Part I — Why Anyone Ever Built a Price Index
In 1707, the Anglican bishop William Fleetwood faced a peculiar problem. An Oxford college statute, written around 1440, disqualified any fellow whose income exceeded £5 per year. Two and a half centuries later, a young fellow wrote to Fleetwood asking whether he was obliged to resign, since £5 now bought considerably less than it once had.
Fleetwood’s answer, published in Chronicon Preciosum, was the first serious attempt to compare the purchasing power of money across time. He assembled prices for corn, meat, drink and cloth from the fifteenth century and from his own, and concluded that roughly £30 in 1707 corresponded to £5 in 1440. The fellow could keep his post with a clear conscience.
Fleetwood had discovered the central problem of index numbers: to compare money across time, you must first decide which basket of things money is meant to buy — and there is no neutral answer.
Two centuries later, Irving Fisher formalised the difficulty in The Making of Index Numbers (1922). He catalogued more than a hundred candidate formulas, tested them against a set of desirable axioms, and demonstrated that no index satisfies all of them simultaneously. Fisher was not describing a temporary state of ignorance. He was describing an impossibility.
Every consumer price index published anywhere in the world today is a compromise chosen from Fisher’s menu. The choice is technical. Its consequences are political.
Part II — What the CPI Actually Is
Consumer Price Index (CPI) — a weighted average of the prices of a fixed representative basket of goods and services purchased by households, expressed relative to a base period set equal to 100.
Note: the CPI measures the price level. Inflation is its rate of change. Confusing the two is the single commonest error in this topic.
How the basket is built
- The expenditure survey. A statistical agency surveys thousands of households, recording what they spend on what. This yields weights — the share of total household expenditure devoted to each category.
- The price collection. Enumerators (increasingly, web scrapers and supermarket scanner feeds) collect hundreds of thousands of individual prices each month, for tightly specified items in specified outlets.
- The aggregation. Individual price changes are averaged within categories, then across categories using the expenditure weights.
A household consumes three goods. Base year is 2020.
| Good | Q2020 | P2020 | P2025 | Weight (2020 spend share) |
|---|---|---|---|---|
| Bread (loaves) | 200 | $2 | $3 | 400 / 2,000 = 20% |
| Petrol (litres) | 400 | $1 | $1.50 | 400 / 2,000 = 20% |
| Rent (months) | 12 | $100 | $115 | 1,200 / 2,000 = 60% |
Cost of basket in 2020: (2×200) + (1×400) + (100×12) = 400 + 400 + 1,200 = $2,000
Cost of the same basket in 2025: (3×200) + (1.50×400) + (115×12) = 600 + 600 + 1,380 = $2,580
CPI2020 = (2,000 ÷ 2,000) × 100 = 100 (always, by construction)
CPI2025 = (2,580 ÷ 2,000) × 100 = 129.0
Cumulative inflation 2020→2025 = 29.0%
Cross-check via weights: Bread rose 50%, petrol 50%, rent 15%. Weighted: (0.20×50) + (0.20×50) + (0.60×15) = 10 + 10 + 9 = 29%. ✓ The two methods must agree — the weighted-average form is just the basket form rearranged.
In the example above, petrol prices rose by the same 50% as bread — but rent, rising only 15%, contributed almost a third of total inflation, because it absorbs 60% of the budget. A large price rise in a small category is almost invisible; a small price rise in housing or energy dominates the index. This is why headline inflation frequently contradicts personal experience: your weights are not the survey’s weights.
Part III — The Four Biases, and the Commission That Found Them
Boskin, M. J., Dulberger, E. R., Gordon, R. J., Griliches, Z., & Jorgenson, D. W. (1996). Toward a More Accurate Measure of the Cost of Living. Final Report to the US Senate Finance Committee.
The charge: Five of the most distinguished economists in the United States concluded that the CPI systematically overstated true cost-of-living inflation, by a little over one percentage point per year.
The four biases:
- Substitution bias. Laspeyres holds Q fixed. When beef rises, households buy chicken. The index does not notice, and therefore overstates the welfare loss from the price rise.
- Outlet substitution bias. Consumers migrate to discount retailers. The index prices the same item at the same surveyed shops.
- Quality change bias. A 2025 laptop at the same nominal price as a 2015 laptop is a vastly better machine. Recorded as “no price change,” it registers zero quality improvement.
- New goods bias. Products enter the basket years after launch — by which time the steepest part of their price decline has already occurred, unmeasured.
The stakes: US Social Security, income tax brackets, and inflation-indexed government bonds are all tied to the CPI. A one-percentage-point overstatement, compounded, transfers hundreds of billions of dollars over a decade. The Commission’s report was, in effect, a proposal to cut entitlements by fixing a statistic.
The counter-argument, which every strong essay makes: the biases do not run in one direction for everyone. Low-income households concentrate spending on rent, food and energy — precisely the categories with the fastest price growth and the least scope for quality-adjusted improvement. For them, the published CPI may understate inflation. There is no single true inflation rate. There is one per household, and the published figure is an average whose weights are themselves a political choice.
Hedonic adjustment: how quality is handled
The response to quality bias is hedonic regression. Treat a good as a bundle of characteristics and regress price on those characteristics:
The coefficients give an implicit price per unit of each characteristic. If this year’s model has more of them at the same nominal price, the statistician records a price fall. The technique traces to Griliches (1961) on automobiles.
Hedonic adjustment is applied heavily to computers and electronics, where characteristics are cleanly measurable. It is applied barely at all to healthcare, education, or legal services, where quality is real but unquantifiable. The consequence is that sectors whose quality gains are easy to measure appear to have falling prices and soaring productivity, while sectors whose gains are hard to measure appear stagnant. Some unknown share of the celebrated “cost disease” in services may be a measurement artefact rather than an economic fact.
Part IV — CPI Is Not the Only Index
| Index | Where used | Formula | Key feature |
|---|---|---|---|
| CPI | US, UK, most countries | Laspeyres (fixed weights) | The headline number; used for indexation |
| CPIH | UK (official designation) | Laspeyres + owner-occupier housing costs | Includes imputed rent for homeowners |
| RPI | UK (legacy; still used for rail fares, student loans) | Uses the Carli arithmetic mean at the elementary level | Systematically higher than CPI — the “formula effect” |
| PCE deflator | US Federal Reserve’s actual target | Chained Fisher index, updating weights | Broader coverage; runs slightly below CPI |
| HICP | Eurozone (ECB target) | Harmonised across member states | Excludes owner-occupied housing entirely |
| GDP deflator | National accounts | Paasche (current weights) | Excludes imports; includes capital goods |
The technical issue: At the lowest level of aggregation — averaging the prices of, say, twenty different brands of shampoo — you must choose a mean. RPI uses the Carli index (arithmetic mean of price relatives). CPI uses the Jevons index (geometric mean).
The mathematics: By the arithmetic–geometric mean inequality, the arithmetic mean is always ≥ the geometric mean, with equality only if all price relatives are identical. RPI is therefore mathematically guaranteed to exceed CPI whenever prices within a category move differently. This wedge is called the formula effect, and it has typically run around 0.7–1.0 percentage points annually.
The consequence: In 2013, the UK Statistics Authority stripped RPI of its designation as a National Statistic, on the grounds that the Carli formula fails a basic index-number test. Yet RPI continued to govern rail fare increases, student loan interest, and index-linked gilt payments — because switching would have transferred billions from bondholders to the Treasury, and vice versa for commuters.
The lesson: a statistic that everyone agrees is technically wrong can persist for decades, because too many contracts are written on it. Index numbers are not merely measurement. They are property rights.
Headline versus core
Core inflation excludes food and energy — not because they don’t matter (they matter most to poor households) but because they are volatile and driven by global supply shocks that domestic monetary policy cannot influence.
Core is a better signal of underlying inflationary pressure and a worse measure of the cost of living. Both statements are true at once. A central bank that ignores core is chasing noise; a politician who quotes core is dismissing the public’s actual experience. Say this explicitly in an essay.
Part V — Case Study: When a Government Lies About the CPI
The motive: Argentina had issued large volumes of inflation-indexed government debt. Every percentage point of reported inflation increased the state’s repayment obligations directly.
What happened: Beginning in 2007, the government intervened in the national statistics institute, INDEC. Senior statisticians were removed. Official inflation figures diverged sharply and persistently from every independent estimate — official rates in the high single digits while private estimates ran at two to three times that level. Economists publishing alternative estimates were fined.
How it was caught: Alberto Cavallo and Roberto Rigobon at MIT launched the Billion Prices Project, scraping prices daily from online retailers across dozens of countries. Cavallo (2013, Journal of Monetary Economics) compared his online index for Argentina against the official series. In every other country studied, online and official indices tracked each other closely. In Argentina alone, they diverged by a factor of roughly three.
The consequences: The Economist stopped publishing Argentina’s official inflation figure. The IMF issued a formal declaration of censure — the first in its history — for failure to provide accurate data. Argentina lost access to international capital markets on ordinary terms.
The lesson: The CPI is not merely an economic statistic. It is the mechanism that transfers wealth between the state and its creditors, between employers and pensioners, between landlords and tenants. Whoever controls the index controls those transfers. Statistical independence is a constitutional matter dressed as a technical one.
Part VI — CPI and Interest Rates: The Transmission
This is where the index stops being an accounting exercise and starts moving trillions of dollars.
Step 1: The Fisher effect
Lenders care about real returns. If they expect 3% inflation, they demand 3% more in nominal interest simply to stand still. A rise in expected inflation therefore pushes nominal interest rates up mechanically, before any central bank does anything at all.
The Fisher equation contains πe, expected inflation — not the CPI print you read in the newspaper, which is realised inflation for a month already past. Markets price the future. This is why a CPI release that comes in as expected moves bond yields almost not at all, while a surprise of 0.2 percentage points can move them sharply. It is the surprise that matters, never the level.
Step 2: The policy reaction function
Look at the coefficient on π. It appears twice: once with coefficient 1 and once inside the 0.5(π − π*) term. Total: 1.5.
This is deliberate. If inflation rises 1 percentage point, the nominal rate must rise by more than 1 point, so that the real rate rises and policy actually tightens. A central bank that raises nominal rates one-for-one with inflation leaves the real rate unchanged and does nothing. Raising them less than one-for-one loosens policy into an inflation. This is the Taylor principle, and violating it is the standard explanation for the Great Inflation of the 1970s.
Step 3: Long-term rates
A long bond yield is, approximately, the average of expected future short rates plus a term premium. A CPI release changes expectations of the entire future path of policy — which is why a single monthly number can reprice a thirty-year bond.
Breakeven inflation rate — the difference between the yield on a conventional government bond and the yield on an inflation-linked bond of the same maturity. It is the market’s implied expectation of average inflation over that horizon, and it is the closest thing we have to a directly observable πe.
Bils, M., & Klenow, P. J. (2004), “Some Evidence on the Importance of Sticky Prices,” Journal of Political Economy 112(5); Nakamura, E., & Steinsson, J. (2008), Quarterly Journal of Economics 123(4)
The question: Standard New Keynesian models assume prices adjust slowly, and calibrate the degree of stickiness to fit aggregate data. Bils and Klenow went to the source: the individual price quotes the Bureau of Labor Statistics collects to build the CPI.
What they found: Prices change far more often than macroeconomists had assumed — the median duration between price changes was a matter of months, not years. This threatened to undermine the entire New Keynesian justification for monetary non-neutrality.
The rescue: Nakamura and Steinsson showed that a large share of observed price changes were temporary sales that reverted to a “regular” price. Excluding sales, prices are considerably stickier. Regular prices, not posted prices, are what matter for monetary transmission.
Why it matters: The micro data that builds the CPI turned out to be one of the most important datasets in macroeconomics. An accounting exercise designed to index pensions became the empirical foundation of modern monetary theory.
Part VII — Practice Questions
In the base year, a household spends 50% on housing, 30% on food, 20% on transport. Over the following year housing rises 4%, food rises 10%, transport falls 5%. Calculate the CPI and the inflation rate.
Show worked answer
Weighted average of price changes:
(0.50 × 4) + (0.30 × 10) + (0.20 × −5)
= 2.0 + 3.0 − 1.0 = 4.0%
CPI = 100 × 1.04 = 104.0. Inflation rate = 4.0%.
Note the trap: the simple unweighted average of 4%, 10% and −5% is 3.0% — a different answer. Weights are not optional decoration.
(a) A worker’s nominal wage rises from $50,000 to $53,000. The CPI rises from 120 to 129. What has happened to the real wage?
(b) A bond pays a nominal 6%. Inflation turns out to be 8%, but investors had expected 3%. Who gains?
Show worked answer
(a) Nominal wage growth = 3,000/50,000 = 6.0%. Inflation = (129−120)/120 = 7.5%.
Exact real wage index: (1.06 ÷ 1.075) − 1 = −1.40%. The real wage fell by about 1.4% despite a $3,000 raise.
Approximation: 6.0 − 7.5 = −1.5%. Close, but the exact multiplicative form is correct.
(b) The nominal rate 6% embedded expected inflation of 3%, implying an expected real return of ~3%. Realised inflation of 8% means the realised real return is roughly 6 − 8 = −2%.
The borrower gains; the lender loses. This is the central redistributive consequence of unanticipated inflation. Had the 8% been anticipated, the nominal rate would have been ~11% and nobody would have been surprised.
Two brands of coffee. Brand A’s price doubles (relative 2.0); Brand B’s price halves (relative 0.5). Compute the elementary index using (a) the Carli arithmetic mean, (b) the Jevons geometric mean. Comment.
Show worked answer
(a) Carli: (2.0 + 0.5) / 2 = 1.25 → the index reports 25% inflation.
(b) Jevons: √(2.0 × 0.5) = √1.0 = 1.00 → the index reports zero inflation.
Comment: One price doubled, one halved. Intuitively, “on average” nothing happened — Jevons agrees. Carli reports 25% inflation from nothing.
Worse, Carli fails the time-reversal test: run the prices backwards and it reports inflation again, rather than the exact offsetting deflation. This is the technical grounds on which the UK Statistics Authority stripped RPI of its National Statistic designation in 2013.
Exam-worthy insight: the arithmetic mean always weakly exceeds the geometric mean (AM–GM inequality), so RPI > CPI structurally — not because prices behave differently, but because of the formula. Anyone whose income is indexed to RPI and whose debts are indexed to CPI gains permanently, and vice versa.
Suppose r* = 2%, target inflation π* = 2%, current inflation π = 6%, and the output gap (y − y*) = +1%. Using the Taylor rule, what policy rate is implied? What if the central bank instead sets the rate at 6%?
Show worked answer
i = r* + π + 0.5(π − π*) + 0.5(y − y*)
i = 2 + 6 + 0.5(6 − 2) + 0.5(1) = 2 + 6 + 2 + 0.5 = 10.5%
If instead the bank sets i = 6%: the implied real rate is 6 − 6 = 0%. Real policy is loose despite a nominal rate that sounds high. Inflation is not being restrained at all.
This is the Taylor principle in action. Because the nominal rate must rise more than one-for-one with inflation to raise the real rate, a bank that “responds” to 6% inflation with a 6% rate has responded with nothing. The Federal Reserve’s behaviour under Arthur Burns in the 1970s is the canonical example, and it is why Volcker’s rates had to reach the levels they did.
Part VIII — Exam Technique
- Construct a CPI from a table of prices and quantities. The base year is always 100. Use this as your arithmetic check.
- Convert nominal to real: Real value = (Nominal ÷ CPI) × 100.
- Apply the Fisher equation. Know that it uses expected, not realised, inflation.
- Identify who gains and loses from unanticipated inflation: borrowers gain, lenders lose.
- Distinguish CPI from the GDP deflator. CPI includes imports; the deflator does not.
“Evaluate the usefulness of the CPI as a measure of the cost of living.”
- Define the CPI precisely as a Laspeyres index of a fixed basket, and distinguish the level from the rate of change.
- Explain construction: expenditure survey → weights → price collection → aggregation. Analysis marks.
- Present the four Boskin biases systematically. Name the Commission.
- Then invert the argument. Note that the biases run the other way for poor households, whose weights on rent, food and energy are far above the survey average. There is no single true inflation rate.
- Discuss the housing problem: CPI excludes owner-occupier costs; CPIH imputes them; HICP omits them entirely. The largest asset most households own is barely in the index.
- Use the Argentina INDEC case to argue that statistical independence is a precondition, not a technicality.
- Use the RPI formula effect to show that an index known to be wrong can persist because contracts depend on it.
- Conclude conditionally: the CPI is fit for indexation and monetary policy at the aggregate level, and unfit as a description of any individual household’s experience. The error lies in the substitution, not the statistic.
- Calling the CPI “the inflation rate.” The CPI is a level. Inflation is its percentage change.
- Taking an unweighted average of price changes. Weights are the whole point.
- Confusing disinflation with deflation. Falling inflation still means rising prices.
- Using realised inflation in the Fisher equation. It takes πe.
- Claiming a one-for-one rate rise “fights inflation.” The real rate is unchanged. See the Taylor principle.
- Asserting that CPI overstates inflation, full stop. It overstates it for the average household under Boskin’s assumptions and may understate it for the poor. Say which.
Summary
The CPI answers a question that has no clean answer: how much does money buy, compared with before? Fisher proved in 1922 that no formula satisfies every reasonable axiom. Every index in use is a chosen compromise, and the choice determines who gains and who loses.
It is nonetheless the pivot on which modern macroeconomics turns. Through the Fisher equation it sets nominal interest rates; through the Taylor rule it sets policy rates; through indexation it sets pensions, wages and the real value of public debt. The micro price quotes that build it turned out, unexpectedly, to be the empirical foundation of monetary theory itself.
Bishop Fleetwood was trying to resolve a dispute about a £5 stipend. He ended up inventing the instrument by which central banks would one day govern the world economy.
Exercise 1 — Whose Basket, Whose Inflation?
The published CPI weights each household’s expenditure by its share of total spending — which means a wealthy household spending ten times as much contributes ten times the weight. This is called plutocratic weighting. A democratic index would weight each household equally.
Should benefits and the state pension be indexed to a democratic or a poverty-weighted CPI rather than the headline figure? Consider: would such an index be manipulable? Would indexing benefits to the fastest-rising categories entrench those consumption patterns? Is the choice of weights a technical question at all — and if it is not, what does that imply about the constitutional status of a statistical agency?
Then push further: if there is no single true inflation rate, what exactly is a central bank targeting when it targets 2%?
📄 Read: Boskin, M. J., et al. (1996). Toward a More Accurate Measure of the Cost of Living. Final Report to the Senate Finance Committee. Work through the four bias categories and ask, for each one, whether it would be larger or smaller for a household in the bottom income decile.
Exercise 2 — Can a Statistic Be Independent of the State That Publishes It?
Argentina’s government had an unambiguous financial interest in understating inflation, because its debt was indexed to the CPI. It acted on that interest. Cavallo and Rigobon caught it only because online prices provided an independent measurement channel that did not exist a decade earlier.
Every government has some version of this incentive. Design an institutional arrangement that makes CPI manipulation impossible rather than merely illegal — and then explain why your arrangement is itself vulnerable. Consider whether privately scraped price data (which is proprietary, unaudited, and covers only online retail) is a genuine check or merely a different set of hands on the same lever.
📄 Read: Cavallo, A. (2013). “Online and Official Price Indexes: Measuring Argentina’s Inflation.” Journal of Monetary Economics, 60(2), 152–165. Then read Cavallo, A., & Rigobon, R. (2016), “The Billion Prices Project: Using Online Prices for Measurement and Research,” Journal of Economic Perspectives, 30(2), 151–178, and assess how far scraped data can substitute for a statistical agency.
References
- Bils, M., & Klenow, P. J. (2004). Some Evidence on the Importance of Sticky Prices. Journal of Political Economy, 112(5), 947–985.
- Boskin, M. J., Dulberger, E. R., Gordon, R. J., Griliches, Z., & Jorgenson, D. W. (1996). Toward a More Accurate Measure of the Cost of Living. Final Report to the US Senate Finance Committee.
- Cavallo, A. (2013). Online and Official Price Indexes: Measuring Argentina’s Inflation. Journal of Monetary Economics, 60(2), 152–165.
- Cavallo, A., & Rigobon, R. (2016). The Billion Prices Project: Using Online Prices for Measurement and Research. Journal of Economic Perspectives, 30(2), 151–178.
- Fisher, I. (1922). The Making of Index Numbers. Boston: Houghton Mifflin.
- Fisher, I. (1930). The Theory of Interest. New York: Macmillan.
- Fleetwood, W. (1707). Chronicon Preciosum: or, an Account of English Gold and Silver Money. London.
- Griliches, Z. (1961). Hedonic Price Indexes for Automobiles: An Econometric Analysis of Quality Change. In The Price Statistics of the Federal Government. NBER.
- Nakamura, E., & Steinsson, J. (2008). Five Facts about Prices: A Reevaluation of Menu Cost Models. Quarterly Journal of Economics, 123(4), 1415–1464.
- Taylor, J. B. (1993). Discretion versus Policy Rules in Practice. Carnegie-Rochester Conference Series on Public Policy, 39, 195–214.
- UK Statistics Authority (2013). Assessment of Compliance with the Code of Practice for Official Statistics: The Retail Prices Index. Assessment Report 246.