Product Churn and the GEKS-Törnqvist Price Index: The “Feenstra Adjustment”

Several statistical agencies are using the multilateral GEKS-Törnqvist method to construct sub-components of the CPI from scanner data, particularly for groceries. This paper examines the relationship between the GEKS-Törnqvist price index and the CES (Constant Elasticity of Substitution) cost-of-living index. We first discuss the unrealistic case with no product churn and show that, under CES assumptions, the substitution bias in the GEKSTörnqvist index against the CES index depends on the extent to which the GEKS-Törnqvist violates the product test, given the value of the elasticity of substitution. Next, we outline the “Feenstra adjustment” to account for new and disappearing goods. We also describe two methods for estimating the elasticity of substitution, an algebraic method that is based on matched-model Törnqvist and Jevons price and quantity indexes and a regression method. The effect of the Feenstra adjustment on GEKS-Törnqvist price indexes is illustrated for a range of product categories using IRI scanner data. The paper concludes with a discussion of potential problems.