An Exact Index for the CES Function with Unobservable Prices

Introduction of new products into the market place poses a difficult problem for the calculation of a cost-of-living (COL) index. The problem is that the reservation prices of new products in the periods before their introduction are unobservable. This paper introduces a new index number formula that overcomes the problem. It is exact for the constant-elasticity-of-substitution (CES) function. Unlike the one introduced to the literature by Feenstra (1994), for which the elasticity of substitution has to be estimated using a separate econometric model, the new index can be computed by simply substituting available prices and quantities into a known exact functional form. The new index number formula is illustrated with the data used in Feenstra (1994).