Abstract This article describes methods for decomposing price indexes into contributions from individual commodities, to help understand the influence of each commodity on aggregate price index movements. Previous authors have addressed the decomposition of bilateral price indexes, which aggregate changes in commodity prices from one time period to another. Our focus is the decomposition of multilateral price indexes, which aggregate commodity prices across more than two time periods or countries at once. Multilateral indexes have historically been used for spatial comparisons, and have recently received attention from statistical agencies looking to produce temporal price indexes from large and high frequency price data sets, such as scanner data. Methods for decomposing these indexes are of practical relevance. We present decompositions of three multilateral price indexes. We also review methods proposed by other researchers for extending multilateral indexes without revising previously published index levels, and show how to decompose the extended indexes they produce. Finally, we use a data set of seasonal prices and quantities to illustrate how these decomposition methods can be used to understand the influence of individual commodities on multilateral price index movements, and to shed light on the relationships between various multilateral and extension methods.

中文翻译：

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将多边价格指数分解为单个商品的贡献

摘要本文介绍了将价格指数分解为单个商品贡献的方法，以帮助了解每种商品对总价格指数变动的影响。先前的作者已经讨论了双边价格指数的分解，该分解将商品价格从一个时间段到另一个时间段的变化汇总在一起。我们的重点是分解多边价格指数，将两个以上时间段或多个国家/地区的商品价格汇总在一起。多边索引在历史上一直用于空间比较，最近已受到统计机构的关注，这些机构希望从大型和高频价格数据集（例如扫描仪数据）中生成时间价格指数。分解这些指标的方法具有实际意义。我们介绍了三个多边价格指数的分解。我们还将回顾其他研究人员提出的在不修改以前发布的索引水平的情况下扩展多边索引的方法，并展示如何分解他们生成的扩展索引。最后，我们使用季节性价格和数量的数据集来说明如何使用这些分解方法来理解单个商品对多边价格指数变动的影响，并阐明各种多边和扩展方法之间的关系。