Laspeyres index
Fixed basket, moving prices — the formula behind most consumer price indices.
In plain words
The Laspeyres index answers a simple question: how much does today's prices raise the cost of last year's shopping basket? You freeze the quantities you bought in the base period, then re-price them at today's prices. If that frozen basket now costs 5% more, inflation is 5%. It's intuitive and easy to compute — which is why Étienne Laspeyres proposed it in 1871 and it remains the backbone of most consumer price indices worldwide. The IMF CPI Manual is the authoritative technical reference for index construction; the BLS history of CPI methodology changes shows how the formula has evolved since 1919.
How national agencies use it in practice
A pure Laspeyres index would never update the basket — the same 1871 shopping list forever. In practice, agencies update basket weights periodically: the BLS uses a two-year average (from the Consumer Expenditure Survey), the ONS updates annually, and Eurostat updates HICP weights yearly. These "modified Laspeyres" indices retain the formula's simplicity while reducing its staleness. The BLS also applies a geometric mean formula at the item level (since 1999) to capture within-category substitution, which partially corrects the substitution bias without abandoning the Laspeyres framework. The Eurostat HICP methodology explains how HICP handles basket updating across EU member states.
Why index choice matters for policy
The choice between Laspeyres, Paasche, and chained indices is not merely academic — it affects the measured inflation rate that central banks target and governments index pensions and wages to. The BLS estimates that substitution bias adds roughly 0.3–0.4 percentage points per year to CPI-U compared to a chain-weighted equivalent. That gap compounds over decades: a pension indexed to CPI-U would grow faster than one indexed to PCE (chain-weighted). This is why the Boskin Commission (1996) recommended shifting toward chain-weighting for some US government programmes, and why the Fed explicitly chose the PCE deflator over CPI as its target measure.
Common misreadings
The Laspeyres formula is not a flaw — it is a deliberate design choice that makes CPI easy to interpret: "how much more does last year's basket cost today?" The substitution bias is well understood and partly corrected via geometric averaging at the elementary level. The BLS and ONS both document these adjustments in their methodology notes. Calling CPI "wrong" because it uses Laspeyres misses the point — the index is constructed to answer a specific question. The PCE deflator, which uses chain-weighting, answers a different but complementary question about actual spending patterns.
Frequently asked questions
What is the Laspeyres index formula?
The Laspeyres price index = Σ(p_current × q_base) / Σ(p_base × q_base) × 100. In words: take the basket of goods from the base period (q_base), price it at current prices (p_current), and divide by what that same basket cost at base-period prices (p_base). The result shows how much more expensive the base-period basket has become. Most national CPIs, including the US CPI-U and the UK CPI, use a Laspeyres-type formula with weights updated periodically (every 1–2 years) rather than a strictly fixed base.
What is the substitution bias in the Laspeyres index?
The Laspeyres index has an upward bias called "substitution bias". When the price of beef rises relative to chicken, consumers shift to chicken — but the Laspeyres index keeps using the original beef-heavy basket, overstating how much it costs to maintain the same standard of living. This is one reason the US Bureau of Economic Analysis uses the PCE deflator (a chain-weighted index) as the Fed's preferred inflation measure — it accounts for substitution. The BLS periodically updates CPI basket weights (currently every two years via the CES) to partially mitigate this bias.
How is the Laspeyres index different from the Paasche index?
The Laspeyres index uses base-period quantities as weights; the Paasche index uses current-period quantities. Laspeyres tends to overstate inflation (substitution bias); Paasche tends to understate it (it assumes consumers substitute freely). The geometric mean of the two is the Fisher "ideal" index, which is theoretically unbiased. The GDP deflator uses a Paasche-type formula; most CPIs use Laspeyres-type. The <a href="https://www.imf.org/en/Data/Statistics/cpi-manual" target="_blank" rel="noopener noreferrer">IMF CPI Manual</a> provides a full technical treatment of index theory.