Best Linear Unbiased Index Numbers and Index Numbers Obtained through a Factorial Approach

PROFESSOR THEIL [5] recently gave the derivation of the best linear (B. L.) index number formulae for price and quantity. In an application of the formulae to Dutch import and export data, Kloek and DeWit [3] found that there is some slight, though persistent, bias to the effect that the index vectors yield larger current values than the individual data do. As this feature is related conceptually to the factor reversal test, they considered it desirable to devise a method which would control this bias on the average and worked out what may be called the best linear average unbiased (B. L. A. U.) index number. The aim of the present note is to indicate what relationship the B. L. and the B. L. A. U. indexes bear to the factorial indexes, that is, to those obtained through the factorial approach [1, 2, 4]. We conclude that the factorial indexes2 appear to compare well with the B. L. A. U. indexes. Incidentally, it is also pointed out that it might be possible to obtain a closer algebraic approximation to the B. L. index number formulae.