Test of Adequacy of Index Numbers

With several different methods available for constructing the same index, a natural question follows: how do we know a particular method is actually reliable? This is what the tests of adequacy answer — a set of consistency checks a good index-number formula is expected to pass. Four such tests are commonly used: the unit test, the time-reversal test, the factor-reversal test, and the circular test. This chapter focuses on the first two.

The unit test requires that the method chosen to construct an index should not depend on the units in which prices or quantities of the commodities happen to be recorded — for instance, wheat might be priced per kilogram while milk is priced per litre, and a sound index formula should still combine them sensibly. Every method covered in this chapter satisfies the unit test except the simple aggregative method.

The time-reversal test checks that an index gives a consistent answer regardless of which period is treated as the base. If the time subscripts of a price or quantity index are swapped, the resulting index should be the exact reciprocal of the original — comparing year 0 against year 1 should undo comparing year 1 against year 0: