Lowe and Cobb-Douglas consumer price indices and their substitution bias

Catching the effect of substitution behaviour in a Consumer Price Index (CPI) as good as possible is a goal pursued by statistical agencies throughout the world. The difference between a CPI and a certain target cost-of-living index is called substitution bias. Balk and Diewert (2003) considered the substitution bias of a Lowe Consumer Price Index; see also CPI Manual (2004: Chapter 17). The present paper considers the substitution bias of a Cobb-Douglas (or Geometric Young) CPI, and compares the two price indices with respect to their substitution bias. It appears difficult to draw a clear-cut conclusion.