runs a little lower.

The third is what counts as the same good. A laptop at last year's price is not last year's laptop. Agencies use hedonic methods — regressions attributing part of a price to measurable characteristics — to strip out quality improvements. The correction is large in some categories, and whether it over- or under-corrects is genuinely disputed.

The fourth is which prices. Consider the largest single component. Most households own their homes and pay no rent, yet a house is an asset as much as a monthly service, and its purchase price is not a consumption expense. The American solution is owners' equivalent rent — imputing what the home would rent for, estimated from actual rents on comparable properties. That imputation is roughly a quarter of the whole index. The biggest number in the calculation is a price nobody paid.

And there is a fifth choice hiding beneath all of them, which sounds like a technicality and is not. Before any weights are applied, the individual prices collected for a single item in different shops must be averaged — and how you average matters. Britain's Retail Prices Index used an arithmetic mean of price ratios, the Carli formula, which is upward biased relative to the geometric alternative. The resulting gap, known as the formula effect, ran to several tenths of a percentage point a year, and in 2013 the UK Statistics Authority withdrew the RPI's designation as a national statistic largely because of it. A choice made at the very bottom of the calculation, invisible in every headline, moved a number that indexed pensions and rail fares.

How large are these effects together? In 1996 the Boskin Commission concluded that the US consumer price index overstated the growth in the cost of living by around 1.1 percentage points a year. Methodology changed substantially afterwards; later estimates of residual bias are considerably smaller, and are still argued over.

Three refinements that keep this from sliding into "the number is made up".

The index is not arbitrary and not opaque. The choices above are documented, stable over time, and argued about publicly. Consistency does much of the work: even if the level is debatable, the change from one year to the next is measured the same way, which is what most uses of it need.

The complaint that "my inflation is higher than the official figure" is usually correct, and is not evidence of a fault. A household that rents in a hot market, drives a long commute, and pays for childcare has a basket nothing like the average one, and its own rate can differ by several points. The index never claimed to be a personal figure.

The last refinement is where the stakes are. A price index is used to uprate pensions, wages, benefits and contracts, and to deflate output into real terms. That means each design choice moves real money and real published history. Substitution adjustments lower the measured rate and thereby lower indexed payments. There is no neutral option available — only choices whose consequences should be stated out loud rather than buried in a formula.

• Chained versus fixed-basket indices, and what each is the right tool for.
• Why different countries handle owner-occupied housing so differently, and what that does to international comparisons.

Every term the collection defines is gathered in the glossary.