Estimating the elasticity of substitution: An index-number approach

This paper presents a new way to estimate the constant elasticity of substitution (σ). We show that the link between σ and Divisia index numbers gives rise to a revealing way to obtain preliminary estimates of σ. This approach, which is related to stochastic index numbers, is illustrated with time-series and cross-country data. Using consumption data for 12 commodities over time from 23 European countries, we obtain 400 + estimates of σ, which mostly lie between 0 and 1. The cross-country estimates are broadly similar. Extensions of the approach to deal with endogenous prices and non-homothetic demand are also considered.