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Banerjee’s Factorial Index Numbers

  • G. Stuvel

Abstract

The underlying idea of Banerjee’s so-called factorial approach to the construction of index numbers1 appears to be that if commodity aggregates, like single commodities, had a price measure and a volume measure of their own, then these measures (which we shall denote by symbols with an asterisk) should be such that
$$P_j^*Q_k^* = \Sigma P_j^iQ_k^i\quad \left( {j,k = 0,1} \right)$$
and the index numbers of price and volume based on them should be
$$P = P_1^*/P_0^*\;and\;Q = Q_1^*/Q_0^*$$
Forming (as in factorial design analysis) the products
$$\begin{gathered} \left[ {P_1^* + P_0^*} \right]\left[ {Q_1^* + Q_0^*} \right] = a \hfill \\ \left[ {P_1^* - P_0^*} \right]\left[ {Q_1^* - Q_0^*} \right] = b \hfill \\ \left[ {P_1^* + P_0^*} \right]\left[ {Q_1^* + Q_0^*} \right] = c \hfill \\ \left[ {P_1^* - P_0^*} \right]\left[ {Q_1^* - Q_0^*} \right] = d \hfill \\ \end{gathered}$$
and dividing them by \({V_0} = P_0^*Q_0^* = \Sigma P_0^iQ_0^i\) Banerjee then concludes that the aggregate price and volume indices should be such that
$$P_{j}^{*}Q_{k}^{*}=\Sigma P_{j}^{i}Q_{k}^{i}\quad \left( {j,k=0,1} \right)$$
It is at this point that it becomes clear that the underlying idea of the factorial approach is erroneous, because there exist no P, Q pair that can satisfy simultaneously all four of these relations.

Keywords

Volume Change Block Design Analytical Point Randomise Block Design Randomise Block 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Copyright information

© G. Stuvel 1989

Authors and Affiliations

  • G. Stuvel
    • 1
  1. 1.All Souls CollegeOxfordUK

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