Standard errors as weights in multilateral price indices
A number of multilateral methods for computing price indexes use bilateral comparisons as their basic building blocks. Some of these methods, such as the weighted-EKS and minimum-spanning-tree (MST) methods, give greater weight to those bilateral comparisons that are deemed more reliable (an adjustment that is particularly important for a heterogeneous set of countries). No consensus currently exists in the literature as to the best measure of reliability. Diewert (2002), in particular, proposes a number of reliability measures in an axiomatic setting. Existing measures (including all of Diewert’s), however, fail to penalize bilateral comparisons when there is a small overlap in the products priced by each country. It is exactly in such situations that weighted methods are potentially most useful, but only if the reliability measure penalizes bilateral comparisons containing lots of gaps. Using a stochastic model, we show how the standard errors on bilateral price indexes provide a natural measure of reliability that automatically penalizes comparisons containing lots of gaps. Furthermore, we link these standard errors with the existing literature by showing that they are a generalization of one of Diewert’s reliability measures. This finding provides an interesting new link between the axiomatic and stochastic approaches to index numbers. Also, these standard errors can be modified for use in consumer data sets below the basic-heading level (where no expenditure shares are available), a scenario of direct relevance to the latest round of the International Comparison Program (ICP) currently being undertaken at the World Bank. Finally, we apply our methodology to an international data set on agricultural production that contains a lot of gaps. Our results clearly demonstrate the appeal of weighted methods and the importance of adjusting the reliability measures for gaps in the data. Failure to do so may compromise weighted methods precisely in situations where they are most needed.
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