Linking factor
Topic: Inflation and Index Numbers: CPI, WPI, IIP and the Deflator · NCERT: Beyond NCERT
Meaning
A linking factor is a multiplier that joins an old index series to a new one after a base-year revision. A base-year revision means shifting the year whose value is set at 100. Without the link, old and new numbers sit on different bases and cannot be compared. The factor is worked out from a period covered by both series. For each month in that period, you divide the old index by the new index. You then average those ratios, and a geometric mean (an average of ratios) suits indices best. Joining the two series this way is called splicing. It gives one continuous long-run history, which matters for things like Dearness Allowance (DA).
Old-base value = New-base value × Linking factor
Example
When CPI-IW moved from base 2001 to base 2016 (released 2020), the linking factor was 2.88. So a new-series reading of 120 equals 120 × 2.88 = 345.6 on the 2001 base. When the IIP moved from base 2011-12 to base 2022-23 in 2026, linking factors were worked out only for the General Index and the broad sectors. So long-run comparison is possible for headline IIP, but not for each small industry.
Don't confuse with
- Base-year revision: this is the change itself, with a new basket, new weights and a new base. The linking factor is only the bridge that keeps old and new figures comparable.
- Chain-linking: in a chain-linked index, weights are updated about every year and joined each time. A linking factor joins two fixed-base series once, at the point where the base is revised.