Editing Price index (section)

=== Chained vs. unchained calculations ===
Unchained indices compare all periods to a fixed base (e.g., 2010), amplifying bias over time as quantities diverge. Chained indices update the base each period, calculating period-to-period changes (e.g., 2010 to 2011, 2011 to 2012) and multiplying them:<ref>ILO CPI manual</ref>

: <math>P_{t_n} = \prod_{i=1}^{n} \frac{\sum (p_{c,t_i} \cdot q_{c,t_{i-1}})}{\sum (p_{c,t_{i-1}} \cdot q_{c,t_{i-1}})}</math>

Chaining reduces bias (e.g., reflecting recent substitution) but requires more data and can drift if errors accumulate.<ref>ILO CPI manual</ref>