Index Number
What is Index Number?
Index numbers express a value as a percentage of its own level in a chosen base period, which is set equal to 100.
An index converts a series into relative terms by dividing each period's value by the base period value and multiplying by 100. That makes series comparable which could not otherwise be added, which is why prices for thousands of goods, output across dozens of industries and share values across firms all get reported as indexes. The cost is that an index has no units: a consumer price index does not say what a basket costs in dollars, only how its cost compares with the base period. Two conventions cause most student errors, the difference between a change in index points and a percentage change, and the fact that a level is uninterpretable unless you know the base. A weighted index also depends on how its weights are chosen, which is how two indexes measuring the same thing can drift apart.
Index Number: a worked example
Suppose a price index reads 125 in one year and 130 the next. The rise of 5 index points is not 5 percent: the percentage change is (130 - 125) ÷ 125 = 0.04, or 4 percent. Had the index moved from 100 to 105, that same 5 point rise would be exactly 5 percent, because the starting level was 100. The gap between points and percent widens as the index level moves further from its base, which is why a series with an old base can show large point moves that are small percentage changes.
The mistake students make with index number
The standard error is reading a rise from 125 to 130 as 5 percent inflation. That is a rise of 5 index points, which works out to 4 percent because the denominator is 125, not 100. Points and percent coincide only when the starting value is exactly 100. A second error is thinking an index level means something on its own; without knowing the base period, 130 is just a number.
Index Number questions
How do you calculate an index number?
Divide the value in the period you care about by the value in the base period, then multiply by 100. A basket costing 260 dollars now and 200 dollars in the base year gives (260 ÷ 200) × 100 = 130. The base period always works out to exactly 100.
What is the difference between index points and percent?
Index points are the raw difference between two index values, while percentage change divides that difference by the starting value. The two match only when the starting index is 100. A move from 200 to 210 is 10 points but 5 percent.
Why do economists use index numbers instead of dollars?
Indexes let you combine and compare things measured in different units, such as the prices of thousands of goods or output across many industries, which cannot simply be summed. They also make comparisons across countries and long stretches of time readable. The trade-off is that an index carries no units and means nothing without its base.
Formula / Example
Related terms
Common comparisons
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