Measuring Spatial Price Differentials: A Comparison of Stochastic Index Number Methods

Abstract

Spatial price comparisons rely to a high degree on the quality of the underlying price data that are collected within or across countries. Below the basic heading level, these price data often exhibit large gaps. Therefore, stochastic index number methods like the CPDmethod and the GEKS method are utilised for the aggregation of the price data into higher-level indices. Although the two index number methods produce differing price level estimates when prices are missing, the present paper demonstrates that both can be derived from exactly the same stochastic model. In addition, for a specific case of missing prices, it is shown that the formula underlying these price level estimates differs between the CPD method and the GEKS method only with respect to the weighting pattern applied. Lastly, the impact of missing prices on the efficiency of the price level estimates is analysed in two simulation studies. It can be shown that the CPD method slightly outperforms the GEKS method. Using price data of Germany's Consumer Price Index, it can be observed that more narrowly defined products lead to efficiency gains in the estimation.