Second Thoughts on Wald's Cost-of-Living Index and Frisch's Double Expenditure Method - Balk, Bert M. (Econometrica, 1981)
THE RESEARCH on the economic theory of the cost-of-living index has not paid much attention to the proposals made by Frisch and Wald in the thirties. In Frisch [3,4] the was developed and tested on certain examples. Wald [8] succeeded in deriving a new for the index of cost of living in an article containing a curious editorial footnote by Frisch on the comparative advantages of both methods. Banerjee [1] presented a simplification of the derivation of Wald's new formula. In an article commemorating Frisch, Samuelson [7] asked for a study of the relative merits of Frisch's and Wald's proposals to which he added a variant of his own. Recently Banerjee [2] succeeded in showing that Wald's new formula is the true cost-of-living index for a general quadratic utility function. In this paper I give an alternative, mathematically equivalent but economically more meaningful, derivation which highlights the resemblance of Wald's index to the true cost-of-living index corresponding to the familiar Klein-Rubin-Stone-Geary utility function (Section 2). This derivation provides a convenient framework for discussing Frisch's double-expenditure method (Section 3) and Samuelson's proposal (Section 4) and for assessing the relative merits of them. I hope this note is a (partial) answer to Samuelson's question.