Households diverge in a shock, not in general
Rebuilding US CPI from its eight components recovers the published headline to 0.083 percentage points. Reweighting it for different households shows they live at much the same rate for years, then come apart exactly when the number is quoted hardest.
Inflation is announced as one number. That number is an average across everything people buy, weighted by how much of it they buy, so it describes a household spending something like 45% of its budget on housing, 17% on transport and 8% on medical care, all at once. Almost nobody has that budget. The average is real and carefully measured, and it describes a composite person who does not exist.
The obvious next thought is that different households therefore live at different rates, persistently, and that the gap compounds into something large over a decade. That is what I set out to measure, and it is wrong. Averaged across ten years the baskets land within about a point of each other, and the cumulative difference comes to roughly 1%. On a ten-year view the headline is a decent summary of nearly everyone.
What actually happens is that the disagreement is concentrated. It is small when inflation is low, and it opens up sharply when inflation is high.
- mean spread between households, headline below 3%, 56 months
- 0.78 pp
- headline between 3% and 5%, 21 months
- 0.96 pp
- headline at 5% and above, 24 months
- 2.45 pp
Three times wider in the shock than in the calm. The one national figure is least representative at precisely the moment it is quoted hardest, in pay negotiations, in benefit uprating, and in central bank press conferences.
Why the reconstruction comes first
Reweighting a basket and drawing a line is easy, and on its own it proves nothing, because a reader has no way to know whether the machinery underneath is sound. So the tool is built on a check it has to pass before any of this is allowed to be interesting.
Take the eight published component indices, weight them by the official relative importances, and you should recover the published all-items rate. You do.
- mean absolute error against the published headline
- 0.083 pp
- months compared
- 101
- worst single month, May 2021
- 0.42 pp
The comparison is against a figure the BLS itself publishes to one decimal place. Everything the tool does afterwards is the same arithmetic with one table swapped, a household’s weights instead of the official ones. Had the official weights failed to rebuild the official index, the honest response would have been to stop and find out why, not to publish household comparisons resting on a method that demonstrably does not work.
On checks that cannot fail
The residual error is not noise either. It peaks in 2021, and it peaks there because the rebuild uses one year’s weights across the whole decade while the BLS re-estimates them annually. The reconstruction drifts most exactly where real spending patterns moved most. That is a satisfying kind of error, because it has a reason.
Wrong first
Different households live at persistently different inflation rates, and the gap compounds.
It does not compound. Over ten years the baskets converge to within about a point and the cumulative difference is around 1%, which is close to nothing. I had the shape of the answer backwards: the interesting variable is not who you are, it is when you are asking.
March 2022
The clearest single month. The headline was 8.7%, and inside that one number two ordinary households were living three and a half percentage points apart.
8.7%published headline
Neither household is unusual, and neither is wrong about what they are experiencing. The commuter spends more of their budget on the thing that spiked, and the student spends less.
This is also why people say, during an inflationary episode, that it feels worse than the official figure admits. For a good many baskets it genuinely is worse. Not because the statistic is wrong, but because it is an average, and averages hide their tails at exactly the moment the tails get long.
Set your own basket
The browser version runs the same reconstruction with eight sliders in front of it. Move them to match how you actually spend and it shows the rate you are living against the published one, and where the two came apart over the decade.
What this does not show
It does not measure your spending. It lets you assert it. The output is only as good as the shares you set, and the presets are informed guesses rather than anybody’s receipts.
United States only, and eight expenditure groups rather than the full basket. Nothing here transfers to another country’s index without redoing the work against that country’s data.
The arithmetic is a weighted sum of group rates, not a chained index. Over a twelve-month window the two agree closely, because the weights barely move inside a year. Over longer spans the chained calculation is the correct one, and this is not it.
The household baskets are illustrative constructions. They are meant to show that the verdict moves with the situation, not to claim that any particular student or commuter spends precisely these shares.