3.3 Fixed-base indices and chain indices

One key decision in the choice of an index is whether to opt for a fixed-base index or a chain index. In the fixed-base index, price at time _t is always compared with the base period or time ₀ (illustrated by the top arrows in the graph below). In a fixed-base index, the weights are usually changed once a year or once every five years. In a chain index, by contrast, comparisons are always made between subsequent points of measurement (lower arrows). In a chain index the change between two points of measurement carries forward the base period index score. Weights are changed at every point of measurement.

In the case of two commodities the fixed-base indices and chain indices are calculated with the Laspeyres index as follows:

	Time X0	X1	X2	X3
Price A (PA)	50	55	60	60
Quantity A (QA)	10	15	15	10
Value A (PA*QA)	500	825	900	600
Price B (PB)	25	20	20	25
Quantity B (QB)	15	20	25	20
Value B (PB*QB)	375	400	500	500
Fixed-base X0=100	100.0	97.14	102.85	= 111.42
Chain X0=100	100.0	0.9714 * 100.0 = 97.14	1.0612 * 97.14= 103.08	= 1,0892 = 1,0892 * 103,08 = 112,27