Notes on Unit Value Index Bias

It is often the case that the value of a number of somewhat similar units (e. g., automobiles of a certain general type) is divided by the number of units in order to form a unit value price and these unit value prices are compared over two periods in order to form a unit value price index. This unit value price index or Drobisch price index can then be compared with other standard index number formulae and the bias in the index can be determined. The present paper presents most of the known results on this bias (and derives some new ones) in a coherent framework using a simple identity from the statistics literature. A related question first considered by Pa´ rniczky (1974) is also considered: does disaggregation of a unit value into more homogeneous subgroups reduce the unit value bias? The answer seems to be: probably yes.