  There is generally a need to deal with quality change and new goods in the
consumer price index due to the underlying dynamic item universe. Traditionally
axiomatic tests are defined for a fixed universe. We propose five tests
explicitly formulated for a dynamic item universe, and motivate them both from
the perspectives of a cost-of-goods index and a cost-of-living index. None of
the indices satisfies all the tests at the same time, which are currently
available for making use of scanner data that comprises the whole item
universe. The set of tests provides a rigorous diagnostic for whether an index
is completely appropriate in a dynamic item universe, as well as pointing
towards the directions of possible remedies. We thus outline a large index
family that potentially can satisfy all the tests.
