Price indices on the basis of unit values: Unit value indices as proxies for price indices

In some countries a Paasche price index based on unit values is compiled as a proxy for a true Paasche (or Laspeyres) price index on the basis of prices. This is for example the case in German foreign trade statistics. Unit values are average prices referring to a 'commodity number' (CN), that is an aggregate of (more or less homogeneous) commodities defined by a commodity classification. They are often easily available as free by-products of other statistics (foreign trade or wage statistics for example) and therefore less costly than true transaction prices of well-defined specific products as they are in general reported in price statistics. Changes in unit values between two points in time, however, do not only reflect a price movement but also changes in the quantities transacted. They are, in other words, affected by a structural component, the changing mix of commodities within CNs and therefore biased relative to genuine price indices. The focus of the paper is on explaining this bias. It is shown that amount and sign of the 'unit value bias' depends on the correlation between the change of quantities of the goods included in the CNs and their respective base period prices, while current period prices do not matter. This result is useful as it may help to define 'homogeneity' with respect to CNs and thus conditions under which unit values may be acceptable as (cost-effective) substitutes for prices.