Index number

Topic: Inflation and Index Numbers: CPI, WPI, IIP and the Deflator · NCERT: Class 11, Ch 5 "Measures of Central Tendency"; Class 11, Ch 7 "Index Numbers"

Meaning

An index number is a statistical tool that measures the average change in a group of related variables between two situations. The two situations can be two periods of time or two places. It is written as a percentage, but the "%" sign is left out. The base period is always set at 100.

It matters because thousands of prices and quantities move in different directions, and an index number sums them up in one figure. Every headline inflation number (CPI, WPI), industrial output figure (IIP) and real-wage calculation is built on it. The core formula is the Laspeyres price index, which keeps the base-period basket fixed:

Laspeyres price index = Σp₁q₀ / Σp₀q₀ × 100

(p = price, q = quantity; subscript 0 = base period, 1 = current period)

Explanation

How to read an index number

• Base period: the period we compare against. Its value = 100.
• Current period: the period being compared with the base.
• Reading the number:
• Index of 250 → the value is 2.5 times the base value, a rise of 150%.

• Index of 90 → a 10% fall from the base.

• Two main kinds:

• Price index tracks changes in the prices of a chosen set of goods. Examples are CPI (Consumer Price Index, retail prices paid by households) and WPI (Wholesale Price Index, prices in bulk trade).

• Quantity index tracks changes in physical volume (production, construction, employment). Example: IIP (Index of Industrial Production), which measures "changes in the volume of production" of a basket of items compared with its base year [6].

• Why we need it: money income is not real income.

• A worker's wage rises from ₹1,000 (1982) to ₹12,000 today, which is 12 times more rupees.
• Suppose (for illustration) the consumer price index rose from 100 to 600.
• Real wage = 12,000 ÷ (600/100) = ₹2,000 at 1982 prices.
• So the worker is only 2 times better off, not 12 times. Dividing a money value by a price index like this is called deflating.

Methods of construction (with one worked dataset)

Commodity	p₀	q₀	p₁	q₁	Price relative	Weight W
A	2	10	4	5	200	40
B	5	12	6	10	120	30
C	4	20	5	15	125	20
D	2	15	3	10	150	10

• Simple aggregative index = ΣP₁ / ΣP₀ × 100
• (4+6+5+3) / (2+5+4+2) × 100 = 18/13 × 100 = 138.5

• Weaknesses: it adds prices quoted in different units (per kg, per litre), so changing the unit changes the answer. It is also unweighted, so salt counts as much as food.

• Laspeyres index (base-period quantities) = Σp₁q₀ / Σp₀q₀ × 100

• Σp₁q₀ = 40+72+100+45 = 257. Σp₀q₀ = 20+60+80+30 = 190.
• Index = 257/190 × 100 = 135.3.
• Meaning: a basket that cost ₹100 in the base year now costs ₹135.3.

• (NCERT prints the denominator as 100. The correct figure is 190.)

• Paasche index (current-period quantities) = Σp₁q₁ / Σp₀q₁ × 100

• Σp₁q₁ = 185. Σp₀q₁ = 140. Index = 132.1.

• Drawback: quantity data are needed every period, which is costly, and each period uses a different basket.

• Fisher's ideal index (beyond NCERT) = √(Laspeyres × Paasche)

• √(135.3 × 132.1) ≈ 133.7. It lies between the two.

• Price relative = (p₁/p₀) × 100. This is the index for one good. Commodity A: 4/2 × 100 = 200. It has no unit, so the "per kg vs per litre" problem disappears.

• Simple average of relatives = (1/n) Σ(p₁/p₀) × 100 → ¼ (2 + 1.2 + 1.25 + 1.5) × 100 = 149 (148.75 rounded).
• Weighted index of relatives = ΣWR / ΣW
• (8,000 + 3,600 + 2,500 + 1,500) / 100 = 156, a 56% rise.
• It is higher than 149 because A has the largest weight (40) and its price doubled.
• If W is the actual base-period spending (p₀q₀), this method gives exactly the Laspeyres index.

Substitution bias: why the formula changes the answer

• When a good's price rises fast, people switch to cheaper goods.
• Laspeyres keeps the old basket → it gives too much weight to goods that became costly → it tends to overstate the rise in the cost of living.
• Paasche uses the new basket, already tilted towards cheaper goods → it tends to understate the rise.

• In our data, Laspeyres 135.3 > Paasche 132.1.

• The geometric mean of price relatives (the Jevons index) gives a lower figure than a simple average. This partly allows for shoppers switching to cheaper varieties.

Weights and base year

• A weighted index takes the importance of each item into account. It uses quantities or spending shares as weights.
• Why base-period weights are preferred (NCERT): recalculating weights every year is inconvenient. Also, indices with changing weights price different baskets, so they are not strictly comparable over time.
• A good base year is a normal, stable year, not a year of war, drought or pandemic. It should also match the base years of other indicators.
• Why bases are revised: to reflect changes in the structure of the economy, new technology, and new products and industries [6].
• Linking (splicing) factor: when the base changes, old figures are converted so the series stays continuous.
• LF = (average of the new series in the overlap period) ÷ (average of the old series in the same period). The average used is the geometric mean [3][6].
• Old index × LF = the same value on the new base.

In India

• Measuring inflation (MoSPI formula): Inflation rate (%) = (Iₜ − Iₜ₋₁₂) / Iₜ₋₁₂ × 100. Here Iₜ is the CPI for month t and Iₜ₋₁₂ is the CPI for the same month last year [3].

• CPI (2024 = 100) inflation was 2.75% in January 2026 (provisional). Rural was 2.73% and urban 2.77% [2].

• CPI (MoSPI): Rural, Urban and Combined

• First released in January 2011 with base 2010 = 100, then moved to 2012 = 100 [3]. NCERT uses base 2012.
• Base revised to 2024 = 100, released on 12 February 2026 [2].
• Weighted items rose from 299 to 358: goods from 259 to 308 and services from 40 to 50 [2][3].
• Prices are collected from 1,465 rural markets and 1,395 urban markets in 434 towns, plus 12 online markets [2][3].
• Structure: 12 Divisions, 43 Groups, 92 Classes, 162 Sub-classes. It follows COICOP 2018 (the UN's international grouping of household spending by purpose) [3].
• Three reference periods [3]:
  • Index reference period (index = 100): 2024.
  • Weight reference period: HCES 2023-24 (Household Consumption Expenditure Survey).
  • Price reference period: calendar year 2024.
• Formulas [3]:
  • Elementary indices (the lowest level, built from price quotes for one item) use the Jevons index, a geometric mean of price relatives.
  • Higher levels use the Young / Modified Laspeyres index, which takes weights from one period and base prices from another.
• Food & Beverages weight [3]:
  • 45.86% in CPI 2012.
  • 36.75% in CPI 2024.
  • 40.10% in 2024 if measured under the old classification.

• Overlap year for linking: 2025. The linking factors are about 0.52–0.53 (Rural 0.5222, Urban 0.5320, Combined 0.5267) [3].

• CPI-IW (Labour Bureau): the CPI for Industrial Workers, used to revise dearness allowance (DA, extra pay to cover price rises).

• Base moved from 2001 = 100 to 2016 = 100 in 2020, with a linking factor of 2.88 [7].

• Coverage: 88 centres (up from 78), 317 markets (up from 289) and 463 items (up from 392) [7].

• WPI (Office of the Economic Adviser, DPIIT):

• Base revised from 2011-12 to 2022-23. Approved 25 May 2026 and released 15 June 2026, together with new Producer Price Indices (PPIs) [4][5].
• Compiled with the Laspeyres formula [4][5].

• Items rose from 697 to 957. Price quotations rose from 8,331 to 15,254 [4][5].

• IIP (NSO, MoSPI): a quantity index.

• Base revised from 2011-12 to 2022-23, with release planned for 1 June 2026. This is the 10th revision. The first IIP had base 1937 [6].
• Uses a "Laspeyres fixed base type" formula: each item's weight × its production relative (current production ÷ base production) [6].
• Item groups rose from 407 to 463, including 120 new item groups [6].
• Sector weights come from each sector's share in GVA (Gross Value Added: value of output minus cost of inputs) in FY 2022-23 [5]. Item weights come from GVO (Gross Value of Output) as per ASI 2022-23 (Annual Survey of Industries) [6].
• Released monthly, 28 days after the reference month [6].

• 2022-23 was chosen to line up with GDP and WPI [6].

• Other uses: the RBI's inflation target is set in terms of CPI inflation, and index numbers are used to convert nominal GDP into real GDP.

Don't confuse with

• Price index vs quantity index: CPI and WPI track prices. IIP tracks physical volume of production, not prices [6].
• Laspeyres vs Paasche: Laspeyres uses base-period quantities (fixed basket) and tends to overstate inflation. Paasche uses current-period quantities and tends to understate it.
• CPI vs GDP deflator: the GDP deflator (Nominal GDP ÷ Real GDP × 100) is a Paasche-type index. It covers all goods and services produced in India and excludes imports. CPI is a Laspeyres-type fixed-basket index of what households buy, and it includes imported consumer goods.
• Index reference period vs weight reference period: in CPI 2024 the index equals 100 in 2024, but the weights come from HCES 2023-24. They are not the same [3].

Prelims Hooks

• The base period of any index = 100. An index of 250 means 2.5 times the base value, a 150% rise.
• Laspeyres = Σp₁q₀/Σp₀q₀, Paasche = Σp₁q₁/Σp₀q₁, Fisher = √(L × P). A weighted average of price relatives with base-period spending weights gives the Laspeyres index.
• WPI is compiled by the Office of the Economic Adviser, DPIIT, not MoSPI. The new base is 2022-23, with 957 items [4][5].
• IIP is a quantity (volume) index compiled by NSO, MoSPI. Its new base is 2022-23 and it uses a Laspeyres fixed-base formula [6].
• CPI (2024 = 100): weights from HCES 2023-24, 358 items, COICOP 2018. Jevons (geometric mean) at the elementary level and Young / Modified Laspeyres at higher levels [2][3].
• CPI-IW (Labour Bureau) moved to base 2016 with a linking factor of 2.88. Its main use is setting DA [7].

Mains Points

• The choice of formula affects policy.
• A fixed-basket (Laspeyres-type) index ignores people switching to cheaper goods, so it can overstate the rise in the cost of living.
• This matters because CPI drives the RBI's inflation target, CPI-IW drives DA, and indices are used to adjust wages and pensions.

• Regular base revision and geometric-mean elementary indices (Jevons in CPI 2024) reduce this bias [3].

• Old weights give a false picture.

• CPI 2012 gave food a weight of 45.86%. CPI 2024 gives it 36.75% [3].
• In a food-heavy index, a jump in vegetable prices pushes up headline inflation, and that can push the RBI to raise rates.

• Weights from HCES 2023-24 match what households actually buy today. Also, GDP, WPI and IIP now share the base 2022-23 [4][6], so converting nominal figures to real ones and comparing indicators gives consistent results.

• Index numbers have limits.

• Quality changes are hard to measure. A higher price may partly reflect a better product.
• New goods enter only when the base is revised.
• Free public services are left out. CPI excludes free social transfers, following the IMF CPI manual [3].
• Prices differ between rural and urban areas and across regions.
• So one headline index should be read together with its sub-indices and other data.

Related concepts

• Price index
• Quantity index
• Simple aggregative price index
• Weighted index
• Weighted aggregative price index
• Laspeyres price index
• Paasche price index
• Price relative
• Method of averaging relatives
• Weighted index of price relatives

Read more

• Index numbers: meaning and construction