Using a Constant Elasticity of Substitution Index to Estimate a Cost of Living Index: From Theory to Practice

Indexes often incorporate various biases due to their methods of construction. The Constant Elasticity of Substitution (CES) index can potentially eliminate substitution bias without needing current period expenditure data. The CES index requires an elasticity parameter. We derive a system of equations from which this parameter is estimated. We find that consumers are highly responsive to price changes at the elementary aggregation level. The results support the use of a geometric rather than arithmetic mean index at the elementary aggregate level. However, we find that even the use of a geometric mean index at the elementary aggregate level may not sufficiently account for the observed level of consumer substitution.