Chapter 7 — Index Numbers

An index number is a statistical device for measuring changes in the magnitude of a group of related variables. It represents the general trend of diverging ratios from which it is calculated and is expressed as a percentage, with the base period given the value 100. An index number of 250, for example, indicates the value is two and a half times that of the base period.

Index numbers can be constructed by (1) the aggregative method, which sums prices (or quantities) in the current and base periods and forms their ratio, and (2) the method of averaging relatives, which takes the arithmetic mean of individual price relatives (each commodity's current price divided by its base price, multiplied by 100). Each method has a simple (unweighted) and a weighted variant.

Both are weighted aggregative price indices, and the only difference is the weights used. Laspeyre's index uses base-period quantities as weights; it answers how much the base-period basket costs today relative to the base period. Paasche's index uses current-period quantities as weights; it answers how much the current-period basket costs today relative to what it would have cost in the base period. In the chapter's worked example, Laspeyre's gave 135.3 and Paasche's gave 132.1.

The Consumer Price Index, also known as the cost of living index, measures the average change in retail prices of a typical basket of commodities for a specified category of consumers. The RBI uses the All-India Combined CPI (base 2012=100) as its primary measure of consumer price changes. If the CPI for industrial workers (2001=100) is 277 in December 2014, it means that a basket costing Rs 100 in 2001 would cost Rs 277 in December 2014.

The WPI indicates changes in the general price level at the wholesale stage. Unlike the CPI, it has no reference consumer category and excludes service items such as barber charges and repairs. The current WPI is prepared with base 2011-12=100; its value for May 2017 was 112.8. Manufactured products carry the highest weight (64.23%), followed by primary articles (22.62%) and fuel and power (13.15%).

The 'All Commodities Inflation Rate' derived from the WPI is referred to as 'Headline Inflation'. 'Core Inflation' focuses on wholesale prices of manufactured goods, excluding food articles and fuel; it makes up around 55% of the total weight of the WPI. The WPI Food Index, which covers food articles and food products, accounts for 24.23% of the total weight.

The IIP tries to measure changes in quantities of industrial output. With effect from April 2017, the base year was fixed at 2011-12=100. It is calculated as a weighted arithmetic mean of quantity relatives using Laspeyre's formula, with weights proportional to value added by manufacture in the base year. The three main sectors are manufacturing (77.6%), mining (14.4%), and electricity (8.0%); the Eight Core Industries account for 40.27% of the total IIP weight.

Sensex is the short form of the Bombay Stock Exchange Sensitive Index with 1978-79 as the base. It consists of 30 stocks representing 13 sectors of the economy, and the companies listed are leaders in their respective industries. A rising Sensex indicates that investors expect better earnings from companies and reflects growing confidence in the basic health of the economy.

The chapter gives two formulas: (1) Purchasing power of money = 1 ÷ Cost of Living Index; (2) Real wage = (Money wage ÷ Cost of Living Index) × 100. For example, if the CPI (1982=100) is 526 in January 2005, a rupee is worth only 100/526 = Rs 0.19 in 1982 terms, and a money wage of Rs 10,000 corresponds to a real wage of Rs 10,000 × (100/526) ≈ Rs 1,901 in 1982 purchasing power.

The chapter lists five issues: (1) clarity about the purpose — a volume index and a value index serve different needs; (2) careful selection of representative items, since items are not equally important for all consumer groups; (3) choosing a normal base year, not one with extreme values, and not one too far in the past; (4) selecting an appropriate formula — the key difference between Laspeyre's and Paasche's is only the weights; and (5) ensuring data reliability, since poor data produces misleading results.

A weighted index number takes into account the relative importance of different items. In a simple aggregative index all items are treated as equally important, which is unrealistic — food items, for instance, occupy a large share of household expenditure. When the most important item A doubled in price in the chapter's Example 3, the weighted index rose to 156 while the unweighted index gave a lower value, showing that weighting captures the true impact of price changes more accurately.

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